Performance Comparison of Spatial Modulation Detectors under Channel Impairments

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.

Multiple transmit antennas can be employed in a downlink channel to serve multiple users under the assumption of perfect channel state information (CSI) of all users at the base station. In practice, however, the channel knowledge available at the base station is not perfect. For instance, in case of a time division duplex (TDD) system, the transmit CSI is the estimated uplink channel. On the other hand, in a frequency division duplex (FDD) system, feedback from the users is required to obtain transmit CSI. In this case, we assume the transmit CSI consists of a quantized version of the normalized estimated channel vector and the statistics of the channel norm of each user. In this work we consider the transceiver design of the downlink of a multiuser MISO system based on the minimum mean square error (MMSE) criterion with imperfect CSI as discussed above.

In this paper, we explore the use of reconfigurable intelligent surface (RIS) in unmanned aerial vehicle (UAV) based multiuser downlink communications, where a flying UAV serves multiple single antenna users through multiple RISs mounted on various buildings. More specifically, we consider the selection of RISs based on the outdated and imperfect channel state information (CSI) of the composite UAV-RIS-User channels at the UAV. After selection process, the UAV communicates to the user via the selected RISs and also with the direct link. Particularly, we derive an infinite series based expression for selection probability of RISs under both the outdated and imperfect CSI of composite channels based selection scheme. We also derive the statistical distribution of instantaneously received signal-to-noise ratio (SNR) under outdated and imperfect CSI conditions of both the direct and composite links at the user. Next, using the derived statistics, we analyze the network’s performance in terms of the average coverage probability (ACP) and average bit error rate (ABER) over the complete UAV flight time. Moreover, we discuss the behavior of ACP and ABER for very small and very large values of UAV transmit power, respectively. It is depicted through numerical results that selecting more RISs from a group of small-sized RISs may not be as advantageous as selecting fewer RISs from a group of large-sized RISs. Moreover, we also demonstrate the effect of several system parameters such as number of RIS reflecting elements, number of selected RISs, the severity of UAV-RIS and RIS-User links, and the severity of imperfect and outdated CSI on the network’s performance. The analytical results are corroborated with Monte-Carlo simulations.

In the presence of perfect channel state information (CSI), the achievable degrees of freedom (DoF) in wireless interference networks can be linearly scaled up with the number of users. Achievability is based on the idea of interference alignment (IA). However, in the presence of imperfect CSI, the sum rate becomes degraded, and full DoF may no longer be achievable. In this paper, the authors propose novel least squares (LS)- and minimum mean square error (MMSE)-based IA schemes that adaptively design beamformers by relying on the availability of imperfect CSI and knowledge of the channel estimation error variance in advance. Interestingly and unlike the other robust algorithms, the proposed adaptive schemes do not impose extra computational complexity compared to their nonadaptive counterparts. It is shown that the LS-based IA is able to outperform interference leakage minimization algorithms under both perfect and imperfect CSI. Furthermore, the authors compare the performance of the proposed MMSE-based IA with maximum signal-to-interference-plus-noise ratio (Max-SINR) algorithm. The authors show that while under perfect CSI, the MMSE-based IA achieves the same performance as that of Max-SINR, the former outperforms the latter under CSI mismatch. Meanwhile, it is shown that the proposed MMSE-based IA needs less CSI to be available and has less computational complexity compared to Max-SINR.

A novel interference alignment (IA) scheme based on the errors-in-variables (EIV) mathematic model has been proposed to overcome the channel state information (CSI) estimation error for the MIMO interference channels. By solving an equivalently unconstrained optimization problem, the proposed IA scheme employing a weighted total least squares (WTLS) algorithm can obtain the solution to a constrained optimization problem for transmit precoding (TPC) matrices and minimizes the distortion caused by imperfect CSI according to the EIV model. It is shown that the design of TPC matrices can be realized through an efficient iterative algorithm. The convergence of the proposed scheme is presented as well. Simulation results show that the proposed IA scheme is robust over MIMO interference channels with imperfect CSI, which yields significantly better sum rate performance than the existing IA schemes such as distributed iterative IA, maximum signal-to-interference-plus-noise ratio (Max SINR), and minimum mean square error (MMSE) schemes.

Interference alignment (IA) is a multi-user wireless communication strategy that enables several transmitters simultaneous communicate with their paired receivers without interfering each other. IA is a multiplexing gain optimal strategy at the expense of requiring the global channel state information (CSI) at the transmitters. Most previous works assume the availability of perfect CSI which is not possible in practice. The performance of IA algorithms based on perfect CSI drop dramatically in circumstance where CSI errors exist. In this paper we propose a robust minimum mean square error (MMSE) IA algorithm with imperfect CSI. Based on a Gaussian statistic channel error model, we give the mean square error objective function with per transmitter power constraint. The objective function is not joint convex in precoders and decoders, but convex in precoders with fixed decoders and vice versa. We convert the problem to two convex sub problems and iteratively find the solutions. Numerical results are presented to validate the effectiveness of proposed algorithm when CSI errors exist.

