Unique Words Blind Identification of Time Division Multiple Access Modulated Data Based on Fourth Order Correlation
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摘要: 针对非合作通信中时分多址(TDMA)信号的独特码(UW)盲识别问题，该文首次提出分布式独特码的盲识别算法。区别于比特层的独特码识别算法，该文分别针对集中式独特码和分布式独特码，提出面向调制数据不同窗口之间相关性的波形层独特码识别算法。算法利用独特码的一致性与相关性，分两步进行，首先通过差分累积消除不同突发信号间频偏与相偏的影响，来纵向对齐各个突发信号的独特码，然后通过多层差分共轭4阶相关算法识别出独特码的位置和长度。仿真分析了不同突发个数、信噪比和有无频偏相偏情况下算法的性能，验证了波形层识别独特码的有效性，针对集中式独特码和分布式独特码，所提算法在信噪比为5 dB时均达到了95%以上的识别率，具有一定的工程应用价值。Abstract: Considering the problem of blind identification of Unique Words (UW) for Time Division Multiple Access (TDMA) signals in non-cooperative communication, a blind identification algorithm for distributed UW is proposed in this paper. Different from the unique codes recognition algorithm at the bit layer, a unique words recognition algorithm at the waveform layer oriented to the correlation is proposed between different windows of the modulated data for centralised unique words and distributed unique words, respectively. The algorithm takes advantage of the consistency and correlation of the unique words and proceeds in two steps: firstly, the unique words of different burst signals are vertically aligned by eliminating the effects of frequency and phase bias between the different burst signals through differential accumulation, and then the positions and lengths of the unique words are identified by the multilayer differential conjugate fourth order correlation algorithm. The performance of the algorithm is simulated and analysed with different number of bursts, signal-to-noise ratios, and with or without frequency and phase biases, and the effectiveness of the waveform layer identification of unique words is verified, and the algorithm achieves more than 95% of the identification rate at a signal-to-noise ratio of 5dB for both centralized and distributed unique words, which is of certain value for engineering applications.
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算法1 集中式独特码盲识别算法 输入：接收信号$ {\mathbf{r}} $，$ n $个突发的粗起始位置${s_1},{s_2}, \cdots ,{s_n}$，对齐所
用数据长度${L_0}$，判决阈值${\text{th}}$输出：独特码起止位置 (1)${{\mathbf{B}}_1} = r({s_1},{s_1} + 1, \cdots ,{s_1} + {L_0} - 1)$ (2)for $k = 2,3, \cdots ,n$ do (3) for $m = - c, - c + 1, \cdots ,c - 1,c$ do(其中$\left[ { - c,c} \right]$假设为延
迟范围)(4) ${\mathbf{B}}_k^m = r({s_k} + m,{s_k} + m + 1, \cdots ,{s_k} + m + L{}_0 - 1)$； (5) 利用式(9)计算${R_{1k}}(m)$； (6) end for (7) ${R_{1k}}(m)$的最大值对应的$m$为${{\mathbf{B}}_1}$与${{\mathbf{B}}_k}$之间的延迟； (8)end for (9) 令已对齐独特码的$ n $个突发信号纵向排列； (10) for $i = 2,3, \cdots ,{L_0} - {w_0} - 1$ do (11) 利用式(17)计算${\text{Corr(}}i{\text{)}}$，并进行能量归一化； (12) if ${\text{Corr(}}i{\text{) > th}}$ then (13) 认为$i$所处位置为独特码的一部分； (14) end if (15)end for (16)判断出集中式独特码位置； 
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算法2 分布式独特码盲识别算法 输入：接收信号$ {\mathbf{r}} $，$ n $个突发的粗起始位置${s_1},{s_2}, \cdots ,{s_n}$，对齐所
用数据长度${L_0}$，判决阈值${\text{th}}$输出：独特码起止位置及分布格式 (1) ${{\mathbf{B}}_1} = r({s_1},{s_1} + 1, \cdots ,{s_1} + {L_0} - 1)$ (2) for $k = 2,3, \cdots ,n$ do (3) for $m = - c, - c + 1, \cdots ,c - 1,c$ do (4) ${\mathbf{B}}_k^m = r({s_k} + m,{s_k} + m + 1, \cdots ,{s_k} + m + L{}_0 - 1)$； (5) for ${N'} = {N_1},{N_1} + 1, \cdots ,{N_2}$ do (6) for ${H'} = {H_1},{H_1} + 1, \cdots ,{H_2}$ do (7) 利用式(14)计算${R_{1k}}(m,{N'},{H'})$； (8) end for (9) end for (10) end for (11) ${R_{1k}}(m,{N'},{H'})$的最大值对应的$m$为${{\mathbf{B}}_1}$与${{\mathbf{B}}_k}$的延迟； (12)end for (13) 令已对齐独特码的$ n $个突发信号纵向排列； (14) for $i = 2,3, \cdots ,{L_0} - {w_0} - 1$ do (15) 利用式(17)计算${\text{Corr(}}i{\text{)}}$，并进行能量归一化； (16) if ${\text{Corr(}}i{\text{) > th}}$ then (17) 认为$i$所处位置为独特码的一部分； (18) end if (19) end for (20) 判断出分布式独特码位置以及分布格式；
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表 1 突发信号格式统计
TDMA信号 突发信号格式 集中式独特码TDMA信号1 128独特码采样点+不定长度数据 集中式独特码TDMA信号2 256独特码采样点+不定长度数据 分布式独特码TDMA信号1 16独特码采样点+104数据采样点+···+16独特码采样点+104数据采样点 分布式独特码TDMA信号2 32独特码采样点+208数据采样点+···+32独特码采样点+208数据采样点
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表 2 6 dB信噪比下独特码识别结果统计
TDMA信号 识别结果 集中式独特码TDMA信号1 独特码长度为127个采样点 集中式独特码TDMA信号2 独特码长度为259个采样点 分布式独特码TDMA信号1 每个模块为16个独特码采样点+104个数据采样点 分布式独特码TDMA信号2 每个模块为31个独特码采样点+209个数据采样点
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