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2008 Vol. 30, No. 4
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2008, 30(4): 763-767.
doi: 10.3724/SP.J.1146.2006.01604
Abstract:
This paper investigates the distributed allocation control of multi-access channel in broadband satellite mesh network. A novel combined Dynamic Allocation Multi-Access (DAMA) scheme is proposed, which is based on the chaotic prediction of self-similar traffic. The OPNET simulation system is built for comparing the performance of several schemes under different channel allocation cycle and channel load. The influence of traffic with different degree of self-similarity is also studied. Simulation results indicate that the novel scheme has better performance under high channel load in broadband satellite Mesh network with GEO, LEO and MEO satellite constellations.
This paper investigates the distributed allocation control of multi-access channel in broadband satellite mesh network. A novel combined Dynamic Allocation Multi-Access (DAMA) scheme is proposed, which is based on the chaotic prediction of self-similar traffic. The OPNET simulation system is built for comparing the performance of several schemes under different channel allocation cycle and channel load. The influence of traffic with different degree of self-similarity is also studied. Simulation results indicate that the novel scheme has better performance under high channel load in broadband satellite Mesh network with GEO, LEO and MEO satellite constellations.
2008, 30(4): 768-771.
doi: 10.3724/SP.J.1146.2006.01467
Abstract:
In this paper, digital part of LEO CDMA satellite transmitter is researched, and its structure, algorithm and implementation are introduced.The emphasis is pressed upon implementation of signal processing part of the digital transmitter, especially upon the processing of data stream, the shaping filtering, interpolating CIC filtering, and digital up-converting, etc. This method uses the shaping filter based on polyphase filter and Distribute Arithmetic(DA) and efficient CIC interpolating filter, and with this method the performance of the transmitter and the usage of resource have been remarkably improved.
In this paper, digital part of LEO CDMA satellite transmitter is researched, and its structure, algorithm and implementation are introduced.The emphasis is pressed upon implementation of signal processing part of the digital transmitter, especially upon the processing of data stream, the shaping filtering, interpolating CIC filtering, and digital up-converting, etc. This method uses the shaping filter based on polyphase filter and Distribute Arithmetic(DA) and efficient CIC interpolating filter, and with this method the performance of the transmitter and the usage of resource have been remarkably improved.
2008, 30(4): 772-775.
doi: 10.3724/SP.J.1146.2006.01492
Abstract:
This paper discusses the feasibility of LEO satellite of fixation antenna and low or middle power accessing to the TDRSS and realizing space-ground data transmission through TDRS. The precondition of communication between LEO satellite and TDRS are given, then the general idea and method of computing the data throughout in bits and on day are provided by computer simulation, this method provides bases to test the feasibility of LEO satellites of fixation antenna accessing to the TDRSS.
This paper discusses the feasibility of LEO satellite of fixation antenna and low or middle power accessing to the TDRSS and realizing space-ground data transmission through TDRS. The precondition of communication between LEO satellite and TDRS are given, then the general idea and method of computing the data throughout in bits and on day are provided by computer simulation, this method provides bases to test the feasibility of LEO satellites of fixation antenna accessing to the TDRSS.
2008, 30(4): 776-779.
doi: 10.3724/SP.J.1146.2006.01590
Abstract:
In practical wireless communication networks, downlink beamforming weights at the node B of smart antenna systems can be deteriorated due to variation of spatial signal vectors corresponding to mobile users or DOA estimation error. In this paper, the methodology for smart antenna systems with imperfect beamforming is proposed, the performance of smart antenna systems is studied in existing beamforming error scenarios and the accepted tolerance of the beamforming error in TD-SCDMA systems is researched on from the aspect of system capacity. On the one hand, the theoretical and simulation results show that beamforming accuracy of the smart antenna systems have great effect on the system capacity. On the other hand, they also indicate that the performance deterioration is remarkable if the beamforming error exceeds a threshold which is related to the system load.
In practical wireless communication networks, downlink beamforming weights at the node B of smart antenna systems can be deteriorated due to variation of spatial signal vectors corresponding to mobile users or DOA estimation error. In this paper, the methodology for smart antenna systems with imperfect beamforming is proposed, the performance of smart antenna systems is studied in existing beamforming error scenarios and the accepted tolerance of the beamforming error in TD-SCDMA systems is researched on from the aspect of system capacity. On the one hand, the theoretical and simulation results show that beamforming accuracy of the smart antenna systems have great effect on the system capacity. On the other hand, they also indicate that the performance deterioration is remarkable if the beamforming error exceeds a threshold which is related to the system load.
2008, 30(4): 780-783.
doi: 10.3724/SP.J.1146.2005.01603
Abstract:
The incremental redundancy type-II HARQ has been applied into the cross layer design. The closed-form expressions of the packet error rate and average spectral efficiency for the transmissions over Nakagami- channel have been derived. Numerical results show that the type-II HARQ with high complexity could achieve higher spectral efficiency and lower packet error rate compared with the cross layer design system with type-I HARQ. While the type-I HARQ has the lower spectral efficiency and the higher packet error rate, but its complexity is low.
The incremental redundancy type-II HARQ has been applied into the cross layer design. The closed-form expressions of the packet error rate and average spectral efficiency for the transmissions over Nakagami- channel have been derived. Numerical results show that the type-II HARQ with high complexity could achieve higher spectral efficiency and lower packet error rate compared with the cross layer design system with type-I HARQ. While the type-I HARQ has the lower spectral efficiency and the higher packet error rate, but its complexity is low.
2008, 30(4): 784-787.
doi: 10.3724/SP.J.1146.2006.01487
Abstract:
Based on the minimum Bit Error Rate (BER) criterion, a greedy bit allocation algorithm and bisection-method based bit allocation algorithm are proposed for Multiple-Input Multiple-Output (MIMO) spatial multiplexing systems. Under the constraint of total bit rate and equal power allocation to each transmit antenna, the proposed transmit bit allocation algorithms can achieve better performance by optimizing the modulation order of each transmit antenna. The simulation results show that the proposed system can obtain significant Signal-to-Noise Ratio (SNR) gain relative to the conventional MIMO system. In addition, compared with the transmit power allocation scheme, the requirements on the dynamic range of the power amplifiers for each transmit antenna are reduced with little performance loss.
Based on the minimum Bit Error Rate (BER) criterion, a greedy bit allocation algorithm and bisection-method based bit allocation algorithm are proposed for Multiple-Input Multiple-Output (MIMO) spatial multiplexing systems. Under the constraint of total bit rate and equal power allocation to each transmit antenna, the proposed transmit bit allocation algorithms can achieve better performance by optimizing the modulation order of each transmit antenna. The simulation results show that the proposed system can obtain significant Signal-to-Noise Ratio (SNR) gain relative to the conventional MIMO system. In addition, compared with the transmit power allocation scheme, the requirements on the dynamic range of the power amplifiers for each transmit antenna are reduced with little performance loss.
2008, 30(4): 788-791.
doi: 10.3724/SP.J.1146.2006.01583
Abstract:
In this paper, the scheduling strategy of minimizing power under delay constraint is proposed in wireless channel. The problem is first formulated as an unconstrained Markov Decision Process（MDP）and solved by dynamic programming. But its final decision which is made over all processes instead of individual one make it with high convexity and bad real time property. So a simple strategy which is based on the current channel state and queue length is given for its good real time property and simple arithmetic. And by this strategy the steady-state distribution of the queue exists, which makes the queue stable. Finally, the simulation results show the performance of the simple strategy is approximate to the optimal one.
In this paper, the scheduling strategy of minimizing power under delay constraint is proposed in wireless channel. The problem is first formulated as an unconstrained Markov Decision Process（MDP）and solved by dynamic programming. But its final decision which is made over all processes instead of individual one make it with high convexity and bad real time property. So a simple strategy which is based on the current channel state and queue length is given for its good real time property and simple arithmetic. And by this strategy the steady-state distribution of the queue exists, which makes the queue stable. Finally, the simulation results show the performance of the simple strategy is approximate to the optimal one.
2008, 30(4): 792-796.
doi: 10.3724/SP.J.1146.2006.01538
Abstract:
When PABT (Pilot-Assisted Block Transmission) signal is transmitted over severe multipath channels, consecutive pilot block and data block may partially overlap each other. If no guard interval is inserted between them, a process to cancel the mutual interference is usually adopted in the receiver. But this process, as well as channel equalization, may suffer severe performance degradation when channel estimation is not so reliable. A hybrid modulation scheme is proposed in this paper, in which the overlapped part in data block is modulated using lower order constellation, while the other part keeps using higher order constellation. Its advantage in BER performance and robustness over conventional PABT schemes is demonstrated with simulation in some multipath channels with large delay spread.
When PABT (Pilot-Assisted Block Transmission) signal is transmitted over severe multipath channels, consecutive pilot block and data block may partially overlap each other. If no guard interval is inserted between them, a process to cancel the mutual interference is usually adopted in the receiver. But this process, as well as channel equalization, may suffer severe performance degradation when channel estimation is not so reliable. A hybrid modulation scheme is proposed in this paper, in which the overlapped part in data block is modulated using lower order constellation, while the other part keeps using higher order constellation. Its advantage in BER performance and robustness over conventional PABT schemes is demonstrated with simulation in some multipath channels with large delay spread.