In this paper, with the aid of new analytical method, we present a new closed-form expression for the ergodic capacity of full-duplex relaying (FDR) systems, with multiple antenna amplify-and-forward (AF) cooperative networks and imperfect channel state information (CSI). At the relay, the loopback self-interfernce (LI) is mitigated by using receive zero-forcing (ZF) precoding scheme, then steering the signal to the destination by using the maximum-ratio transmission (MRT) technique. To facilitate comparison, a closed-form expression for the ergodic capacity of half-duplex relaying (HDR) systems with multiple antenna AF cooperative networks is also addressed, when maximum-ratio combining (MRC)/MRT precoding schemes are performed at the relay input/output, respectively. Therefore, since perfect CSI is not available in practice, this paper investigates the impact of channel estimation errors on the performance of receive ZF/MRT and MRC/MRT schemes. These expressions are exact in the case of perfect CSI and form a very tight indistinguishable lower-bound in the case of imperfect CSI. Numerical results sustained by Monte-Carlo simulations show the exactness of the proposed analytical expressions in perfect CSI and the tightness of the lower-bounds in imperfect CSI. In addition, it is seen here that the FDR AF cooperative systems outperforms the HDR AF cooperative systems in terms of capacity. Furthermore, in contrast to perfect CSI, in the presence of imperfect CSI, an ergodic capacity ceiling is seen as SNR increases. Besides, it is seen that the ergodic capacity degradation due to imperfect CSI is higher in the FDR case because of the extra LI estimation errors.

Spatial Modulation (SM) is a recently proposed single-RF multiple-input-multiple-output (MIMO) technique, which is capable of outperforming many conventional MIMO transmission schemes with low implementation and computational complexity. Recently, there have been some attempts in understanding the performance of SM in multi-user environments. However, most of the work has been oriented towards uplink multi-access scenarios. Also, conventional downlink/broadcast MIMO precoding techniques such as Zero Forcing (ZF) or Minimum Mean Square Error (MMSE) cannot be used in Multi-User SM (MU-SM), as part of the data in SM is also encoded into the Channel Impulse Responses (CIRs). In this paper, a novel precoding scheme for single-cell downlink MU-SM systems is proposed with a two-fold objective: i) the precoder needs to be able to completely eliminate the Multi-User Interference (MUI) by taking advantage of the Channel State Information (CSI) at the transmitter and ii) it needs to allow the users to use a single-user Maximum Likelihood (ML) optimum detector while achieving the same performance as interference-free point-to-point SM transmission. Finally, we also develop an interference-aware multi-user detection scheme, which does not require any CSI at the transmitter, and compare its performance with that of single-user detection schemes based on precoding.

In wireless interference networks, orthogonal medium access techniques like time division multiple access (TDMA) and frequency division multiple access (FDMA) achieve merely one degree of freedom (DoF). However, by using interference alignment (IA) the achievable DoF can be linearly scaled up with the number of users. Nevertheless, this outperformance of IA heavily depends on the availability of perfect channel state information (CSI), which is not a realistic assumption in practice. Since under imperfect CSI, the performance of IA may become severely degraded, design of enhanced IA algorithms by relying on the availability of merely imperfect CSI is of particular interest. In this paper, we propose a least squares (LS)-based IA algorithm which adaptively designs the beamformers based on the knowledge of the channel estimation error variance, which is possible to be known in advance. Then, we compare the performance of the proposed scheme with interference leakage minimization algorithms. It is shown that under both perfect and imperfect CSI, the proposed LS-based IA outperforms interference leakage minimization algorithms.

In this letter, we analyze the ergodic capacity of bidirectional amplify-and-forward relay selection network. The imperfect channel state information (CSI) is taken into account, which includes outdated CSI and channel estimation error, caused by the time-variation of channel and the imperfect channel estimation, respectively. The lower bound of the ergodic capacity for this network is derived in a closed-form, and verified by the Monte-Carlo simulations. Furthermore, the effects of the imperfect CSI and the number of relays on the ergodic capacity are investigated. The results manifest that imperfect CSI will jeopardize the capacity, and increasing the number of relays contributes to enhance the capacity with imperfect CSI.

Spatial modulation (SM) has been shown to be a promising low-complexity alternative to the state-of-art multiple-input multiple-output (MIMO) schemes due to its novel transmission approach. This paper investigates the performance of SM-MIMO systems in the presence of two practical undesirable effects, namely in-phase (I) and quadrature-phase (Q) imbalance (IQI) and imperfect channel state information (ICSI). An optimum maximum likelihood detection (MLD) method is proposed to tackle the effects of self-interference and signal distortion caused by IQI impairment by adapting the traditional MLD technique in accordance with the asymmetric characteristics of the IQI. More particularly, upper-bounds of the closed-form average pairwise error probability (APEP) and the average bit error rate (ABER) are derived for generalized Beckmann fading channels. As erroneously interpreted channel coefficients at the receiver (Rx) cause the error rate to increase and the detection to fall short, Cramer-Rao bound, which is a lower bound on the variance of the channel estimator, is utilized to assess the estimation accuracy. The system performance is evaluated by analytical derivations that are corroborated with computer simulations. The obtained results show that ICSI and IQI should be seriously considered while designing the future SM-based wireless communication systems.

