Research on Double-Layer Multi-Mode Index Modulation Techniques for Orthogonal Time Sequency Multiplexing
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摘要: 为兼顾不同业务数据的传输可靠性与频谱效率，提出一种双层多模正交时间序列复用索引调制(DLMM-OTSM)方案。在OTSM系统时延–序列域采用双层传输结构，基础层采用稀疏单模索引调制(IM)，以保障重要信息的可靠传输，增强层采用全载波双模IM，以提高信息传输效率。接收端在最大似然(ML)检测基础上，介绍了一种基于对数似然比(LLR)的低复杂度分层检测方法。进一步提出一种基于Top-K候选的检测算法，通过保留多个高可靠索引候选并进行欧氏距离校正，改善LLR单次判决造成的误码性能损失。文章对所提系统的检测复杂度、频谱效率和误比特率上界进行了理论分析和仿真。结果表明，在4-QAM调制条件下，所提方案频谱效率达到1.75 bit/s/Hz，较以往算法最高提高75%，同时误码性能优于现有方案。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, Jb=Je =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 Jb/N= Je/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. -
表 1 M=N=8，Jb=Je=2条件下索引规则示例
序号 索引比特 所选载波位置 序号 索引比特 所选载波位置 0 0000 {1,4} 8 1000 {3,6} 1 0001 {1,6} 9 1001 {3,8} 2 0010 {1,8} 10 1010 {1,5} 3 0011 {2,3} 11 1011 {4,7} 4 0100 {2,4} 12 1100 {5,6} 5 0101 {2,5} 13 1101 {5,8} 6 0110 {2,7} 14 1110 {7,8} 7 0111 {3,4} 15 1111 {6,7} 
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1 Top-K候选检测算法
(1) 根据式(22)对ym进行MMSE均衡 (2) for n=1,2, ···,N do 根据式(25)或式(29)计算位置n的LLR值 end (3) $ \boldsymbol{V}_{m}^{\text{b}}=\arg \text{Top}_{{\boldsymbol{I}}_{\text{b}}\in {\boldsymbol{U}}_{\text{b}}}^{K}\left(\displaystyle\sum \nolimits_{n\in {\boldsymbol{I}}_{\text{b}}}\gamma _{n}^{\text{b}}\right) $ $ \boldsymbol{V}_{m}^{\text{e}}=\arg \text{Top}_{{\boldsymbol{I}}_{\text{e}}\in {\boldsymbol{U}}_{\text{e}}}^{K}\left(\displaystyle\sum \nolimits_{n\in {\boldsymbol{I}}_{\text{e}}}\gamma _{n}^{\text{e}}\right) $ (4) for k=1,2, ···,K do 根据式(33)或式(36)构造候选向量$ {{\hat{\boldsymbol{x}}}}_{m,k} $ $ \widehat{k}=\arg \underset{k=1, 2, \cdots, K}{\min }{\left|\left|{\boldsymbol{y}}_{m}-{\boldsymbol{H}}_{m}\boldsymbol{x}_{\text{e},k}^{m}\right|\right|}^{2} $ end (5) 返回$ {{\hat{\boldsymbol{x}}}}_{m,k} $
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表 2 不同网格规模下各系统理论频谱效率对比/(bit/s/Hz)
网格规模 DLMM-OTSM OTSM-IM PSeIM OTSM 8×8 1.7500 1.0000 1.5000 2.0000 16×16 1.8750 1.1250 1.5000 2.0000 32×32 1.9688 1.2188 1.5000 2.0000 64×64 2.0000 1.2500 1.5000 2.0000
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