2008, 30(4): 797-800.
doi: 10.3724/SP.J.1146.2006.01478
Abstract:
Based on the m-sequence，a time-domain channel estimation algorithm for Multi-Input Multi-Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) is designed. The m-sequence with Cyclic Prefix (CP) is inserted between OFDM symbols in time domain as training sequence. The cross-correlation is calculated between the received sequence with CP removed and the appointed circular shifted m-sequence, which takes reliability of the estimation of channel impulse response on account of the two-valued auto-correlation property of the m-sequence, thereby the channel frequency response can be advisably decided. The results of both theoretical analysis and simulation show that the proposed algorithm possesses an impressive performance with less system overhead and lower computation burden than conventional algorithms.
Based on the m-sequence，a time-domain channel estimation algorithm for Multi-Input Multi-Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) is designed. The m-sequence with Cyclic Prefix (CP) is inserted between OFDM symbols in time domain as training sequence. The cross-correlation is calculated between the received sequence with CP removed and the appointed circular shifted m-sequence, which takes reliability of the estimation of channel impulse response on account of the two-valued auto-correlation property of the m-sequence, thereby the channel frequency response can be advisably decided. The results of both theoretical analysis and simulation show that the proposed algorithm possesses an impressive performance with less system overhead and lower computation burden than conventional algorithms.
2008, 30(4): 801-804.
doi: 10.3724/SP.J.1146.2006.01465
Abstract:
Triangular Cell Communication System (TCCS) is a novel distributed Base Station (BS) system. Its cell structure is an equilateral triangle, and it is composed of 3 Uni-Cover Regions (UCR) and 1 Cross-Covered Region (CCR). Mobile Station (MS) communicates with one near BS in UCR, and communicates with all 3 BSs of the cell in CCR. In this paper, a frequency plan scheme is proposed, which adopts frequency reuse in UCR, and macro diversity in CCR. Under this frequency plan and the per-antenna maximum transmit power constraint, the ergodic capacity of TCCS in multi-cell environment is calculated, and it shows that TCCS offers large capacity gain over Generalized Distributed Antenna System (GDAS).
Triangular Cell Communication System (TCCS) is a novel distributed Base Station (BS) system. Its cell structure is an equilateral triangle, and it is composed of 3 Uni-Cover Regions (UCR) and 1 Cross-Covered Region (CCR). Mobile Station (MS) communicates with one near BS in UCR, and communicates with all 3 BSs of the cell in CCR. In this paper, a frequency plan scheme is proposed, which adopts frequency reuse in UCR, and macro diversity in CCR. Under this frequency plan and the per-antenna maximum transmit power constraint, the ergodic capacity of TCCS in multi-cell environment is calculated, and it shows that TCCS offers large capacity gain over Generalized Distributed Antenna System (GDAS).
2008, 30(4): 805-808.
doi: 10.3724/SP.J.1146.2006.01518
Abstract:
Based on Ultra-WideBand (UWB) conventional Transmitted Reference (TR) technology, the interference model which reference and data receive waveforms are both contaminated by inter-pulse interference is analyzed relying on Time Division Multiple Access. On account of the slow varying character of the UWB channel, some non-overlapped pilot pulses are utilized to estimate the model coefficients, and the coefficients are tracked by Volterra LMS algorithm. A root method is adopted to equalize the second-order non-linear inter-symbol interference. Simulation result in IEEE 802.15.3as indoor multipath channel model shows that the non-linear equalization receiver can eliminate the ISI better than linear equalization receiver.
Based on Ultra-WideBand (UWB) conventional Transmitted Reference (TR) technology, the interference model which reference and data receive waveforms are both contaminated by inter-pulse interference is analyzed relying on Time Division Multiple Access. On account of the slow varying character of the UWB channel, some non-overlapped pilot pulses are utilized to estimate the model coefficients, and the coefficients are tracked by Volterra LMS algorithm. A root method is adopted to equalize the second-order non-linear inter-symbol interference. Simulation result in IEEE 802.15.3as indoor multipath channel model shows that the non-linear equalization receiver can eliminate the ISI better than linear equalization receiver.
2008, 30(4): 809-813.
doi: 10.3724/SP.J.1146.2006.01521
Abstract:
The selection of cooperative partner is a key problem in the cooperative network. All the former solutions to this problem in essence base on the performance of the transceiver while neglecting the fairness among the cooperative partners. In this paper, a new scheme is described as following to achieve the balance between the performance and the fairness among the nodes. Firstly, using the counter of each node in the network to establish the mechanism based on the idea help others equal to help yourself to avoid the self-interest users. Secondly, a threshold about instant SNR at the destination receiver is used to decide whether needing relay. Thirdly, the algorithm established keeps a balance between maximizing the throughput and minimizing the variance of the lifetime of all the candidate partners in the network. The simulation results under all kinds of conditions indicate that the scheme can get dynamic balance between performance and fairness and lead to more fairness in the cooperative network, the performance of fairness of the scheme outperforms the other of the references the best knowledge .
The selection of cooperative partner is a key problem in the cooperative network. All the former solutions to this problem in essence base on the performance of the transceiver while neglecting the fairness among the cooperative partners. In this paper, a new scheme is described as following to achieve the balance between the performance and the fairness among the nodes. Firstly, using the counter of each node in the network to establish the mechanism based on the idea help others equal to help yourself to avoid the self-interest users. Secondly, a threshold about instant SNR at the destination receiver is used to decide whether needing relay. Thirdly, the algorithm established keeps a balance between maximizing the throughput and minimizing the variance of the lifetime of all the candidate partners in the network. The simulation results under all kinds of conditions indicate that the scheme can get dynamic balance between performance and fairness and lead to more fairness in the cooperative network, the performance of fairness of the scheme outperforms the other of the references the best knowledge .
2008, 30(4): 814-816.
doi: 10.3724/SP.J.1146.2006.01601
Abstract:
This paper presents two kinds of methods for constructing perfect ternary array pairs by using perfect ternary array pairs properties. They are periodic multiplication of perfect ternary array pairs and recursing construction of perfect ternary array pairs. Perfect ternary array pairs can be proposed.
This paper presents two kinds of methods for constructing perfect ternary array pairs by using perfect ternary array pairs properties. They are periodic multiplication of perfect ternary array pairs and recursing construction of perfect ternary array pairs. Perfect ternary array pairs can be proposed.
2008, 30(4): 817-821.
doi: 10.3724/SP.J.1146.2006.01531
Abstract:
This paper introduces a single-carrier system with hybrid time-frequency domain Decision Feedback Equalization (DFE), in which the short pn (Pseudo-Noise) sequence with fixed waveform replaces the cyclic prefix (CP) in the conventional Single Carrier systems with Frequency Domain Equalization (SC-FDE), and the long PN sequences composed of several short pn sequences are employed as the channel training sequences to complete the initial estimation and tracking for fast-varying channel. In this system, the received training sequences are averaged in time domain and then the channel is estimated in frequency domain. In comparison with traditional SC-FDE systems, its complexity is lower. Furthermore, an approach of adding sum-check blocks to original Low-Density Parity-Check (LDPC) blocks is presented, and the effective improvements of this system performance can be achieved. Finally, the simulation results show that this system works well over the fading channel.
This paper introduces a single-carrier system with hybrid time-frequency domain Decision Feedback Equalization (DFE), in which the short pn (Pseudo-Noise) sequence with fixed waveform replaces the cyclic prefix (CP) in the conventional Single Carrier systems with Frequency Domain Equalization (SC-FDE), and the long PN sequences composed of several short pn sequences are employed as the channel training sequences to complete the initial estimation and tracking for fast-varying channel. In this system, the received training sequences are averaged in time domain and then the channel is estimated in frequency domain. In comparison with traditional SC-FDE systems, its complexity is lower. Furthermore, an approach of adding sum-check blocks to original Low-Density Parity-Check (LDPC) blocks is presented, and the effective improvements of this system performance can be achieved. Finally, the simulation results show that this system works well over the fading channel.
2008, 30(4): 822-825.
doi: 10.3724/SP.J.1146.2006.01505
Abstract:
Digital fountain is a packet oriented forward error correction technology for channels with erasures, which has obvious efficiency advantage in broadcast. In the paper, LDPC code is put into practice in digital fountain encoding, and a fast decoding algorithm is presented. The simulation show that the digital fountain scheme base on LDPC code has better error correcting performance and can be implemented with very low complexity to encode and decode.
Digital fountain is a packet oriented forward error correction technology for channels with erasures, which has obvious efficiency advantage in broadcast. In the paper, LDPC code is put into practice in digital fountain encoding, and a fast decoding algorithm is presented. The simulation show that the digital fountain scheme base on LDPC code has better error correcting performance and can be implemented with very low complexity to encode and decode.
2008, 30(4): 826-830.
doi: 10.3724/SP.J.1146.2006.01416
Abstract:
A class of structured irregular Low-Density Parity-Check (LDPC) codes with high performance and low complexity is proposed in this paper. First, a global matrix M with a triangular plus dual-diagonal form based on Improved eIRA (IeIRA) method is designed. Then, each 1 in the global matrix M is replaced with a permutation matrix; each 0 is replaced with a null matrix to generate the parity check matrix H. Finally, the relationship between the length of short cyclic in the parity matrix H and the cyclic shift coefficient is given. Based on the relationship, error floor of BER is lowed by selecting proper cyclic shift coefficient of each permutation matrix. Simulation shows that the proposed method can reduce the number of small stopping set, increase the minimum distance of LDPC codes, and achieve very low error floor with linear encoding complexity.
