Probabilistic SINR constrained robust transmit beamforming: A Bernstein-type inequality based conservative approach

In this paper, we consider a new design problem of optimizing a linear transceiver for correlated multiple-input multiple-output (MIMO) interference channels in the presence of channel state information (CSI) errors, which is a more realistic and practical scenario than those considered in the previous studies on uncorrelated MIMO interference channels. By taking CSI errors into account, the optimization problem is initially formulated to minimize the average mean square error (MSE) under the general power constraints. Since the objective function is not jointly convex in precoders and receive filters, we split the original problem into two convex subproblems, and then linear precoders and receive filters are obtained by solving two subproblems iteratively. It is shown that the proposed algorithm is guaranteed to converge to a local minimum. The numerical results show that the proposed algorithm can significantly reduce the sensitivity to CSI errors compared with the existing robust schemes in the correlated MIMO interference channel.

Multicell coordinated beamforming (MCBF) has been recognized as a promising approach to enhancing the system throughput and spectrum efficiency of wireless cellular systems. In contrast to the conventional single-cell beamforming (SBF) design, MCBF jointly optimizes the beamforming vectors of cooperative base stations (BSs) (via a central processing unit (CPU)) in order to mitigate the intercell interference. While most of the existing designs assume that the CPU has the perfect knowledge of the channel state information (CSI) of mobile stations (MSs), this paper takes into account the inevitable CSI errors at the CPU, and study the robust MCBF design problem. Specifically, we consider the worst-case robust design formulation that minimizes the weighted sum transmission power of BSs subject to worst-case signal-to-interference-plus-noise ratio (SINR) constraints on MSs. The associated optimization problem is challenging because it involves infinitely many nonconvex SINR constraints. In this paper, we show that the worst-case SINR constraints can be reformulated as linear matrix inequalities, and the approximation method known as semidefinite relation can be used to efficiently handle the worst-case robust MCBF problem. Simulation results show that the proposed robust MCBF design can provide guaranteed SINR performances for the MSs and outperforms the robust SBF design.

In systems employing pilot-symbol aided channel estimation, the pilot-to-data power ratio is known to have a large impact on performance. Therefore, previous works proposed methods setting the pilot power such that either the weighted sum of the mean squared error (MSE) of the estimated data symbols is minimized or the overall spectral efficiency (SE) is maximized. However, previous works did not take into account the impact of correlated antennas and channel state information (CSI) errors on the optimal pilot power setting. In this paper, we consider the uplink of a multiuser multiple-input multiple-output (MU MIMO) system employing a receiver that minimizes the MSE of the received data symbols in the presence of CSI errors and derive closed-form expressions for the MSE and the achievable SE. These expressions take into account the impact of antenna correlation and CSI errors, and are a function of pilot power and the number of receive antennas. The analytical and numerical results can help set the pilot power, minimizing the MSE in multiple antenna systems.

We propose an iterative detection scheme for Turbo-BLAST system with optimal power allocation in the presence of channel state information imperfection. The proposed scheme uses the channel estimation matrix for detection and treats the interference caused by channel estimation errors and additive white Gaussian noise as equivalent noise where the channel estimation matrix and the statistical characteristic of channel estimation errors are necessitated. Simulation results show the proposed algorithm is effective to improve bit error rate (BER) performance through iterative detection for modified Turbo-BLAST system with optimal power allocation in the presence of imperfect channel state information.

We propose a novel restriction and relaxation (RAR) method for robust relay beamforming design in cognitive two-way relay networks with imperfect channel state information (CSI). Due to the uncertainty in CSI, the self-interference cannot be completely canceled. Hence, both channel uncertainties and residual self-interference should be considered. The proposed RAR method aims to minimize the transmit power of relay nodes while guaranteeing the worst-case signal-to-interference plus noise ratio (SINR) of secondary users (SUs) as well as satisfying the interference temperature (IT) constraints. Specifically, in the restriction step of RAR, infinite number of complicated constraints are reformulated into a finite number of linear matrix inequalities (LMIs). In the relaxation step of RAR, the nonconvex robust design problem is transformed into a convex semidefinite program (SDP), which can be efficiently solved by interior-point methods. Simulation results verify the effectiveness and robustness of the proposed method.

Multiple-input multiple-output (MIMO) amplify-and- forward (AF) relaying is designed for secure communication between a source-destination pair in the presence of multiple eavesdroppers. Assuming statistical knowledge of the eavesdroppers' channel state information (ECSI) errors, we introduce a probabilistically robust design method, which aims to optimize the source transmission power and AF relaying matrix by maximizing the received signal-to- interference-plus-noise ratio (SINR) at the destination, while satisfying a set of intercept probability constraints. The resultant optimization problem becomes nonconvex, and hence we propose a conservative two-step solution, where the source transmission power and the relaying matrix are sequentially optimized. Our simulation results demonstrate the improved secrecy of the proposed relaying design against eavesdropping and its robustness against the channel uncertainties.

