Research on Double-Layer Multi-Mode Index Modulation Techniques for Orthogonal Time Sequency Multiplexing

DONG Xiaoqi; ZHANG Siyu; YUE Xinwei; WANG Chaowei

doi:10.11999/JEIT260899

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DONG Xiaoqi, ZHANG Siyu, YUE Xinwei, WANG Chaowei. Research on Double-Layer Multi-Mode Index Modulation Techniques for Orthogonal Time Sequency Multiplexing[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260899

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DONG Xiaoqi, ZHANG Siyu, YUE Xinwei, WANG Chaowei. Research on Double-Layer Multi-Mode Index Modulation Techniques for Orthogonal Time Sequency Multiplexing[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT260899

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Research on Double-Layer Multi-Mode Index Modulation Techniques for Orthogonal Time Sequency Multiplexing

doi: 10.11999/JEIT260899 cstr: 32379.14.JEIT260899

DONG Xiaoqi^1
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ZHANG Siyu^{1, 2
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YUE Xinwei^{1, 2},
WANG Chaowei³

1.
School of Information and Communication Engineering, Beijing Information Science and Technology University, Beijing 102206, China
2.
Center for Target Cognition Information Processing Science and Technology, Beijing Information Science and Technology University, Beijing 102206, China
3.
School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China

Funds: National Natural Science Foundation of China (62301058)，R&D Program of Beijing Municipal Education Commission (KM202411232010)