A class of structured irregular Low-Density Parity-Check (LDPC) codes with high performance and low complexity is proposed in this paper. First, a global matrix M with a triangular plus dual-diagonal form based on Improved eIRA (IeIRA) method is designed. Then, each 1 in the global matrix M is replaced with a permutation matrix; each 0 is replaced with a null matrix to generate the parity check matrix H. Finally, the relationship between the length of short cyclic in the parity matrix H and the cyclic shift coefficient is given. Based on the relationship, error floor of BER is lowed by selecting proper cyclic shift coefficient of each permutation matrix. Simulation shows that the proposed method can reduce the number of small stopping set, increase the minimum distance of LDPC codes, and achieve very low error floor with linear encoding complexity.
2008, 30(4): 831-835.
doi: 10.3724/SP.J.1146.2006.01586
Abstract:
Based on the FFT of a single-tone sequence, this paper presents a novel Moving Average Maximum Likelihood (MAML) frequency estimator, which develops a Moving Average (MA) model by the real part relationship between different significant FFT coefficients firstly and a MA model-based maximum likelihood estimation technique. Simulation results show that the algorithm is effective and the proposed estimator outperforms the traditional Rifes and Quinns estimator in both accuracy and the CRLB approximate RMSE of estimation. It is also shown that MAML has the merit of little computation effort and as lower SNR threshold as to -9dB.
Based on the FFT of a single-tone sequence, this paper presents a novel Moving Average Maximum Likelihood (MAML) frequency estimator, which develops a Moving Average (MA) model by the real part relationship between different significant FFT coefficients firstly and a MA model-based maximum likelihood estimation technique. Simulation results show that the algorithm is effective and the proposed estimator outperforms the traditional Rifes and Quinns estimator in both accuracy and the CRLB approximate RMSE of estimation. It is also shown that MAML has the merit of little computation effort and as lower SNR threshold as to -9dB.
2008, 30(4): 836-839.
doi: 10.3724/SP.J.1146.2006.01490
Abstract:
In this paper, the sensitivity of MAP algorithm and its reduced ones as Max-Log-MAP and Scaled Max-Log-Map to SNR mismatch in turbo detection systems are analyzed. Due to the fact of insensitivity of Scaled Max-Log-MAP algorithm to SNR mismatch, a new SNR estimation method is proposed using the soft output extrinsic information. Then, a new turbo equalization scheme is also provided utilizing the SNR estimation algorithm, and the corresponding performance of new equalization algorithm is also studied. The simulation results show that new equalization scheme with reliability-based SNR estimation method performs very close to MAP algorithm with known SNR, although it does not need pilot symbols.
In this paper, the sensitivity of MAP algorithm and its reduced ones as Max-Log-MAP and Scaled Max-Log-Map to SNR mismatch in turbo detection systems are analyzed. Due to the fact of insensitivity of Scaled Max-Log-MAP algorithm to SNR mismatch, a new SNR estimation method is proposed using the soft output extrinsic information. Then, a new turbo equalization scheme is also provided utilizing the SNR estimation algorithm, and the corresponding performance of new equalization algorithm is also studied. The simulation results show that new equalization scheme with reliability-based SNR estimation method performs very close to MAP algorithm with known SNR, although it does not need pilot symbols.
2008, 30(4): 840-842.
doi: 10.3724/SP.J.1146.2006.01345
Abstract:
Based on the periodicity that the signals which are gotten by doing delay-multiply with the Direct Sequence Spread Spectral (DSSS) signals, the paper proposes an efficient method for the detection of DSSS signals: the detection, symbol period and chip width estimation of DSSS signals based on delay-multiply, correlation and spectrum analysis. The computer simulations show that it can not only fit the need of the low signal to noise ratio which is quite common in the detection of DSSS signals, but also can give the estimations of the symbol period and chip width in a simple way. Especially, the method proposed in the paper can enhance the precision of the symbol period estimation by increasing the processed sampling data when the sampling rate is fixed, which is very important for the detection of DSSS signals.
Based on the periodicity that the signals which are gotten by doing delay-multiply with the Direct Sequence Spread Spectral (DSSS) signals, the paper proposes an efficient method for the detection of DSSS signals: the detection, symbol period and chip width estimation of DSSS signals based on delay-multiply, correlation and spectrum analysis. The computer simulations show that it can not only fit the need of the low signal to noise ratio which is quite common in the detection of DSSS signals, but also can give the estimations of the symbol period and chip width in a simple way. Especially, the method proposed in the paper can enhance the precision of the symbol period estimation by increasing the processed sampling data when the sampling rate is fixed, which is very important for the detection of DSSS signals.
2008, 30(4): 843-847.
doi: 10.3724/SP.J.1146.2006.00925
Abstract:
Recently, a Multiple Symbol Differential Sphere Decoding (MSDSD) algorithm for unitary space-time modulation over quasi-static channel is proved to achieve the performance of Maximum-Likelihood (ML) detection with relatively low complexity. However, an error floor occurs if the algorithm is applied to rapid-fading channels. Based on the assumption of continuous fading, a Multiple Symbol Differential Automatic Sphere Decoding (MSDASD) is developed by incorporating a recursive form of an ML metric in the automatic sphere decoding algorithm. The proposed algorithm is suitable for arbitrary unitary constellations and eliminates the error floor caused by MSDSD over fast fading channels. Compared with decision-feedback detection under the same assumption, MSDASD achieves performance of ML detection with much lower complexity at moderate to high signal-to-noise ratios.
Recently, a Multiple Symbol Differential Sphere Decoding (MSDSD) algorithm for unitary space-time modulation over quasi-static channel is proved to achieve the performance of Maximum-Likelihood (ML) detection with relatively low complexity. However, an error floor occurs if the algorithm is applied to rapid-fading channels. Based on the assumption of continuous fading, a Multiple Symbol Differential Automatic Sphere Decoding (MSDASD) is developed by incorporating a recursive form of an ML metric in the automatic sphere decoding algorithm. The proposed algorithm is suitable for arbitrary unitary constellations and eliminates the error floor caused by MSDSD over fast fading channels. Compared with decision-feedback detection under the same assumption, MSDASD achieves performance of ML detection with much lower complexity at moderate to high signal-to-noise ratios.
2008, 30(4): 848-852.
doi: 10.3724/SP.J.1146.2006.01403
Abstract:
Multi-Lag High-order Instantaneous Moment (ML-HIM), an encoding method removing signal phase ambiguity, can correct not only the constant phase offset but also Doppler frequency shift. Differential coding method can mitigate constant phase offset excluding Doppler frequency shift which also can not be removed in blind constant modulus equalization. This paper, therefore, introduces ML-HIM in the constant modulus algorithm for recovering received signal phase. The experimental results show that the modified constant modulus algorithm here is more optimal than other methods represented before and the ML-HIM is thoroughly adapted to blind equalization algorithms.
Multi-Lag High-order Instantaneous Moment (ML-HIM), an encoding method removing signal phase ambiguity, can correct not only the constant phase offset but also Doppler frequency shift. Differential coding method can mitigate constant phase offset excluding Doppler frequency shift which also can not be removed in blind constant modulus equalization. This paper, therefore, introduces ML-HIM in the constant modulus algorithm for recovering received signal phase. The experimental results show that the modified constant modulus algorithm here is more optimal than other methods represented before and the ML-HIM is thoroughly adapted to blind equalization algorithms.
2008, 30(4): 853-858.
doi: 10.3724/SP.J.1146.2006.01408
Abstract:
The researches of FREquency-SHift (FRESH) filter are usually based on the hypothesis that the receivers precisely know the cycle frequencies of signal or interference. However, in the practical application circumstances of FRESH filter, Cycle Frequency Error (CFE) sometimes exists unavoidably. Based on the model of DSSS/BPSK system with FRESH filter to suppress narrow-band interference, the tap coefficients, the estimate error of FRESH filter and the system bit error performance under CFE are analyzed and an improved CFE correction algorithm is proposed in this paper. The results from theoretical analysis and numerical simulations indicate that the performance of FRESH filter is very sensitive to CFE, and the proposed algorithm can correct CFE effectively, keeping FRESH filter robust and excellent under CFE.
The researches of FREquency-SHift (FRESH) filter are usually based on the hypothesis that the receivers precisely know the cycle frequencies of signal or interference. However, in the practical application circumstances of FRESH filter, Cycle Frequency Error (CFE) sometimes exists unavoidably. Based on the model of DSSS/BPSK system with FRESH filter to suppress narrow-band interference, the tap coefficients, the estimate error of FRESH filter and the system bit error performance under CFE are analyzed and an improved CFE correction algorithm is proposed in this paper. The results from theoretical analysis and numerical simulations indicate that the performance of FRESH filter is very sensitive to CFE, and the proposed algorithm can correct CFE effectively, keeping FRESH filter robust and excellent under CFE.
2008, 30(4): 859-862.
doi: 10.3724/SP.J.1146.2006.01519
Abstract:
Spatial smoothing techniques are effective to estimate the directions of coherent arrivals. The performance of these techniques deteriorates rapidly as the coherent arrivals become closely spaced. In this correspondence, an improved spatial smoothing technique is proposed. The algorithm makes cross-correlation of all auto-correlation matrixes of subarray output, and then takes the spatial spectrum estimation to the equivalent spatial smoothing matrix after the forward and backward correlation matrixes averaged. The formula for the algorithm is derived, and the performance of the algorithm is also analyzed. Simulation results demonstrate that the improved algorithm possesses a better resolving ability and a lower SNR threshold than conventional SS technique and subarray-covariance SS technique for DOA estimation of coherent signals.