As a building block toward a simple and scalable solution for massive random access, we introduce collision-resolution algorithms using successive interference cancellation (SIC) based on the received signals, with no need for any coordination or codebook differentiation. We first consider two-user multiple access with the ZigZag algorithm. We prove that the original ZigZag and a modified version of it, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">double-zipper ZigZag</i> , attain the same performance as the optimal coordinated time-sharing in the high signal to noise ratio (SNR) regime, even in the presence of channel state information (CSI) errors. We then extend the results to the case of arbitrary number of users employing delay-domain processing. Specifically, we introduce delay-domain zero forcing and its regularized version, which are able to cancel and suppress the interference among users, respectively. By obtaining a post-processing system model and characterizing the accumulated noise during the decoupling process, we also derive bounds on the achievable sum-rates of the proposed algorithm for both cases of perfect and imperfect CSI. Simulation results show that the newly proposed approach have comparable performance with coordinated time-sharing at high SNRs.

In this paper, we investigate the problem of sum-rate maximization in a millimeter-wave (mmWave) multi-user downlink system employing non-orthogonal multiple access (NOMA). Specifically, we consider the design of optimal transmit beamformer and power allocation that is robust in the presence of channel state information (CSI) errors. In order to reduce hardware complexity, we consider analog beamforming using a single RF chain and a double-phase shifter network. The original formulation of this problem is nonconvex; however, we reformulate this problem as an equivalent but tractable weighted mean squared error (MSE) minimization problem. We propose an iterative algorithm to solve this reformulated problem. We demonstrate the robust performance of the proposed algorithms via simulations.

Integrated sensing and communication (IS-AC) is an appealing approach to address spectrum congestion and beamforming is an effective method to realize ISAC. In this paper, we investigate the beamforming design problem for multiple-input multiple-output (MIMO) ISAC systems and propose to maximize the radar beampattern gain of the target direction while ensuring the signal-to-interference-plus-noise ratio (SINR) constraints of communication users. Particularly, we discuss two cases of ISAC transmit beamforming, i.e., Case-I and Case-II, which do not have and do have the dedicated probing signal, respectively. For these two cases of transmit beamforming design problems, we start from the single-user scenario and provide the closed-form solutions for MIMO ISAC beamforming vectors. Then, we consider the multiuser scenario and utilize the semidefinite relaxation technique to convert the beamforming design problems into convex semidefinite programming problems. Furthermore, we investigate the impact of the channel correlation between radar and communication on the performance gain of MIMO ISAC systems and characterize the performance tradeoff. Numerical results validate that the dedicated probing signal is unnecessary in the single-user scenario, whereas it has a slight improvement in target detection performance at low SINR thresholds in the multi-user scenario. It is also shown that the stronger the correlation between radar and communication channels, the greater the performance gain of the system.

The IEEE802.11a standard for indoor wireless LAN systems was released commercially and is wide spread in the marketplace. To achieve higher throughput, IEEE802.11n was proposed and is now undergoing standardization. The MIMO-OFDM technique, which employs multiple antennas for transmission and reception, is the core technology for IEEE802.11n (Foshini and Gans, 1998). This technique requires estimation of channel state information (CSI) on the receiving side. Using the technique called adaptive MIMO-OFDM (Telatar, 1999) in which CSI is applied to both the transmitting and receiving sides, an even higher throughput is achieved. To achieve the maximum performance from adaptive MIMO-OFDM, we must accurately estimate the CSI for all the subcarriers; however, numerous calculations are needed to obtain this estimation. So, to actualize the adaptive MIMO-OFDM system, the calculation load must be decreased. This can be accomplished by applying one CSI to other subcarriers. However, channel error exists between the actual channel and the applied CSI. The channel error also plays a role in decreasing the communications quality (Medard, 2000). The communications quality when using the adaptive MIMO-OFDM technique that has CSI error was evaluated by simulation (Narula et al., 1998). However, there are few measurement evaluation reports on CSI error. This paper focuses on the ratio between the power of the eigenvalue and the interference power that suppresses the communication quality based on the measurement results. We propose an empirical formula for predicting the signal to interference ratio (SIR), which is the ratio between the power of the eigenvalue and the interference power. This SIR empirical formula helps to predict the communication quality and simplify the simulation.

In this paper, we propose a robust collaborative relay beamforming scheme in the presence of imperfect channel state information (CSI) for a multiple single-antenna two-way relays network with reciprocal channels. Many existing beamforming schemes have been investigated using perfect CSI for relay-aided systems. However, in practical communication systems the channel estimation is always inaccurate at relay nodes, leading to the deviation between the true CSI and the estimated CSI. Aiming to tackle the performance degradation caused by the CSI mismatch, a constrained optimization problem corresponding to the robust relay beamforming vector is formulated, in which the channel estimation error is characterized by the stochastic error model. Herein the commonly used performance metric, expected weighted sum mean squared error, is adopted as design objective to evaluate the overall link reliability. It is found that due to the intractable expression of the cost function, we can not resort to the traditional methods for solving the involved optimization problem. Whereas, by exploring the lower bound of the cost function using Jensen's inequality and the Taylor series expansion, the original optimization problem is recast to a convex optimization in the form of Rayleigh---Ritz ratio, which results in a closed-form robust relay beamforming solution. Numerical results verify the robustness and superiority of the proposed scheme against CSI errors in terms of system sum rate and average BER.

