Performance Analysis of SM-Index Modulation Based Cooperative Wireless Communication System

In spatial modulation (SM) system, the information bits can be transmitted through two ways, the selection of both the transmit antenna and the constellation symbol. However, conventional bit-to-symbol mapping scheme in SM system only selects the transmit antenna or the constellation symbol independently. With the consideration of the similarity among the transmit antennas and the joint selection of the transmit antenna and the constellation symbol, cosine similarity based bit to symbol-and-antenna mapping scheme is proposed in this paper to reduce the hamming distance between adjacent symbols and achieve better system performance. Simulation results and performance analysis show that the proposed scheme can improve the system average bit error rate (BER) effectively compared with the conventional bit-to-symbol mapping scheme.

Spatial modulation (SM) is a novel and promising approach that has been introduced as an alternative to classical multiple-input multiple-output (MIMO) spatial multiplexing techniques. Cooperative communications, on the other hand, provides additional diversity gains and high data rates by improving coverage. Combining the advantages of SM and cooperative communications would then further improve efficiency. Most of the studies in the literature of cooperative SM systems consider the space shift keying (SSK) modulation, which is a special case of SM, and single receive/transmit antenna relay (R) and destination (D). In this work, we investigate the average bit error probability (ABEP) of a decode-and-forward (DF) cooperative SM system where all nodes have multiple transmit and/or receive antennas which has not been studied before. It is shown that the derived analytical expressions for the ABEP are in close match with the computer simulation results. Furthermore, it is demonstrated that the cooperative SM scheme provides 4 dB SNR gain compared to classical M-ary modulated cooperative systems.

Spatial modulation (SM) is a transmission scheme that uses multiple transmit antennas but only one transmit RF chain. At each time instant, only one among the transmit antennas will be active and the others remain silent. The index of the active transmit antenna will also convey information bits in addition to the information bits conveyed through modulation symbols. Pseudo-random phase precoding (PRPP) is a technique that can achieve high diversity orders even in single antenna systems without the need for channel state information at the transmitter and transmit power control. In this paper, we exploit the advantages of both SM and PRPP simultaneously. We propose a pseudo-random phase precoded SM (PRPP-SM) scheme, where both the modulation bits and the antenna index bits are precoded by pseudo-random phases. The proposed PRPP-SM system gives significant performance gains over SM system without PRPP and PRPP system without SM. Since maximum likelihood (ML) detection becomes exponentially complex in large dimensions, we propose a low complexity local search based detection (LSD) algorithm suited for PRPP-SM systems with large precoder sizes. Our simulation results show that with 4 transmit antennas, 1 receive antenna, 5 × 20 pseudo-random phase precoder matrix and BPSK modulation, the performance of PRPP-SM using ML detection is better than SM without PRPP with ML detection by about 9 dB at 102 BER. This performance advantage gets even better for large precoding sizes. We also propose a precoder index modulation (PIM) scheme, which conveys additional information bits through the choice of a precoding matrix among a set of pre-determined PRPP matrices. Finally, combining the PIM and PRPP-SM schemes, we propose a PIM-SM scheme which conveys bits through both antenna index as well as precoder index.

In this paper, the error performance analysis of an amplify-and-forward (AF) relay-aided cooperative multi-antenna system using spatial modulation (SM) over Rayleigh channels is presented. The SM is a simple and spectral efficient modulation technique that can increase the data rate by using input data bits to select a transmit antenna to send a constellation point. The relay transmission deploying SM not only can enhance the coverage and but also can improve the spectral efficiency. In the performance analysis, the overall average bit error rate (BER), which is related to the error probability of an antenna index detection ( $P_{a}$ ) and the error probability of symbol detection ( $P_{d}$ ) given transmit antenna index, is analyzed. With the derivation of the probability density function and the moment generating function of output signal-to-noise ratio (SNR), closed-form expressions of $P_{a}$ and $P_{d}$ are obtained to compute the overall BER. With the obtained BER expression, asymptotical BER expressions are derived to reveal the BER performance of the system at high SNR. By minimizing the asymptotical BER, a suboptimal power allocation (PA) scheme is developed. The diversity gain is analyzed at high SNR. The results indicate that the cooperative AF-SM can achieve full diversity order. Simulation results verify the effectiveness of the theoretical BER analysis, and the cooperative AF-SM with PA scheme outperforms upon the equal PA scheme.