Spatial smoothing techniques are effective to estimate the directions of coherent arrivals. The performance of these techniques deteriorates rapidly as the coherent arrivals become closely spaced. In this correspondence, an improved spatial smoothing technique is proposed. The algorithm makes cross-correlation of all auto-correlation matrixes of subarray output, and then takes the spatial spectrum estimation to the equivalent spatial smoothing matrix after the forward and backward correlation matrixes averaged. The formula for the algorithm is derived, and the performance of the algorithm is also analyzed. Simulation results demonstrate that the improved algorithm possesses a better resolving ability and a lower SNR threshold than conventional SS technique and subarray-covariance SS technique for DOA estimation of coherent signals.
2008, 30(4): 863-867.
doi: 10.3724/SP.J.1146.2006.01414
Abstract:
This paper gives a new method to estimate the number of source signals and recover them by the characteristics of sparse source signals in underdetermined blind separation. It is well known that source signals can be recovered through the two-step algorithms generally. The first step is to estimate the mixture matrix by K-means clustering algorithm using the sensor signals, and then, the shortest path algorithm is used to recover source signals, whereas, people suppose that the number of source signals is known when they estimate the mixture matrix by the K-means clustering algorithm generally. In fact, the number of source signals is unknown or blind, so it is very important to estimate the number of source signals. In this paper, a new two-step algorithm is proposed, which not only can estimate the number of source signals but also get the mixture matrix instead of K-means algorithm through the characteristics of sensor signals. The last simulation results show the algorithm simply, efficient and good performance.
This paper gives a new method to estimate the number of source signals and recover them by the characteristics of sparse source signals in underdetermined blind separation. It is well known that source signals can be recovered through the two-step algorithms generally. The first step is to estimate the mixture matrix by K-means clustering algorithm using the sensor signals, and then, the shortest path algorithm is used to recover source signals, whereas, people suppose that the number of source signals is known when they estimate the mixture matrix by the K-means clustering algorithm generally. In fact, the number of source signals is unknown or blind, so it is very important to estimate the number of source signals. In this paper, a new two-step algorithm is proposed, which not only can estimate the number of source signals but also get the mixture matrix instead of K-means algorithm through the characteristics of sensor signals. The last simulation results show the algorithm simply, efficient and good performance.
2008, 30(4): 868-871.
doi: 10.3724/SP.J.1146.2006.01412
Abstract:
The problem of estimating the phase parameters of chirp signals embedded in noise is concerned in this paper. The computationally efficient cyclostationary estimation method is introduced, and in order to avoid its disadvantages, an iterative estimation algorithm based on cyclostationarity is proposed. The main characteristics of the proposed algorithm include low calculation complexity inherited from the cyclostationary method, reduction in error propagation effect, increase in estimation accuracy, and operation over a wider range of phase parameter values. Simulation results demonstrate that the new iterative algorithm has better performance as compared with the conventional cyclostationary estimation method.
The problem of estimating the phase parameters of chirp signals embedded in noise is concerned in this paper. The computationally efficient cyclostationary estimation method is introduced, and in order to avoid its disadvantages, an iterative estimation algorithm based on cyclostationarity is proposed. The main characteristics of the proposed algorithm include low calculation complexity inherited from the cyclostationary method, reduction in error propagation effect, increase in estimation accuracy, and operation over a wider range of phase parameter values. Simulation results demonstrate that the new iterative algorithm has better performance as compared with the conventional cyclostationary estimation method.
2008, 30(4): 872-875.
doi: 10.3724/SP.J.1146.2006.01398
Abstract:
A decision-theoretic based scheme is developed for modulation classification in a fading environment. The proposed method takes into account a flat Rayleigh fading propagation channel. The likelihood function is derived according to the channel and signals parameters character and classifier is constructed. Spatial diversity technique with multi-antennas array receiver is exploited to improve the correct classification probability. A method dealing with the effect for diversity induced by the displacement of receiving antennas is also proposed. Simulations demonstrate that the proposed scheme is efficient in fading situations.
A decision-theoretic based scheme is developed for modulation classification in a fading environment. The proposed method takes into account a flat Rayleigh fading propagation channel. The likelihood function is derived according to the channel and signals parameters character and classifier is constructed. Spatial diversity technique with multi-antennas array receiver is exploited to improve the correct classification probability. A method dealing with the effect for diversity induced by the displacement of receiving antennas is also proposed. Simulations demonstrate that the proposed scheme is efficient in fading situations.
2008, 30(4): 876-880.
doi: 10.3724/SP.J.1146.2006.01339
Abstract:
Conjugate Extended MUSIC (CE-MUSIC) and MUSIC-like algorithm can be used to estimate the directions of arrival of noncircular signals (e.g. BPSK modulated signals) which are widely used in communication systems. The performance of these two algorithms is not so good because no high order information is used in CE-MUSIC algorithm and no noncircular information is used in MUSIC-like algorithm which is based on forth-order cumulants. In this paper, a new direction finding algorithm called Forth-Order Extended MUSIC (FO-EMUSIC) for noncircular signals is proposed. It can detect more noncircular signals than MUSIC-like and CE-MUSIC algorithms and has better performance (in terms of resolution and angular precision) than MUSIC-like algorithm, and a little better than CE-MUSIC)algorithm. A new FO-EMUSIC algorithm for Uniform Linear Array (ULA) called FO-EMUSIC/ULA which needs much less computation load than FO-EMUSIC is also proposed in this paper. Simulation results show the better performance of FO-EMUSIC than MUSIC-like and CE-MUSIC algorithms.
Conjugate Extended MUSIC (CE-MUSIC) and MUSIC-like algorithm can be used to estimate the directions of arrival of noncircular signals (e.g. BPSK modulated signals) which are widely used in communication systems. The performance of these two algorithms is not so good because no high order information is used in CE-MUSIC algorithm and no noncircular information is used in MUSIC-like algorithm which is based on forth-order cumulants. In this paper, a new direction finding algorithm called Forth-Order Extended MUSIC (FO-EMUSIC) for noncircular signals is proposed. It can detect more noncircular signals than MUSIC-like and CE-MUSIC algorithms and has better performance (in terms of resolution and angular precision) than MUSIC-like algorithm, and a little better than CE-MUSIC)algorithm. A new FO-EMUSIC algorithm for Uniform Linear Array (ULA) called FO-EMUSIC/ULA which needs much less computation load than FO-EMUSIC is also proposed in this paper. Simulation results show the better performance of FO-EMUSIC than MUSIC-like and CE-MUSIC algorithms.
2008, 30(4): 881-884.
doi: 10.3724/SP.J.1146.2006.01240
Abstract:
The two-dimensional ADBF method at subarray level is studied. The signal model of ADBF at subarray level is presented which is suitable for plane phased array. The conventional two-dimensional ADBF at subarray level is given which is generalized by one-dimensional ADBF at element level. The two-dimensional ADBF at subarray level based on subspace projection is introduced, and the desired quiescent pattern can be achieved in the absence of jammer, so the conversion problem between adaptive and non-adaptive work modes is resolved, while in the presence of jammer, the jammer is suppressed effectively, and the sidelobe level is improved markedly compared with the conventional method. Simulation results indicate the validity of the introduced methods.
The two-dimensional ADBF method at subarray level is studied. The signal model of ADBF at subarray level is presented which is suitable for plane phased array. The conventional two-dimensional ADBF at subarray level is given which is generalized by one-dimensional ADBF at element level. The two-dimensional ADBF at subarray level based on subspace projection is introduced, and the desired quiescent pattern can be achieved in the absence of jammer, so the conversion problem between adaptive and non-adaptive work modes is resolved, while in the presence of jammer, the jammer is suppressed effectively, and the sidelobe level is improved markedly compared with the conventional method. Simulation results indicate the validity of the introduced methods.
2008, 30(4): 885-888.
doi: 10.3724/SP.J.1146.2006.01453
Abstract:
Wavelet-based image denoising algorithms is a hot point in image processing applications. In this paper, a doubly local Wiener filtering algorithm using elliptic directional window and mathematical morphology is proposed, in which the mathematical morphology is first used to divide the image into texture and smooth regions, and then combine the elliptic directional window to estimate the signal variance of each wavelet coefficients in different oriented subbands, finally the doubly local Wiener filtering is used to denoise the observed image. Experiment results show that the proposed algorithm is better than the existing image denoising algorithms using 2-D real separable wavelets.
Wavelet-based image denoising algorithms is a hot point in image processing applications. In this paper, a doubly local Wiener filtering algorithm using elliptic directional window and mathematical morphology is proposed, in which the mathematical morphology is first used to divide the image into texture and smooth regions, and then combine the elliptic directional window to estimate the signal variance of each wavelet coefficients in different oriented subbands, finally the doubly local Wiener filtering is used to denoise the observed image. Experiment results show that the proposed algorithm is better than the existing image denoising algorithms using 2-D real separable wavelets.
2008, 30(4): 889-892.
doi: 10.3724/SP.J.1146.2006.01482
Abstract:
Single orbit bistaitc space based radar is composed of two radars in the same orbit. The paper analyzes the clutter angle-Doppler spectrum in this radar system, and finds out that minimum detectable velocity(MDV) is dependent on detecting angles and will degrade a lot in some angles. A new combined monostatic and bistatic radar mode with potential savings in size and weight of the solar array-battery system on-board each satellite is then introduced and angle threshold is calculated. Simulation results with Space-Time Adaptive Processing(STAP) also verify the improved detection performance.