In this paper, we investigate the problem of robust beamforming for multiple-input multiple-output (MIMO) dual-function radar-communication (DFRC) system, when there exist radar look direction mismatch and communication channel state information (CSI) error. To address these system imperfections, a region-of-interest (ROI) rather than a specific angle is considered for radar sensing, and the communication CSI is assumed to be available with a bounded unknown error. With these considerations, we design a robust dual-function beamformer through optimizing the radar sensing performance in terms of the energy radiated towards the ROI, while guaranteeing the communication quality-of-service (QoS) measured by the per-user signal-to-interference-plus-noise ratio (SINR) as required. For this robust design, a max-min optimization problem is formulated and a semidefinite programming (SDP) reformulation based on the S-procedure is presented. The popular semidefinite relaxation (SDR) technique is employed to solve the resulting non-convex problem, and the tightness of SDR is discussed. Further, we propose to incorporate an extra constraint of main beam control into the problem to achieve a flat magnitude response of the beampattern over the ROI. In addition, it is shown that the proposed approach is straightforwardly applicable to the scenario of multiple targets. Numerical examples are carried out to show the tightness, and demonstrate the effectiveness and robustness of the proposed MIMO-DFRC beamforming approach.

The Taguchi robust design method traditionally deals with single‐characteristic problems. Various methods have been developed for extending the Taguchi single‐characteristic robust design method to the case of multi‐characteristic robust design problems. However, most of those methods have shortcomings in that they do not properly consider the variance–covariance structures among performance characteristics and/or do not preserve the original properties of the Taguchi signal‐to‐noise ratio for single‐characteristic robust design problems. To overcome these shortcomings, this paper develops a multivariate loss function approach to multi‐characteristic robust design problems with an appropriately defined signal‐to‐noise ratio. Its performance is evaluated using simulated examples, and the results indicate that it generally outperforms existing representative methods for correlated as well as uncorrelated experimental data. Copyright © 2016 John Wiley &amp; Sons, Ltd.

• In wireless communication systems, the combination of STAR-RIS and NOMA results in a revolutionary method greatly improving signal strength and coverage for end users. • Under STAR-RIS-NOMA, the study assesses the Ergodic capacity of two users considering the effect of fading parameters, the number of STAR-RIS elements, the number of interferers, and errors in CSI and SIC. • An increase in CSI error has a detrimental impact on both near and edge users. On the other hand, channel uncertainty and weaker signals make the edge user more susceptible to CSI mistakes. • The ergodic capacity of the nearby user declines with increasing SIC error. • Far users' ergodic capacity falls with the number of interferers, while larger N values alleviate this. Future wireless technologies must adhere to elevated requirements by providing increased data throughput, reduced latency, and enhanced flexibility. Integration of Non-Orthogonal Multiple Access (NOMA) with Reconfigurable Intelligent Surfaces (RIS) has attracted major interest to satisfy these needs. Specifically, Simultaneously Transmitting and Reflecting RIS (STAR-RIS) offers an advanced way to manage signals by controlling them in both sending and bouncing directions, which improves how well the system uses its frequency and extends its range. To put STAR-RIS-NOMA into practice, we need to closely examine how successive interference cancellation (SIC), interference from nearby cells, and errors in channel state information (CSI) affect it. In this paper, we derive mathematical formulas for STAR-RIS-NOMA's ergodic capacity across Nakagami-m fading channels. These formulas take into account the effects of SIC errors, inter-cell interference, and CSI errors. We look at the STAR-RIS-NOMA system with two users and evaluate our analytical results using important system factors like the number of interferers, CSI error, the fading parameter (m), SIC error, and the number of STAR-RIS elements. These findings are validated by simulated outcomes.

With the ellipsoid‐bounded channel state information (CSI) errors, this study investigates the robust secrecy energy efficiency (SEE) optimisation in a wireless powered heterogeneous network. Specifically, the authors consider the network where multiple femtocell base stations (FBSs) are deployed under the coverage of one macrocell base station (MBS). Meanwhile, the MBS serves multiple macrocell users in the presence of a malicious multiple‐antenna eavesdropper (Eve) while each FBS serves a pair of information receiver (IR) and energy receiver (ER) with multiple antennas, where the ER attempts to wiretap the information of IR in the same femtocell. To promote the secrecy performance, artificial noise (AN) is aided into the downlink signal at the MBS and FBSs, and the problem of maximising SEE is formed in a cross‐tier multi‐cell AN‐aided transmit beamforming design. This problem is non‐convex while containing infinite constraints caused by CSI errors, which cannot be solved directly. In this regard, the authors resort to the successive convex approximation, semi‐definite relaxation techniques and Lagrange duality theory to acquire its solvable form. Moreover, to reduce the overhead of information exchange among coordinated BSs, they further propose a distributed approach based on alternative direction multiplier method. Finally, simulation results validate the effectiveness of the proposed design.