The Spatial Modulation (SM) transmission scheme boosts the spectral efficiency and achieves the multiplexing gain by activating a single transmit antenna in each time slot. Radio wave propagation characteristics determined by the environment is a decisive factor for the SM system. In this paper, we investigate the performance of the SM scheme over real-world 4×4 Multi-Input Multi-Output (MIMO) channels measured in typical indoor scenarios. Firstly, a MIMO channel sounder is established. Based on the sounder, 15150 complex 4×4 MIMO channel matrices are measured inside a typical teaching building under both Line of Sight (LOS) and None Line of Sight (NLOS) scenarios. Secondly, by comparing the SM system over the measured channel and commonly-used channel models, we prove that both the Independently and Identically Distribute (i.i.d.) Rayleigh and the Spatial Correlation (SC) channel model are oversimplified, and that only practical experiences can yield definitive answers to the achievable real-world system performance. Thirdly, the Average Bit Error Probability (ABEP) performance of the SM system is studied based on the measured data under a variety of system configurations. The study of different receive antenna array settings (4×4, 4×2 and 4×1 MIMO setups) approves the significance of combining scheme at the receiver. SM systems employing different signal constellations (Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK) and 16 Quadrature Amplitude Modulation (16QAM)) are also investigated and some interesting results are revealed. Lastly, performance assessment of SM against State-Of-The-Art (SOTA) MIMO schemes (Space-Time Block Code (STBC) and Vertical Bell Labs Layered Space-Time (V-BLAST) code) is conducted. Results show that for a 4×4 MIMO, the low-complexity SM scheme outperforms both STBC and V-BLAST.

SummaryGeneralised spatial modulation (GSM) is a recently developed multiple‐input multiple‐output (MIMO) technique aimed at improving data rates over conventional spatial modulation (SM) systems. However, for identical antenna array size and configurations (AASC), the bit error rate (BER) of GSM systems in comparison with SM systems is degraded. Recently, a GSM system with constellation reassignment (GSM‐CR) was proposed in order to improve the BER of traditional GSM systems. However, this study focused on M‐ary quadrature amplitude modulation (M‐QAM) schemes. The focus of this paper is the application of a circular constellations scheme, in particular, amplitude phase shift keying (APSK) modulation, to GSM and GSM‐CR systems. An analytical bound for the average BER of the proposed M‐APSK GSM and M‐APSK GSM‐CR systems over fading channels is derived. The accuracy of this bound is verified using Monte Carlo simulation results. A 4 × 4 16‐APSK GSM‐CR system achieves a gain of 2.5 dB at BER of 10−5 over the traditional 16‐APSK GSM system with similar AASC. Similarly, a 6 × 4 32‐APSK GSM‐CR system achieves a gain of 2 dB at BER of 10−5 over equivalent 32‐APSK GSM system.

This paper proposes, for the first time, a two-source asymmetric turbo-coded-cooperative spatial modulation (SM) scheme over the slow Rayleigh fading channel. As in any coded cooperative communication, the interleaver plays a vital role in mitigating the harsh effect of the wireless channel. Therefore, the code matched interleaver (CMI) is effectively used in the proposed design. The simulated results reveal that the bit error rate (BER) performance of the proposed coded cooperative communication system outperforms the asymmetric turbo-coded non-cooperative scheme under identical conditions. This prominent performance improvement has been made possible due to the joint asymmetric turbo decoding at the destination node. Furthermore, to check the effectiveness of the proposed scheme, we have also developed a two-source asymmetric turbo-coded cooperative scheme based on the vertical bell labs layered space-time (VBLAST), incorporating the CMI as the suitable benchmark. It is observed that the proposed scheme employing SM has a better BER performance than the VBLAST scheme under identical conditions.