Single orbit bistaitc space based radar is composed of two radars in the same orbit. The paper analyzes the clutter angle-Doppler spectrum in this radar system, and finds out that minimum detectable velocity(MDV) is dependent on detecting angles and will degrade a lot in some angles. A new combined monostatic and bistatic radar mode with potential savings in size and weight of the solar array-battery system on-board each satellite is then introduced and angle threshold is calculated. Simulation results with Space-Time Adaptive Processing(STAP) also verify the improved detection performance.
2008, 30(4): 893-897.
doi: 10.3724/SP.J.1146.2006.01532
Abstract:
This paper deals with the influence of ground fluctuation and roughness on the correlation between distributed Satellites SAR echoes. The model for a rough surface is presented based on the facet theory followed by the analysis of its statistical scattering property. Their influences are shown with several simulation results, where the terrain fluctuation is imitated with a 2-dimention correlative stochastic process，which indicate that the ground fluctuation and roughness deteriorate the correlation if the two satellites are cross-track separated, but have a little influence on the correlation if the two satellites are along-track separated.
This paper deals with the influence of ground fluctuation and roughness on the correlation between distributed Satellites SAR echoes. The model for a rough surface is presented based on the facet theory followed by the analysis of its statistical scattering property. Their influences are shown with several simulation results, where the terrain fluctuation is imitated with a 2-dimention correlative stochastic process，which indicate that the ground fluctuation and roughness deteriorate the correlation if the two satellites are cross-track separated, but have a little influence on the correlation if the two satellites are along-track separated.
2008, 30(4): 898-901.
doi: 10.3724/SP.J.1146.2006.01483
Abstract:
Since factors such as turbulence and pilot error make it impossible for an aircraft to flight along the nominal straight flight path, SAR motion compensation technology is crucial to acquiring high quality image. When the aircraft changes in the roll, pitch or heading, it is necessary to track the real time attitudes to stabilize the antenna pointing. While the strapdown inertial navigation system can fulfill the requirement. The instant attitude updating is one of the main tasks of attitude measurement for strapdown system. Consideration of the real time ability and stable performance, a new derivation method of the transformation equations between quaternion and attitudes is proposed. The influence of angle motion in airplane on SAR imaging is analyzed based on the derived equations. The method given in the paper can highly reduce the operation of triangle function and improve the efficiency of the system.
Since factors such as turbulence and pilot error make it impossible for an aircraft to flight along the nominal straight flight path, SAR motion compensation technology is crucial to acquiring high quality image. When the aircraft changes in the roll, pitch or heading, it is necessary to track the real time attitudes to stabilize the antenna pointing. While the strapdown inertial navigation system can fulfill the requirement. The instant attitude updating is one of the main tasks of attitude measurement for strapdown system. Consideration of the real time ability and stable performance, a new derivation method of the transformation equations between quaternion and attitudes is proposed. The influence of angle motion in airplane on SAR imaging is analyzed based on the derived equations. The method given in the paper can highly reduce the operation of triangle function and improve the efficiency of the system.
2008, 30(4): 902-905.
doi: 10.3724/SP.J.1146.2006.01418
Abstract:
It is known that for Linear Frequency Modulation (LFM) Synthetic Aperture Radar (SAR) echo signal, the obtained SAR image by 2-dimensional matched filtering has relatively high sidelobe level. Though such sidelobe can be depressed with amplitude weighting, the resolution of mainlobe will be accordingly reduced. To resolve this problem, in this paper, the apodization filtering technique is discussed and then applied to sidelobe suppression of SAR imaging with the detailed realization procedure presented. The theoretical analysis and simulation results show that in comparison with amplitude weighting, this technique can preserve the resolution of original SAR imaging whilst reducing the sidelobe level. The advantage of this technique has been verified with the simulation results of SAR image in multi-object case.
It is known that for Linear Frequency Modulation (LFM) Synthetic Aperture Radar (SAR) echo signal, the obtained SAR image by 2-dimensional matched filtering has relatively high sidelobe level. Though such sidelobe can be depressed with amplitude weighting, the resolution of mainlobe will be accordingly reduced. To resolve this problem, in this paper, the apodization filtering technique is discussed and then applied to sidelobe suppression of SAR imaging with the detailed realization procedure presented. The theoretical analysis and simulation results show that in comparison with amplitude weighting, this technique can preserve the resolution of original SAR imaging whilst reducing the sidelobe level. The advantage of this technique has been verified with the simulation results of SAR image in multi-object case.
2008, 30(4): 906-910.
doi: 10.3724/SP.J.1146.2007.00424
Abstract:
Space-Time Adaptive Processing (STAP) is a key technology for moving target detection, but nonhomogeneity will cause the covariance matrix estimation error, which substantially results in the STAP performance degradation. Diagonal loading is used as a means to improve the robustness of the spatial filter against mismatches in both the desired spatial signature and the spatial correlation matrix. In this paper, we consider the diagonal loading is applied to the case of covariance matrix mismatch (statistical mismatch) for STAP, i.e. when there is a mismatch between the actual covariance matrix of interest and the presumed one. The selecting method of the loading level is given, and the particular performance analysis indicates that the rational diagonal loading can improve the detection probability and the output signal-to-noise ratio. Numerical simulations attest the validity of the analysis.
Space-Time Adaptive Processing (STAP) is a key technology for moving target detection, but nonhomogeneity will cause the covariance matrix estimation error, which substantially results in the STAP performance degradation. Diagonal loading is used as a means to improve the robustness of the spatial filter against mismatches in both the desired spatial signature and the spatial correlation matrix. In this paper, we consider the diagonal loading is applied to the case of covariance matrix mismatch (statistical mismatch) for STAP, i.e. when there is a mismatch between the actual covariance matrix of interest and the presumed one. The selecting method of the loading level is given, and the particular performance analysis indicates that the rational diagonal loading can improve the detection probability and the output signal-to-noise ratio. Numerical simulations attest the validity of the analysis.
2008, 30(4): 911-915.
doi: 10.3724/SP.J.1146.2006.01684
Abstract:
In this paper, the focusing has been on spatial interpolation in correcting atmospheric effects using Interferometric SAR based on external data. Several factors have been discussed separately by using both simulated data and GPS data. The results indicate that the inverse distance weighted and kriging interpolation methods are more suitable than the function method and statistical method. And the validity of calibration is influenced by the type and quality of external data. When the external data is precise and regular, the result will be the best. Moreover, the improved interpolation methods by incorporating terrain elevation information have proved to be better.
In this paper, the focusing has been on spatial interpolation in correcting atmospheric effects using Interferometric SAR based on external data. Several factors have been discussed separately by using both simulated data and GPS data. The results indicate that the inverse distance weighted and kriging interpolation methods are more suitable than the function method and statistical method. And the validity of calibration is influenced by the type and quality of external data. When the external data is precise and regular, the result will be the best. Moreover, the improved interpolation methods by incorporating terrain elevation information have proved to be better.
2008, 30(4): 916-920.
doi: 10.3724/SP.J.1146.2006.00927
Abstract:
Dechirping is an effective method for decreasing the bandwidth of input signals. For high velocity moving targets ISAR imaging, the residual phase arisen from dechirping processing and target moving can not be ignored. The theoretic model of phase signatures is derived thoroughly and the compensation methods are presented when dechirping technology is employed. In addition, the factors which influence residual phase and the precision of compensating are analyzed. According to the signatures of residual phase, a new compensation method is proposed in which the range alignment is applied to estimate the residual phase difference of adjacent echoes. Numerical simulation results illustrate the validities of proposed theories and methods.
Dechirping is an effective method for decreasing the bandwidth of input signals. For high velocity moving targets ISAR imaging, the residual phase arisen from dechirping processing and target moving can not be ignored. The theoretic model of phase signatures is derived thoroughly and the compensation methods are presented when dechirping technology is employed. In addition, the factors which influence residual phase and the precision of compensating are analyzed. According to the signatures of residual phase, a new compensation method is proposed in which the range alignment is applied to estimate the residual phase difference of adjacent echoes. Numerical simulation results illustrate the validities of proposed theories and methods.
2008, 30(4): 921-924.
doi: 10.3724/SP.J.1146.2006.01607
Abstract:
It is difficult to directly compress Synthetic Aperture Radar (SAR) raw data for its low relativity. In this paper, a new algorithm is put forward. Range focusing is imposed to SAR raw data, which makes it have comparative high relativity, then a vector linear prediction is performed along the azimuth direction, and block adaptive quantization is used to the prediction error series. By using a real SAR raw data, compression and decompression are made respectively. The SQNR and SDNR are achieved. The images correspond to the three algorithms are gained. The experiments manifest that with same bit rate, SQNR and SDNR after using the algorithm proposed in this paper surpass that of BAQ. The calculation in this paper is far less than that of compression method after range focusing advised in corresponding reference.
It is difficult to directly compress Synthetic Aperture Radar (SAR) raw data for its low relativity. In this paper, a new algorithm is put forward. Range focusing is imposed to SAR raw data, which makes it have comparative high relativity, then a vector linear prediction is performed along the azimuth direction, and block adaptive quantization is used to the prediction error series. By using a real SAR raw data, compression and decompression are made respectively. The SQNR and SDNR are achieved. The images correspond to the three algorithms are gained. The experiments manifest that with same bit rate, SQNR and SDNR after using the algorithm proposed in this paper surpass that of BAQ. The calculation in this paper is far less than that of compression method after range focusing advised in corresponding reference.