Based on imperfect channel state information (CSI) and relay selection, a cross-layer optimization scheme is developed for cooperative MIMO system, and the corresponding system performance is investigated in Rayleigh fading channel. By the theoretical analysis and mathematical manipulation, the average spectral efficiency (SE), packet error rate (PER) and packet loss rate (PLR) are derived. As a result, closed-form expressions of the average SE, PER and PLR are obtained, respectively. According to these, a cross-layer design (CLD) scheme subject to the average PER constraints is proposed to avoid the SE performance loss caused by the conventional instantaneous PER constraints. The scheme optimizes the adaptive thresholds by maximizing the average SE of the system, and an iteration method joint the Lagrange multiplier and Newton methods is presented to solve the above optimization problem. Simulation results verify the validity of the theoretical analysis. The results show that the proposed CLD scheme can improve the SE while target PLR is maintained. The CLD scheme under average PER constraints has higher SE than the conventional CLD scheme under instantaneous PER constraints.

In wireless communication systems, the intended receiver is able to obtain the perfect channel state information (CSI) as long as the training sequence is sufficiently long, and then through a quantized feedback channel (QFC), the transmitter gets imperfect CSI caused by the quantized noise. In general, the design of efficient coding schemes for wireless channels with imperfect CSI at the transmitter (I-CSIT) is difficult and challenging, and one possible method is to construct such a scheme by using channel feedback. In the literature, it has already been shown that the classical Schalkwijk-Kailath (SK) scheme for the additive white Gaussian noise (AWGN) channel with noiseless feedback is a highly efficient coding scheme since its coding complexity is extremely low and the decoding error doubly exponentially decays as the coding blocklength tends to infinity. Existing SK-type schemes mainly focus on the case that perfect CSI is known at the transceiver, and adopt modulo lattice function to eliminate the impact of feedback channel noise (often considered as AWGN) on the performance of SK-type schemes. However, for channels with I-CSIT and QFC, this does not work since the distribution of quantized noise is unknown and I-CSIT brings additional non-convergence estimation error to the transceiver, leading to the application of SK-type schemes to practical wireless scenarios becomes challenging. In this paper, first, for the quasi-static fading channel with I-CSIT and QFC, we design a modulo lattice based SK-type scheme where the receiver adopts an auxiliary signal to decode the message, and numerical results show that the rate of our scheme almost approaches that of the same model with perfect CSI at the transceiver and noise-free feedback for some cases. Next, we further extend the above scheme to the two-path fading scenario, which is modeled as the two-ray channel with I-CSIT and QFC. Treating the signal of the second path as a relay, our extended scheme combines the amplify-and-forward relay strategy and the previously proposed scheme for the same model without ISI. However, this extended scheme cannot be applied to multi-path fading scenario, to this end, we propose a new SK-type scheme for the multi-path fading case. The intuition behind this scheme is to transform the multi-path fading channel into a fading MIMO channel by discrete fourier transform (DFT), and then apply the SK-type scheme to the MIMO channel in frequency domain and use inverse DFT to obtain the codeword in time domain. The study of this paper may provide a way to design efficient coding scheme for fading channels in the presence of imperfect CSI and quantized feedback.

SummaryIn this paper, we analyze the performance of maximum‐ratio combining (MRC) receivers for single‐input multiple‐output (SIMO) non‐orthogonal multiple access (NOMA) system. We explore the aforesaid system performance in presence of impairments like imperfect channel state information (CSI) and successive interference cancellation (SIC) errors. In general, receive diversity provides diversity gain and helps to maintain quality of service (QoS), while the NOMA system achieves higher spectral efficiency compared to orthogonal multiple access (OMA). Power‐domain NOMA system transmits superimposed‐coded signal, which utilize SIC detection method at the receiving users. Here, we derive the closed‐form expression of the average bit error rate (BER) for the MRC‐based NOMA system. We also analyze the performance of the system in high signal‐to‐noise ratio (SNR) regime through derived asymptotic expression. Furthermore, the outage probability, diversity order, and sum rate comparison between NOMA and OMA system are also presented. Simulation results also validate the derived theoretical expressions and confirm the diversity gain achieved for the considered system.

For the next generation wireless communication system, Multi carrier Code Division Multiple Access (MC-CDMA) has become very appealing scheme due to due to high data rates and interference limiting factors. In this research work we analyzes the capacity of MC-CDMA system using adaptive power and sub-channel allocation under perfect, imperfect and predicted channel state information (CSI). The transmitter and receiver both have been targeted in this paper. The proposed scheme is a novel idea that divides the sub-channels into small groups. Each group is assigned power according to the Eigen values and gain of the each sub-channel in that specific group. The receiver calculates optimal feedback vector for the transmitter by calculating the bit error rates using the above strategy and selects the optimal feedback vector. The simulations show that the usage of joint power and sub-channel allocation outperforms the capacity of the system. The capacity of the system is highly improved using adaptive power and sub-carriers allocation along with CSI prediction. The simulation results have been carried out for other power allocation schemes available in literature and results have been compared with perfect, imperfect and predicted CSI.