In spatial modulation (SM) systems, when channel state information is available at the transmitter, adaptive power allocation can be exploited to enhance the SM performance. In this paper, optimal power allocation in SM systems is considered from an information-theoretical view. First, as there is no closed-form expression of the SM capacity, the instantaneous mutual information is formulated in an analytic form for SM systems with two transmit antennas. Then, two power-allocation algorithms are proposed to maximize the SM mutual information. One is a sub-optimal power-allocation algorithm that is established in closed form to maximize the upper bound of SM mutual information. The other is an iterative algorithm for optimal power allocation that is proposed to achieve the maximum mutual information of SM systems while dramatically reducing the operational complexity compared with global computer searching. To evaluate the performance of the proposed power-allocation algorithms, numerical and simulation results are reported in terms of outage capacity and ergodic capacity, which demonstrates that the proposed power-allocation algorithms significantly improve the SM performance, compared with conventional equal-power allocation.

By combing Spatial modulation (SM) with the Amplify-and-forward (AF) cooperative communication, a cooperative SM scheme with AF (AF-SM) protocol is presented, and the corresponding Bit error rate (BER) performance is investigated. Based on the performance analysis, the error probability of antenna index estimation ( P a ) and the error probability of symbol estimation ( P d ), which constitutes the overall average BER, are derived, respectively. As a result, tightly approximate closedform expressions of P a and P d are attained, respectively. Using these expressions, the closed-form overall average BER is achieved. During the analysis, the computational complexity of AF-SM detector is also provided in terms of the complex addition and multiplication numbers. Besides, the asymptotic BER at high SNR and the corresponding diversity gain are further derived, and the resultant diversity gain of N r + 1 is obtained for the system with N r receive antennas. Simulation results show that our theoretical analysis is valid, and provides good performance evaluation method for cooperative SM system. Moreover, the BER performance can be effectively improved as N r increases due to higher diversity gain.

ABSTRACTBy combining Spatial modulation (SM) with cooperative communication, the diversity gain brought by cooperative relaying and high rate of SM can be obtained. In this paper, considering amplify-and-forward (AF) protocol, the performance of cooperative SM system with imperfect channel state information (CSI) over Rayleigh channel is analyzed. According to the performance analysis, the moment generating functions (MGFs) of effective signal-to-noise ratios (SNRs) are derived. With the MGFs, closed-form expressions of the error probability of antenna index detection and the error probability of symbol detection for imperfect CSI are achieved. Thereby, the approximate overall average bit error ratio (BER) is obtained, and these theoretical expressions include those under perfect CSI as special cases. Besides, the asymptotically approximate BER for large SNR is also derived. Based on this, a suboptimal power allocation (PA) scheme is developed, and the corresponding PA coefficients are attained by minimizing the asymptotical BER. As a result, closed-form PA can be attained for the system with multiple receive antennas. Computer simulations show that the theoretical BERs are close to the corresponding simulated results, which illustrates the effectiveness of the derived theoretical expressions. Compared with the conventional equal PA scheme, the proposed PA scheme enhances the BER performance efficiently.

The distributed Goppa-coded generalized spatial modulation (DGC-GSM) scheme with the source, relay, and destination in cooperative communications is proposed, where the source and relay adopt different Goppa codes. Goppa codes have many advantages such as the flexible codeword length, excellent code construction, and easy encoding and decoding complexity. At the relay, we select portions of the source information bits for further encoding. For each selection, the destination constructs a channel code. To obtain the best code in the destination, we propose the optimal information bit selection algorithm at the relay to choose the source information. However, Goppa codes with a large block length will impose high complexity on the optimal algorithm. Thus, the locally optimized selection algorithm is further proposed. At the destination, the joint decoding algorithm is adopted to recover the source information. Our simulated results indicate that the two selection algorithms proposed achieve better performance than the random selection method. This is because the optimized algorithms can generate the code with a larger minimum distance at the destination. Moreover, the proposed DGC-GSM scheme outperforms the non-cooperative system. Moreover, the DGC-GSM scheme can obtain the approximate performance with the distributed Goppa-coded spatial modulation (DGC-SM) scheme but has a significantly reduced transmit antenna number.