Received Date: 2026-07-02
Accepted Date: 2026-10-19
Rev Recd Date: 2026-10-19

Available Online: 2026-10-26

Abstract

Abstract

Objective High-mobility communication scenarios, including low-Earth-orbit satellite links, high-speed railway communications, and unmanned aerial vehicle networks, require reliable control transmission and efficient service-data delivery. Different services have different reliability and throughput requirements, which are difficult to accommodate using a single information mapping structure. Orthogonal Time Sequency Multiplexing (OTSM) operates in the Delay-Sequency (DS) domain and uses the Walsh-Hadamard Transform (WHT) to support transmission over doubly dispersive channels with low implementation complexity. Index Modulation (IM) conveys information through resource indices in addition to constellation symbols. Existing OTSM-based IM schemes improve transmission reliability through sparse activation, but inactive resources limit spectral efficiency. Moreover, applying the same mapping strategy to all information bits does not exploit differences in their importance. To address these limitations, a Double-Layer Multi-Mode OTSM scheme with IM, termed DLMM-OTSM, is proposed. The scheme combines a sparse base layer with a fully activated enhancement layer to support differentiated transmission. Its receiver design balances detection complexity and error performance through layer-specific detection and a limited number of index candidates. Methods Each group of information bits is divided between a base layer and an enhancement layer, which occupy two adjacent rows of the DS-domain grid (Fig. 1). The base layer carries reliability-sensitive information using sparse single-mode IM. Its index bits select a subset of available carriers, and its symbol bits are mapped to constellation A on the selected carriers. The remaining carriers are inactive. The enhancement layer carries throughput-oriented information using full-carrier dual-mode IM. Its index bits determine which carriers use constellation B, while the remaining carriers use constellation C. Both carrier subsets transmit symbols, so all enhancement-layer carriers remain active. Constellations B and C are disjoint to distinguish their modes, and their power allocation and relative rotation help separate the constellation points (Fig. 2). For each layer, index patterns are selected from a shared legal mapping table to establish a one-to-one correspondence between index bits and transmission patterns. The resulting DS-domain symbols undergo the inverse WHT and vectorization before transmission. For eight available carriers and two selected carriers, there are 28 possible position combinations. Sixteen combinations are used to represent four index bits, and the same mapping is available at both the transmitter and receiver (Table 1). With 4-QAM in all three constellations, each group carries eight base-layer bits and twenty enhancement-layer bits. This legal-pattern constraint is applied during detection, preventing the receiver from selecting combinations that do not correspond to transmitted index bits. At the receiver, Maximum Likelihood (ML) detection searches legal index patterns and constellation symbol combinations and serves as a performance benchmark. To reduce the search burden, a Log-Likelihood Ratio (LLR) detector is developed following Minimum Mean Square Error (MMSE) equalization. The detector calculates per-carrier metrics for activation in the base layer and constellation membership in the enhancement layer. These metrics are accumulated over legal index patterns, followed by pattern selection and symbol decisions. A single selected pattern may exclude the correct transmitted vector when individual LLR values are unreliable. Therefore, a Top-K candidate detector retains the K legal patterns with the largest accumulated metrics for each layer. Candidate signal vectors are constructed, and their Euclidean distances are evaluated using the received signal and equivalent channel matrix. The candidate with the minimum distance is selected (Algorithm 1). When K = 1, the method reduces to LLR detection. The additional search effort is controlled by the number of retained candidate patterns. Detection complexity and spectral efficiency are analyzed, and an analytical approximation to the Average Bit Error Probability (ABEP) union bound is derived. Results and Discussions Simulations use an Extended Vehicular A (EVA) multipath Rayleigh fading channel with nine propagation paths, a carrier frequency of 4 GHz, and a subcarrier spacing of 15 kHz. The equivalent channel matrix is assumed known at the receiver. Unless otherwise specified, the relative speed is 500 km/h. Spectral efficiency is calculated from the information bits carried by the data grid, excluding cyclic-prefix overhead, using the same convention for all schemes. For M=N=8, J_b=J_e =2, and 4-QAM, DLMM-OTSM achieves a spectral efficiency of 1.75 bit/s/Hz. This is 75% higher than OTSM-IM and approximately 16.7% higher than Pairwise Sequency Index Modulation with OTSM (PSeIM). With the carrier-selection ratios J_b/N= J_e/N maintained, its spectral efficiency reaches 2 bit/s/Hz for a 64 × 64 DS-domain grid (Table 2). At a signal-to-noise ratio (SNR) of 25 dB, the bit error rates (BER) of the base and enhancement layers are approximately 1.59 × 10^–4 and 4.29 × 10^–4, respectively. Thus, the base-layer BER is approximately 37% of the enhancement-layer BER, demonstrating differentiated reliability through the two IM structures (Fig. 5). Increasing K from 1 to 4 reduces BER by approximately 13.1% at 10 dB and 33.1% at 20 dB (Fig. 3). The analytical ABEP approximation approaches the ML simulation results in the high-SNR region. Compared with ML detection, the Top-K detector incurs SNR losses of approximately 0.5 dB and 0.7 dB at BERs of 10^–3 and 10^–4, respectively, while reducing detection complexity (Fig. 6). Under equal spectral-efficiency conditions, DLMM-OTSM achieves SNR gains of approximately 4.0 dB, 3.4 dB, and 3.3 dB over OTSM-IM, PSeIM, and conventional OTSM, respectively, at a target BER of 10^–3 (Fig. 7). A modulation-order comparison gives spectral efficiencies of 1.125, 1.75, and 2.375 bit/s/Hz for BPSK, 4-QAM, and 8-QAM, respectively. Moving from BPSK to 4-QAM increases spectral efficiency by approximately 55.6%, with an SNR loss of approximately 0.55 dB at a BER of 10^–3. Moving from 4-QAM to 8-QAM increases spectral efficiency by approximately 35.7%, but requires approximately 4.5 dB of additional SNR at the same target BER (Fig. 8). Conclusions DLMM-OTSM combines layered transmission and multiple IM modes to support heterogeneous data requirements in high-mobility channels. By assigning reliability-sensitive information to a sparse base layer and throughput-oriented information to a full-carrier dual-mode enhancement layer, the proposed scheme achieves flexible unequal error protection and improved spectral efficiency. The LLR detector reduces receiver complexity, while the Top-K mechanism recovers much of the performance loss caused by single-pattern LLR decisions with comparatively low complexity. Theoretical and simulation results demonstrate that the proposed DLMM-OTSM provides an effective tradeoff among reliability, spectral efficiency, and detection complexity.
- Index modulation,
- Orthogonal time sequency multiplexing,
- Log-likelihood ratio detection,
- Spectral efficiency,
- Bit error rate

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References(18)

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