2008, 30(4): 925-928.
doi: 10.3724/SP.J.1146.2006.00920
Abstract:
Ground Penetrating Synthetic Aperture Radar (GPSAR), working in low frequency, has the capability of ground penetrating to obtain the two-dimensional high-resolution image of shallow buried targets. Vehicle-borne forward-looking GPSAR can detect landmines and minefields in front from a standoff distance quickly, which is a trend of landmine detection. Because speckle noise will influence target detection, the multi-look processing is studied in this paper and ground plane focusing BP algorithm and refraction and dispersion effects correction techniques are proposed. The proposed methods can solve the problems of images registration and shallow buried target two-layered medium imaging in multi-look processing. The proposed methods can improve the image Equivalent Number of Looks (ENL) and Radiometric Resolution (RR) efficiently, which is proved by the practical operating condition simulation of vehicle-borne system with the field data collected by the Rail-GPSAR system.
Ground Penetrating Synthetic Aperture Radar (GPSAR), working in low frequency, has the capability of ground penetrating to obtain the two-dimensional high-resolution image of shallow buried targets. Vehicle-borne forward-looking GPSAR can detect landmines and minefields in front from a standoff distance quickly, which is a trend of landmine detection. Because speckle noise will influence target detection, the multi-look processing is studied in this paper and ground plane focusing BP algorithm and refraction and dispersion effects correction techniques are proposed. The proposed methods can solve the problems of images registration and shallow buried target two-layered medium imaging in multi-look processing. The proposed methods can improve the image Equivalent Number of Looks (ENL) and Radiometric Resolution (RR) efficiently, which is proved by the practical operating condition simulation of vehicle-borne system with the field data collected by the Rail-GPSAR system.
2008, 30(4): 929-932.
doi: 10.3724/SP.J.1146.2007.01314
Abstract:
The APP method is capable to provide excellent estimation of speech aperiodic / periodic measurement and pitch simultaneously which is useful in speech research and application. However, due to its heavy computational load, APP system is about 110 times real-time, being an extinct flaw for utilization. In this paper, a modified detection of aperiodicity, periodicity and pitch in speech (MAPP) method is presented, which maintains the merit of APP method and eliminates the redundancy of configuration and computation, rationalizing the methodology. Computer simulation shows that MAPP method maintains high accuracy and robustness and that the system is improved to 12.3 times real-time on Pentium processor with 1.70GHz CPU and 512MB RAM, speeding up about one order of magnitude.
The APP method is capable to provide excellent estimation of speech aperiodic / periodic measurement and pitch simultaneously which is useful in speech research and application. However, due to its heavy computational load, APP system is about 110 times real-time, being an extinct flaw for utilization. In this paper, a modified detection of aperiodicity, periodicity and pitch in speech (MAPP) method is presented, which maintains the merit of APP method and eliminates the redundancy of configuration and computation, rationalizing the methodology. Computer simulation shows that MAPP method maintains high accuracy and robustness and that the system is improved to 12.3 times real-time on Pentium processor with 1.70GHz CPU and 512MB RAM, speeding up about one order of magnitude.
2008, 30(4): 933-936.
doi: 10.3724/SP.J.1146.2006.01463
Abstract:
In this paper, a digital watermarking algorithm resistant to the noise, geometric distortion and JPEG compression is proposed. Firstly, in order to enhance the security of the watermarking, the original meaningful binary image watermarking is scrambled with using Arnold transform. Then the scrambled watermarking is encoded by using Turbo code and CDMA technology. Taking into account the characteristics of human visual system (HVS), the positions and strengths of embedding the image are obtained. In the process of watermarks extracting, there must be the influence of Multiple Access Interference (MAI). By taking advantages of good encoding method (such as Turbo code) to lower the threshold of receiver, the influence of MAI can be dropped. The experimental results show that the presented digital watermarking scheme is more secure，and at the same time, keeping the watermarking imperceptible, higher watermarking capacity can be embedded into host image. More important, it is robust against general image processing operations, especially against adding Gaussian noise, geometric distortion (including cropping, horizon moving and rotating), JPEG glossy compression, filter attacks. Even the watermarked image degraded greatly because of the attacks, the watermarking can be extracted very well.
In this paper, a digital watermarking algorithm resistant to the noise, geometric distortion and JPEG compression is proposed. Firstly, in order to enhance the security of the watermarking, the original meaningful binary image watermarking is scrambled with using Arnold transform. Then the scrambled watermarking is encoded by using Turbo code and CDMA technology. Taking into account the characteristics of human visual system (HVS), the positions and strengths of embedding the image are obtained. In the process of watermarks extracting, there must be the influence of Multiple Access Interference (MAI). By taking advantages of good encoding method (such as Turbo code) to lower the threshold of receiver, the influence of MAI can be dropped. The experimental results show that the presented digital watermarking scheme is more secure，and at the same time, keeping the watermarking imperceptible, higher watermarking capacity can be embedded into host image. More important, it is robust against general image processing operations, especially against adding Gaussian noise, geometric distortion (including cropping, horizon moving and rotating), JPEG glossy compression, filter attacks. Even the watermarked image degraded greatly because of the attacks, the watermarking can be extracted very well.
2008, 30(4): 937-940.
doi: 10.3724/SP.J.1146.2006.01397
Abstract:
Many researchers have found it can improve the retrieval performance by combining region-based representation and relevance feedback technology. Since the previous works have ignored the probabilistic distribution of regions in the same semantic class, it is hard to represent the semantic information effectively. In this paper, Bayesian probabilistic model based on region and relevance feedback is proposed. The probability model of image similarity can be constructed via the Bayesian classifier obtained by on-line learning and its certainty based on the least error probability of the nearest region in relevant images set. When it comes to the non-parameter density estimation technique for characterizing the region feature distribution, it also takes the collective distribution into consideration because of inaccurate segmentation. Thus, the posterior distribution of region feature can be estimated accurately, and the experimental results demonstrate its effectiveness.
Many researchers have found it can improve the retrieval performance by combining region-based representation and relevance feedback technology. Since the previous works have ignored the probabilistic distribution of regions in the same semantic class, it is hard to represent the semantic information effectively. In this paper, Bayesian probabilistic model based on region and relevance feedback is proposed. The probability model of image similarity can be constructed via the Bayesian classifier obtained by on-line learning and its certainty based on the least error probability of the nearest region in relevant images set. When it comes to the non-parameter density estimation technique for characterizing the region feature distribution, it also takes the collective distribution into consideration because of inaccurate segmentation. Thus, the posterior distribution of region feature can be estimated accurately, and the experimental results demonstrate its effectiveness.
2008, 30(4): 941-944.
doi: 10.3724/SP.J.1146.2006.01528
Abstract:
Track-Before-Detect(TBD) is an efficient approach which detects and tracks targets in low SNR environment. A multiple model particle filter algorithm is presented in this paper for the maneuvering weak target which dynamics is complicated. In this algorithm a variable which denotes whether the target is existent or not and a variable which denotes the dynamics model of the target are augmented. The hybrid filter which includes two discrete variables is implemented by particle filter. Simulation results show that this algorithm can efficiently detect and track maneuvering targets on the condition of low SNR which the classical tracking methods can not work normally.
Track-Before-Detect(TBD) is an efficient approach which detects and tracks targets in low SNR environment. A multiple model particle filter algorithm is presented in this paper for the maneuvering weak target which dynamics is complicated. In this algorithm a variable which denotes whether the target is existent or not and a variable which denotes the dynamics model of the target are augmented. The hybrid filter which includes two discrete variables is implemented by particle filter. Simulation results show that this algorithm can efficiently detect and track maneuvering targets on the condition of low SNR which the classical tracking methods can not work normally.
2008, 30(4): 945-948.
doi: 10.3724/SP.J.1146.2006.01513
Abstract:
A low bit-rate real time video encoding system on MPEG using DSP TMS320DM642 as core processor is designed. The main features are: Diamond Search is integrated with Center-based Three-step Search (CTSS); A new method for pre-determination of all-zero blocks is proposed; The encoder is specially optimized for DSP. Experimental results show that the search method in this paper is better than CTSS. The pre-determination of all-zero blocks reduces operation and bit rate efficiently with little image quality decrease.
A low bit-rate real time video encoding system on MPEG using DSP TMS320DM642 as core processor is designed. The main features are: Diamond Search is integrated with Center-based Three-step Search (CTSS); A new method for pre-determination of all-zero blocks is proposed; The encoder is specially optimized for DSP. Experimental results show that the search method in this paper is better than CTSS. The pre-determination of all-zero blocks reduces operation and bit rate efficiently with little image quality decrease.
2008, 30(4): 949-952.
doi: 10.3724/SP.J.1146.2006.01468
Abstract:
A novel contour-based shape description and matching method is proposed. It equally segments the contours of the two objects into same numbers of arcs, an approximating polygon is then constructed with connecting the neighbor segmenting points using line segments. The three distance strings which are formed with the distance from the vertexes to the center of shape and the distances from the vertexes to the two subsequence vertexes are used to describe the shape, and the sum of the distances between their three distance strings is used to measure the difference between them. This method possesses uniqueness, compactness and invariance. Furthermore, this method is very simple to compute and can reflect both the global feature and the local feature of the shape. Experiment results show that the proposed method is accurate and reliable for matching shapes.
A novel contour-based shape description and matching method is proposed. It equally segments the contours of the two objects into same numbers of arcs, an approximating polygon is then constructed with connecting the neighbor segmenting points using line segments. The three distance strings which are formed with the distance from the vertexes to the center of shape and the distances from the vertexes to the two subsequence vertexes are used to describe the shape, and the sum of the distances between their three distance strings is used to measure the difference between them. This method possesses uniqueness, compactness and invariance. Furthermore, this method is very simple to compute and can reflect both the global feature and the local feature of the shape. Experiment results show that the proposed method is accurate and reliable for matching shapes.