This work presents an integrated framework that combines polar coding, spatial modulation, and symbol‐level guessing random additive noise decoding (symbol‐level GRAND) aided detection to enhance the reliability and latency performance of CRC‐aided polar codes in 6G ultrareliable low‐latency communication (URLLC) scenarios. The proposed polar‐coded spatial modulation (PCSM) scheme utilizes (CA‐polar) codes to encode information bits transmitted as antenna index and symbol bits over a MIMO Rayleigh fading channel. The receiver employs a two‐stage detection scheme comprising initial spatial signal processing for antenna and symbol detection, followed by symbol refinement through symbol‐level GRAND with final error correction achieved with CRC‐aided successive cancellation list (CA‐SCL) decoding. A sequential detection and decoding strategy is adopted, in which symbol‐level GRAND refines the detected bits before CA‐SCL polar decoding, reducing error propagation into the polar decoder and thereby lowering the overall decoding complexity. Performance of the scheme is evaluated for polar codeword length of 128 bits for modulation orders of 16‐QAM and 64‐QAM, highlighting the scheme's parametric flexibility under short codeword constraints. Simulations carried out in MATLAB demonstrate that error correction with symbol‐level GRAND‐aided detection achieves an improved bit error rate (BER) and a lower system complexity facilitating real‐time hardware realization.

Relay-assisted cooperative free space optical (FSO) communication system is a powerful technique, which offers advantages like fading mitigation and significant gain in spatial diversity due to shorter transmission hops. Even so, it can be hampered by jamming activities which in turn degrade the overall system performance. In this paper, the effect of relay jamming in the decode-and-forward (DF) protocol based cooperative FSO communication system, is introduced and studied thoroughly. The probability density function (pdf) of a random variable containing mixture of the negative exponential and Gaussian random variables is derived. The error performance of the considered FSO system is analysed over this new kind of additive mixture noise for different probabilities of jamming. By utilizing the derived pdf, a closed-form expression of the average bit error rate (BER) of the DF FSO relaying is obtained. A comparison of the BER performance of maximum-likelihood (ML) detector and a derived threshold based detector is also provided. It is observed that the derived threshold based detector offers almost similar performance as that of the ML detector. A thorough numerical study is also provided by considering different pointing error parameters of jammer's and user's channels.

One of the main limitations in Spatial Modulation (SM) systems is the lack of transmit diversity, which directly impacts its error rate performance. The lack of the transmit diversity refers to activating only a single transmit antenna in SM systems. In this paper, we propose a novel scheme that aims at improving the performance of SM systems by achieving half-full transmit diversity. The proposed scheme, called Half-Full Transmit-Diversity SM (HFTD-SM), divides the transmit antennas into two-antenna groups. From each group, only a single antenna is activated, and all active transmit antennas emits one modulated symbol. The proposed HFTD-SM scheme is shown to outperform the conventional SM performance in terms of spectral efficiency, error rate, and design flexibility, while maintaining the main property of SM representing by the need of only a single RF chain. Simulation results corroborate the superior performance of the proposed scheme as compared to other SM variants in the literature.

In this paper, we design a cooperative wavelet scheme for the multi-relay, multi-scale and multi-lag diversity, which can be widely applied in the ultra-wideband communications and underwater acoustic communications. A Decode-and-Forward (DF) cooperative relay network is set for the multi-scale and multi-lag wideband channels. Then, an analytical bit error rate (BER) expression for this DF cooperative wavelet wideband communication system is proposed, which can be used to predict the system performance. Based on the proposed analytical BER expression, we also provide a dynamic optimal selection strategy for relay selection to take advantage of the multi-relay, multi-scale and multi-lag diversity and maximize the system BER performance.