Pre-equalization for MIMO Wireless Systems Using Spatial Modulation

The performance of spatial modulation (SM) is known to be dominated by the minimum Euclidean distance (MED) in the received SM constellation. In this paper, a symbol-scaling technique is proposed for SM in the multiple-input–multiple-output (MIMO) channel that enhances the MED to improve the performance of SM. This is achieved by forming fixed sets of candidate prescaling factors for the transmit antennas (TAs), which are randomly generated and are known at both the transmitter and the receiver. For a given channel realization, the transmitter chooses the specific set of factors that maximizes the MED. Given the channel state information (CSI) readily available at the receiver for detection, the receiver independently chooses the same set of prescaling factors and uses them for the detection of both the antenna index (AI) and the symbol of interest. We analytically calculate the attainable gains of the proposed technique, in terms of its transmit diversity order, based on both the distribution of the MED and on the theory of classical order statistics. Furthermore, we show that the proposed scheme offers a scalable performance–complexity tradeoff for SM by varying the number of candidate sets of prescaling factors, with significant performance improvements, compared to conventional SM.

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.

Spatial modulation (SM) and space shift keying (SSK) represent transmission methods for low-complexity implementation of multiple-input multiple-output (MIMO) wireless systems in which antenna indices are employed for data transmission. In this paper, we focus our attention on the secrecy behavior of SSK and SM. Using an information-theoretic framework, we derive expressions for the mutual information and consequently compute achievable secrecy rates for SSK and SM via numerical evaluations. We also characterize the secrecy behavior of SSK by showing the effects of increasing the number of antennas at the transmitter as well as the number of antennas at the legitimate receiver and the eavesdropper. We further evaluate the secrecy rates achieved by SM with different sizes of the underlying signal constellation and compare the secrecy performance of this scheme with those of general MIMO and SIMO systems. The proposed framework unveils that SM is capable of achieving higher secrecy rates than the conventional single-antenna transmission schemes. However, it underperfoms compared to a general MIMO system in terms of the achievable secrecy rates.

Non-orthogonal multiple access protocol for overlay cognitive radio networks using spatial modulation and antenna selection

In this paper we explore low-complexity transmission in massive multiple-input multiple-output (MIMO) systems by exploiting their tolerance to incomplete channel state information (CSI). We propose a strategy to exploit the transmit antenna correlation that arises in the deployment of size-constrained massive base stations (BSs). The feasibility of acquiring the instantaneous CSI for a subset of antennas and then using averages of the acquired CSI for the remaining array elements is studied. In particular, we focus on determining the influence that the percentage of inactive antennas during the CSI acquisition stage has over the signal processing (SP) complexity and the system performance. The presented results show that the proposed approach significantly reduces the computational complexity of size-constrained BSs while approximately preserving the performance of massive MIMO systems with complete CSI.

In this paper, an emerging wireless communication concept, which is termed as spatial modulation (SM) for large-scale multiple-input–multiple-output (MIMO), is considered. The results show that from the information-theoretic perspective, SM achieves capacity comparable to the open-loop MIMO capacity, although a subset of transmit antennas is activated in every channel use because both the channel coefficients and the input symbols carry information in SM. As a result, SM compensates the loss of information capacity due to a subset of antennas being activated by modulating information in the antenna index; therefore, the total information rate remains high. In particular, an upper bound for the capacity of SM is derived in closed form, and it is shown analytically that this upper bound is almost certainly achievable in the massive MIMO regime. Moreover, it is shown that the upper bound is achievable with no channel state information at the transmitter (CSIT) but with channel distribution information (CDI) at the transmitter (CDIT). The optimum transmission strategy should adapt the channel input distribution to fading using CDI such as the $K$ factor in Rician fading or the shape parameter $m$ in Nakagami- $m$ fading.

In this paper, we propose a new precoding algorithm for orthogonalized spatial multiplexing (OSM) systems over flat-fading multiple-input multiple-output (MIMO) channels. The OSM scheme was recently introduced for closed-loop MIMO systems which allows single symbol decodable maximum likelihood detection. To further improve the performance of the OSM system, we propose a new precoding method by maximizing the minimum Euclidean distance between constellation points in the effective channel. In order to efficiently identify the parameters of a precoder which maximizes the minimum distance, we introduce a partitioning approach. Through analysis, it is shown that one real value parameter and two bits are required for feedback information for precoding in 16-QAM systems. Simulation results demonstrate that our algorithm provides 9 dB and 7.5 dB gains at a bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> over the conventional OSM systems for 4-QAM and 16-QAM, respectively. We also confirm that the performance of the proposed scheme is the same as that of the optimum closed-loop MIMO systems in terms of the minimum distance. Consequently, our precoding algorithm significantly improves the system performance with a small increase of feedback amount.

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Previous designs of Tomlinson–Harashima precoding (THP) for the broadcast channel with multiple (cooperative) transmitters and noncooperative (decentralized) scalar receivers assume complete channel state information (CSI) at the transmitter. Due to its nonlinearity, THP is more sensitive to errors in CSI at the transmitter than linear precoding, which may be large in wireless communications. Thus, THP performance degrades severely—and it is even outperformed by corresponding linear precoders. We propose a novel robust optimization for THP with partial CSI based on mean-square error (MSE), which performs a conditional mean (CM) estimate of the cost function including a novel model of the receivers. This enables a smooth transition of robust THP from complete, via partial, to statistical CSI. The performance is now always superior or in the worst case equal to corresponding linear precoding techniques. With these features, the proposed robust THP is very attractive for application in the wireless broadcast channel. </para>

In heterogeneous networks, interference management is very important since the interference due to spectrum-sharing can significantly decrease the overall performance. In the existing work, various resource allocation methods are proposed to either improve energy efficiency or alleviate interference. Very little research has addressed their joint interaction. Furthermore, most existing work assumes that all of the channel state information is known, which might not be realistic. In this paper, we propose a game-theoretical scheme using energy-efficient resource allocation and interference pricing for an interference-limited environment in two-tier heterogeneous networks without complete channel state information. We formulate the problems of resource allocation and interference management as a two-stage Stackelberg game with incomplete information. A backward induction method is used to analyze the proposed game, since it can capture the sequential dependencies of the decisions in the stages of the game.

Cognitive radio is able to share the spectrum with primary licensed user, which greatly improves the spectrum efficiency. We study the optimal power allocation for cognitive radio to maximize its ergodic capacity under interference outage constraint. An optimal power allocation scheme for the secondary user with complete channel state information is proposed and its approximation is presented in closed form in Rayleigh fading channels. When the complete channel state information is not available, a more practical transmitter-side joint access ratio and transmit power constraint is proposed. The new constraint guarantees the same impact on interference outage probability at primary user receiver. Both the optimal power allocation and transmit rate under the new constraint are presented in closed form. Simulation results evaluate the performance of proposed power allocation schemes and verify our analysis.

On channel estimation for spatial modulated systems over time-varying channels

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.

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.

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.

Energy-efficient resource allocation for D2D communication underlaying cellular networks with incomplete CSI