2008, 30(4): 953-956.
doi: 10.3724/SP.J.1146.2006.01597
Abstract:
During tracking dim and small moving targets in the electrooptical detecting system, many false alarms extracted in the tracking window for low signal-to-noise ratio and high false alarm ratio debase seriously the performance of target recognition and tracking. To solve this problem, the target characters of the infrared imaging tracking system are analyzed, and based on the idea of the probabilistic data association filter, a modified method, which integrates the continuity and consistency of targets amplitude and motion, is proposed. The emphases are laid on the comparison of the target recognition and tracking performances between the original maximum likehood-probabilistic data associated filter and the proposed method. Some experimental results are included and the performance of target recognition and tracking target is improved greatly.
During tracking dim and small moving targets in the electrooptical detecting system, many false alarms extracted in the tracking window for low signal-to-noise ratio and high false alarm ratio debase seriously the performance of target recognition and tracking. To solve this problem, the target characters of the infrared imaging tracking system are analyzed, and based on the idea of the probabilistic data association filter, a modified method, which integrates the continuity and consistency of targets amplitude and motion, is proposed. The emphases are laid on the comparison of the target recognition and tracking performances between the original maximum likehood-probabilistic data associated filter and the proposed method. Some experimental results are included and the performance of target recognition and tracking target is improved greatly.
2008, 30(4): 957-960.
doi: 10.3724/SP.J.1146.2007.00845
Abstract:
An MERF based edge detection algorithm with adaptive threshold is presented in this paper. After analyzing dyadic wavelet transform and different behavior of edge and noise across scales, a Multi-scale Edge Response Function (MERF) is defined as the multiple scales point-wise products of the DWT to enhance significant image structures and suppress noise. Thereafter, an adaptive threshold for MERF is calculated and imposed on the module of MERF to identify edges as the local maxima of the gradient map without synthesizing the edge maps at several scales together, which was employed in many multi-scale techniques. Experiments on synthetic benchmark and natural images showed that the proposed MERF based adaptive threshold edge detection algorithm achieves better detection results than that for a single scale, especially on the localization performance; and edge and noise can be better distinguished by MERF comparing with the Laplacian of Gaussian (LOG), Canny edge detection and Mallat wavelet based edge detection algorithms.
An MERF based edge detection algorithm with adaptive threshold is presented in this paper. After analyzing dyadic wavelet transform and different behavior of edge and noise across scales, a Multi-scale Edge Response Function (MERF) is defined as the multiple scales point-wise products of the DWT to enhance significant image structures and suppress noise. Thereafter, an adaptive threshold for MERF is calculated and imposed on the module of MERF to identify edges as the local maxima of the gradient map without synthesizing the edge maps at several scales together, which was employed in many multi-scale techniques. Experiments on synthetic benchmark and natural images showed that the proposed MERF based adaptive threshold edge detection algorithm achieves better detection results than that for a single scale, especially on the localization performance; and edge and noise can be better distinguished by MERF comparing with the Laplacian of Gaussian (LOG), Canny edge detection and Mallat wavelet based edge detection algorithms.
2008, 30(4): 961-965.
doi: 10.3724/SP.J.1146.2007.00184
Abstract:
A backoff algorithm based on Minimum Contention Window Self-adaptive Adjusting (MCWSA) is proposed in this paper. The idea of this algorithm is that every node in the network adjusts self minimum contention window periodically, according to the comparing result of the present slot utilization and the optimal value, to adopt the congestion status. Simulation result proves that MCWSA can enhance the IEEE 802.11 performance in saturation throughout and delay.
A backoff algorithm based on Minimum Contention Window Self-adaptive Adjusting (MCWSA) is proposed in this paper. The idea of this algorithm is that every node in the network adjusts self minimum contention window periodically, according to the comparing result of the present slot utilization and the optimal value, to adopt the congestion status. Simulation result proves that MCWSA can enhance the IEEE 802.11 performance in saturation throughout and delay.
2008, 30(4): 966-969.
doi: 10.3724/SP.J.1146.2006.01552
Abstract:
Based on the strict energy limitations in wireless sensor network, how to decide the number of clusters, which is influenced with the total number of sensors and the characteristics of the disposed area, is the key idea in clustering algorithm. The energy model used in the communication process is given, the optimization of the number of clusters according to different level of clusters is analyzed theoretically. The simulation results show that the rational number of clusters can unify the energy distributions of sensors and improve the lifetime of network.
Based on the strict energy limitations in wireless sensor network, how to decide the number of clusters, which is influenced with the total number of sensors and the characteristics of the disposed area, is the key idea in clustering algorithm. The energy model used in the communication process is given, the optimization of the number of clusters according to different level of clusters is analyzed theoretically. The simulation results show that the rational number of clusters can unify the energy distributions of sensors and improve the lifetime of network.
2008, 30(4): 970-974.
doi: 10.3724/SP.J.1146.2006.01511
Abstract:
DV-Hop algorithm is one of the important range-free localization algorithms. The algorithm performs better in isotropic density sensor networks, however, it has larger location errors in randomly distributed networks. According to the localization principle of the DV-Hop algorithm, this paper proposes three improvements including the estimation of average single hop distance, the calculation of distance between unknown nodes and reference nodes and the estimation of node positions. These improvements can be used independently or jointly to replace the corresponding steps in the DV-Hop algorithm. The localization performances are analyzed in theory and with simulations. The results show that the proposed improvements can greatly enhance the localization accuracy of the unknown nodes. In addition, the proposed schemes do not change the localization process of the DV-Hop algorithm, and hence they need no further communication resource and additional hardware requirement.
DV-Hop algorithm is one of the important range-free localization algorithms. The algorithm performs better in isotropic density sensor networks, however, it has larger location errors in randomly distributed networks. According to the localization principle of the DV-Hop algorithm, this paper proposes three improvements including the estimation of average single hop distance, the calculation of distance between unknown nodes and reference nodes and the estimation of node positions. These improvements can be used independently or jointly to replace the corresponding steps in the DV-Hop algorithm. The localization performances are analyzed in theory and with simulations. The results show that the proposed improvements can greatly enhance the localization accuracy of the unknown nodes. In addition, the proposed schemes do not change the localization process of the DV-Hop algorithm, and hence they need no further communication resource and additional hardware requirement.
2008, 30(4): 975-978.
doi: 10.3724/SP.J.1146.2006.01431
Abstract:
Multiple dimension packet classification is an enabling function for many Internet applications, such as network security, network monitoring, quality of service, flow routing, etc. It is difficult to develop a packet classification algorithm that is efficient in both space and time. Based on the observation that there are only a few possible values for the protocol field in the classifier, a Multiple Decision Tree (MDT) algorithm is proposed. This algorithm is suitable for both software and hardware implementation, and is applicable for IPv6 in theory. When MDT is implemented with hardware, the multiple tree can be searched in parallel and pipeline can be used to search within a specific tree, thus the search complexity of MDT is O(1). With advantages in preprocessing time, memory consumption, and search time, MDT can be used to improve the widely used HiCuts and HyperCuts algorithms.
Multiple dimension packet classification is an enabling function for many Internet applications, such as network security, network monitoring, quality of service, flow routing, etc. It is difficult to develop a packet classification algorithm that is efficient in both space and time. Based on the observation that there are only a few possible values for the protocol field in the classifier, a Multiple Decision Tree (MDT) algorithm is proposed. This algorithm is suitable for both software and hardware implementation, and is applicable for IPv6 in theory. When MDT is implemented with hardware, the multiple tree can be searched in parallel and pipeline can be used to search within a specific tree, thus the search complexity of MDT is O(1). With advantages in preprocessing time, memory consumption, and search time, MDT can be used to improve the widely used HiCuts and HyperCuts algorithms.
2008, 30(4): 979-983.
doi: 10.3724/SP.J.1146.2006.01422
Abstract:
Priority classification and two-level collision being adopted, Enhanced Distributed Channel Access (EDCA)mechanism of IEEE 802.11e protocol is quite difficult to be modeled and analyzed. According to the characteristics of EDCA mechanism, an effective and simple model for two-level collision is proposed. The probabilities of inner virtual collision and outer collision are calculated based on the formula of sending probability deduced from simple EDCA model, and then integrated. Finally, the simulation of throughput and delay of complicated EDCA under saturation is conducted. The simulation demonstrates that EDCA mechanism, which adopts priority classification and two-level collision, can not only preferentially guarantee the throughput of voice and video, but also greatly decrease the average delay of the system.
Priority classification and two-level collision being adopted, Enhanced Distributed Channel Access (EDCA)mechanism of IEEE 802.11e protocol is quite difficult to be modeled and analyzed. According to the characteristics of EDCA mechanism, an effective and simple model for two-level collision is proposed. The probabilities of inner virtual collision and outer collision are calculated based on the formula of sending probability deduced from simple EDCA model, and then integrated. Finally, the simulation of throughput and delay of complicated EDCA under saturation is conducted. The simulation demonstrates that EDCA mechanism, which adopts priority classification and two-level collision, can not only preferentially guarantee the throughput of voice and video, but also greatly decrease the average delay of the system.
2008, 30(4): 984-987.
doi: 10.3724/SP.J.1146.2006.01254
Abstract:
This paper combines firstly priority control mechanism into integrated service dual token ring LAN, constructs queuing model, and then gets mathematical solving and simulation results for dual token ring LAN of three priorities, and gets important factors of the performance estimate of the computer network, and to proceed numerical calculation and results analysis for resolution results, which could provide theory basis for constructing dual token ring in integrated service condition.
This paper combines firstly priority control mechanism into integrated service dual token ring LAN, constructs queuing model, and then gets mathematical solving and simulation results for dual token ring LAN of three priorities, and gets important factors of the performance estimate of the computer network, and to proceed numerical calculation and results analysis for resolution results, which could provide theory basis for constructing dual token ring in integrated service condition.
2008, 30(4): 988-990.
doi: 10.3724/SP.J.1146.2006.01464
Abstract:
There usually exists the coupling temporal arrearage circs in the real network owing to the congestion, bandwidth and transmission velocity. Therefore, one new kinds of cascading failure model with the coupling temporal arrearage character is come into being. To the emphasis, the new model has been applied into studying the highway traffic network. In this paper, the nonlinear dynamics feature of the traffic congestion has been studied, the formation mechanism of the traffic congestion in the traffic networks has been researched, and its complex dynamics spreading behavior has been probed, the diffusion of traffic congestion in the complex networks has been analyzed. Two kinds of attack strategies, the random and the intentional, which bring the cascading failure of networks are simulated, and then the threshold value distribution is calculated which influent the networks efficiency and networks enduring abilities for the cascading failure.
There usually exists the coupling temporal arrearage circs in the real network owing to the congestion, bandwidth and transmission velocity. Therefore, one new kinds of cascading failure model with the coupling temporal arrearage character is come into being. To the emphasis, the new model has been applied into studying the highway traffic network. In this paper, the nonlinear dynamics feature of the traffic congestion has been studied, the formation mechanism of the traffic congestion in the traffic networks has been researched, and its complex dynamics spreading behavior has been probed, the diffusion of traffic congestion in the complex networks has been analyzed. Two kinds of attack strategies, the random and the intentional, which bring the cascading failure of networks are simulated, and then the threshold value distribution is calculated which influent the networks efficiency and networks enduring abilities for the cascading failure.
2008, 30(4): 991-994.
doi: 10.3724/SP.J.1146.2006.01507
Abstract:
The precise definition and security model of a new signature scheme－limited confederate verifier signatures is proposed based on the idea of threshold. An efficient limited confederate verifier signatures scheme is also constructed for the first time. The new scheme allows confining the right to learn the message and the right to verify the signature within t verifiers, the signature can be verified iff all the t verifiers cooperate. Moreover, the size of the signature does not grow with the number of verifiers. The scheme is proved to achieve the desired security request under the random oracle model.
The precise definition and security model of a new signature scheme－limited confederate verifier signatures is proposed based on the idea of threshold. An efficient limited confederate verifier signatures scheme is also constructed for the first time. The new scheme allows confining the right to learn the message and the right to verify the signature within t verifiers, the signature can be verified iff all the t verifiers cooperate. Moreover, the size of the signature does not grow with the number of verifiers. The scheme is proved to achieve the desired security request under the random oracle model.
2008, 30(4): 995-998.
doi: 10.3724/SP.J.1146.2007.00549
Abstract:
In this paper, the concepts of identity-based linkable ring signature and linkable convertible ring signature are proposed. Taken Zhang and Kims scheme as an example, a general method is given to add linkability and convertibility to some identity-based ring signatures. Then two efficient schemes are given for the first time, besides the complete anonymity and unforgeability under adaptively chosen message attack, one satisfying linkability, and the other satisfying both linkability and convertibility.
In this paper, the concepts of identity-based linkable ring signature and linkable convertible ring signature are proposed. Taken Zhang and Kims scheme as an example, a general method is given to add linkability and convertibility to some identity-based ring signatures. Then two efficient schemes are given for the first time, besides the complete anonymity and unforgeability under adaptively chosen message attack, one satisfying linkability, and the other satisfying both linkability and convertibility.
2008, 30(4): 999-1003.
doi: 10.3724/SP.J.1146.2006.01454
Abstract:
In this paper, a novel splitting technique of ray tubes based on ray tracing method is put forward, which is called the deterministic splitting method of ray tubes. At the same time, the analytic splitting format and the demonstration of self-contained characteristic is provided. The simulation results prove that the proposed method possesses the merits of less CPU time and higher computing efficiency, compared with two known methods of ray tubes on the condition of same prediction precision. The prediction of received power has been done with this method in indoor environment. A good agreement is achieved between the simulated results and the published results.
In this paper, a novel splitting technique of ray tubes based on ray tracing method is put forward, which is called the deterministic splitting method of ray tubes. At the same time, the analytic splitting format and the demonstration of self-contained characteristic is provided. The simulation results prove that the proposed method possesses the merits of less CPU time and higher computing efficiency, compared with two known methods of ray tubes on the condition of same prediction precision. The prediction of received power has been done with this method in indoor environment. A good agreement is achieved between the simulated results and the published results.
2008, 30(4): 1004-1006.
doi: 10.3724/SP.J.1146.2007.00673
Abstract:
Based on the percentage amplitude mismatch, the approximate BER formula of the Successive Interference Canceller (SIC) is presented with the Gaussian approximation method，and the effect of the amplitude mismatch on the Bit Error Rate (BER) performance is discussed. The loss of BER performance of the SIC is described as the positive number . The formula of the quantifiable analysis on the relation among the percentage amplitude mismatch , Signal Noise Ratio (SNR) and is derived with the Lagrange mean value theorem and the approximate analysis method. The Simulation results show that this quantifiable analysis formula describes the effect of amplitude mismatch on system performance well.
Based on the percentage amplitude mismatch, the approximate BER formula of the Successive Interference Canceller (SIC) is presented with the Gaussian approximation method，and the effect of the amplitude mismatch on the Bit Error Rate (BER) performance is discussed. The loss of BER performance of the SIC is described as the positive number . The formula of the quantifiable analysis on the relation among the percentage amplitude mismatch , Signal Noise Ratio (SNR) and is derived with the Lagrange mean value theorem and the approximate analysis method. The Simulation results show that this quantifiable analysis formula describes the effect of amplitude mismatch on system performance well.
2008, 30(4): 1007-1010.
doi: 10.3724/SP.J.1146.2006.01656
Abstract:
In this paper, AP (Amplitude-Phase) algorithm for SAR raw data compression is studied and the formula of bit allocation between amplitude data and phase data is deduced based on the lower bound of rate-distortion inequality of non-normal information resource and the Lagrange multiplier, which points out that the bit allocation is decided by their differential entropy correspondingly. The uniform distribution of phase data and the Rayleigh distribution of amplitude data are investigated and the bit allocation formula is deduced according to the differential entropy of continuous information resource, which points out that the mean of amplitude is the only factor. According to the relationship between the histogram and the probability density function, a general differential entropy calculation formula is given. The two methods have their advantages and both can implement the auto-bit allocation. The validity of this method is proved by the real raw data compression experiments.
In this paper, AP (Amplitude-Phase) algorithm for SAR raw data compression is studied and the formula of bit allocation between amplitude data and phase data is deduced based on the lower bound of rate-distortion inequality of non-normal information resource and the Lagrange multiplier, which points out that the bit allocation is decided by their differential entropy correspondingly. The uniform distribution of phase data and the Rayleigh distribution of amplitude data are investigated and the bit allocation formula is deduced according to the differential entropy of continuous information resource, which points out that the mean of amplitude is the only factor. According to the relationship between the histogram and the probability density function, a general differential entropy calculation formula is given. The two methods have their advantages and both can implement the auto-bit allocation. The validity of this method is proved by the real raw data compression experiments.
2008, 30(4): 1011-1013.
doi: 10.3724/SP.J.1146.2006.01390
Abstract:
In this paper, the theoretical analyses and simulations of the SAR imaging processing are firstly made, the time-domain sub-aperture algorithm which is used to implement missile-borne SAR, are researched and the whole flow of the algorithm are given. Finally, thinking over the need of the practice system, a hardware system using the high performance DSP chip named TS203 to process digital signal practically are designed and the result of imaging are given. The result validates the efficiency of the time-domain sub-aperture algorithm and hardware platform.
In this paper, the theoretical analyses and simulations of the SAR imaging processing are firstly made, the time-domain sub-aperture algorithm which is used to implement missile-borne SAR, are researched and the whole flow of the algorithm are given. Finally, thinking over the need of the practice system, a hardware system using the high performance DSP chip named TS203 to process digital signal practically are designed and the result of imaging are given. The result validates the efficiency of the time-domain sub-aperture algorithm and hardware platform.
2008, 30(4): 1014-1016.
doi: 10.3724/SP.J.1146.2006.01311
Abstract:
Based on the numerical simulation model of OCPAR and paired-echo theory, the phase fluctuation of optic-link, and the pattern and pulse compression of an array, which are influenced by optic-links phase characteristics, are analyzed theoretically and simulated. The results indicate that the pattern and pulse compression of OCPAR are affected by the phase fluctuation of optic-link somewhat. But the influence may be weakened with the combination function of array.
Based on the numerical simulation model of OCPAR and paired-echo theory, the phase fluctuation of optic-link, and the pattern and pulse compression of an array, which are influenced by optic-links phase characteristics, are analyzed theoretically and simulated. The results indicate that the pattern and pulse compression of OCPAR are affected by the phase fluctuation of optic-link somewhat. But the influence may be weakened with the combination function of array.
