Low-Complexity Transceiver Design for Multi-User Millimeter Wave Communication Systems under Imperfect CSI

Millimeter wave (mmWave) communication systems employ hybrid RF/baseband transceivers that divide the spatial signal processing into radio frequency and baseband domains in order to reduce the hardware complexity resulting from the use of large number of antennas elements. In this paper, we consider two designs for hybrid multi-user MIMO downlink that minimizes the sum mean square error (SMSE), based on perfect channel knowledge (non-robust design) and transceiver design considering the channel imperfections (robust design). In the robust design, the channel state information (CSI) is assumed to be perturbed by estimation error and follows Gaussian distribution with known error variance. In both the designs, reduced hardware complexity is achieved by analog-digital hybrid processing by using orthogonal matching pursuit (OMP)-based sparse signal processing. We evaluate the performance of both the proposed schemes based on various parameters and also compare it with conventional fully-digital system. We present numerical results over various dictionaries. The comparison results show that robust design is resilient to the presence of CSI errors. Furthermore, we also demonstrate the convergence of both the proposed algorithms to a limit even though global convergence is hard to prove due to non convex nature of overall optimization problem.

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.

Hybrid analog and digital beamforming (HBF) has been regarded as a key technology for future millimeter wave (mmWave) communication systems due to its ability to obtain a good trade-off between achievable beamforming gain and hardware cost. In this paper, we investigate the channel estimation and hybrid precoding for mmWave MIMO systems with deep learning. We adopt the hierarchical codebook based algorithm for channel estimation as it requires limited number of pilot transmissions, and enhance its performance by proposing a new codebook design algorithm based on manifold optimization (MO). With the estimated channel state information (CSI) as the input, we develop a robust HBF network (HBF-Net) by applying convolutional layers and attention mechanism, which can be trained to generate a robust HBF matrix targeting at spectral efficiency maximization with imperfect CSI. To further improve the performance, we propose a joint channel estimation and HBF optimization network (CE-HBF-Net). Considering that the adaptively selected HBF vectors in the hierarchical codebook based channel estimation are different for different channel realizations, we skillfully propose an index assign-and-input method to efficiently feed such information to the CE-HBF-Net to reduce the network input dimensions and make the network trainable. Furthermore, we propose a signal self-attention mechanism to enable the CE-HBF-Net to intelligently assign larger weight coefficients to those signals that contribute more to channel estimation. Simulation results show that the well-designed HBF-Net and CE-HBF-Net outperform the conventional HBF algorithms with imperfect channel and exhibit robustness to mismatches between offline training and online deployment stages.

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.

We investigate the problem of robust joint transmitter and receiver power allocation for uplink multi-input multi-output (MIMO) transmissions. The channel model is assumed to have Rayleigh flat fading. The objective of power allocation is to minimize the total MSE each of which has limited transmit power. The problem is formulated as a non-linear optimization problem. In addition, we investigate robust joint transmitter and receiver power allocation with imperfect channel state information (CSI). The CSI error is assumed to be unknown but bounded by a constant. This problem is formulated as a semidefinite programming (SDP) problem with bilinear matrix inequality (BMI) constraints. Numerical results indicate that, with imperfect CSI, the BER performance improvement obtained by taking robustness into account in the joint power allocation process.

A robust scheme is proposed to optimize the linear precoders/decoders for MIMO downlinks where the available channel state information (CSI) at base station (BS) is imperfect. The objective is to minimize the sum mean square error (SMSE) over all data sub-streams under a per-user transmit power constraint. By using an iterative procedure, the proposed scheme extends the existing optimization algorithm for the single-user MIMO system with perfect CSI to solve approximately the minimizing SMSE problem in the multiuser MIMO downlink with imperfect CSI at BS. Simulation results demonstrate that the proposed scheme can effectively mitigate the performance loss induced by the imperfect CSI and can provide largest possible diversity as well as increased throughput.

In wideband multi-pair two-way relay networks, the performance of beamforming at a relay station (RS) is intimately related to the accuracy of the channel state information (CSI) available. The accuracy of CSI is determined by Doppler spread, delay between beamforming and channel estimation, and density of pilot symbols, including transmit power of pilot symbols. The coefficient of the Gaussian-Markov CSI error model is modeled as a function of CSI delay, Doppler spread, and signal-to-noise ratio, and can be estimated in real time. In accordance with the real-time estimated coefficients of the error model, an adaptive robust maximum signal-to-interferenceand- noise ratio (Max-SINR) plus maximum signal-to-leakage-and-noise ratio (Max-SLNR) beamformer at an RS is proposed to track the variation of the CSI error. From simulation results and analysis, it is shown that: compared to existing non-adaptive beamformers, the proposed adaptive beamformer is more robust and performs much better in the sense of bit error rate (BER); with increase in the density of transmit pilot symbols, its BER and sum-rate performances tend to those of the beamformer of Max-SINR plus Max-SLNR with ideal CSI.

In this paper, we adopt a three-stage based uplink channel estimation protocol with reduced pilot overhead for an reconfigurable intelligent surface (RIS)-aided multi-user (MU) millimeter wave (mmWave) communication system, in which both the base station (BS) and the RIS are equipped with a uniform planar array (UPA). Specifically, in Stage I, the channel state information (CSI) of a typical user is estimated. To address the power leakage issue for the common angles-of-arrival (AoAs) estimation in this stage, we develop a low-complexity one-dimensional search method. In Stage II, a re-parameterized common BS-RIS channel is constructed with the estimated information from Stage I to estimate other users’ CSI. In Stage III, only the rapidly varying channel gains need to re-estimated. Furthermore, the proposed method can be extended to multi-antenna UPA-type users, by decomposing the estimation of a multi-antenna channel with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$J$ </tex-math></inline-formula> scatterers into estimating <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$J$ </tex-math></inline-formula> single-scatterer channels for a virtual single-antenna user. An orthogonal matching pursuit (OMP)-based method is proposed to estimate the angles-of-departure (AoDs) at the users. Simulation results demonstrate that the proposed algorithm significantly achieves high channel estimation accuracy, which approaches the genie-aided upper bound in the high signal-to-noise ratio (SNR) regime.

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.

For the next generation of wireless communication network, a heterogeneous network architecture with macro cells, small cells, and relays offers numerous advantages, such as higher spectrum efficiency, better fairness in resource allocation, and energy efficient usage as well as optimal coverage. However, this approach encounters various network management challenges, including interference mitigation techniques. In this paper, we consider a multi-user half-duplex amplify-and-forward-MIMO relay system, where a macro basis station communicates with edge cell users via relays and each node has multiple antennas. In this context, we propose two interference alignment (IA) schemes, for which a hybrid approach of the problem formulation based on zero-forcing (ZF) and minimum-mean-square-error optimization criteria was developed to deal with interferences in perfect and imperfect channel state information (CSI) cases. In the case of perfect CSI, simulation results show that this approach provides a SNR gain of about 4 dB regarding BER performance in comparison to that achieved by the reference approach, where all filters are determined solely based on ZF criterion. Furthermore, the achieved capacity and effective signal-to-interference-plus-noise ratio at each edge node are improved by around 5 dB. Having CSI errors, the system performance is significantly improved using the robust design IA approach by minimizing the expected value of cost functions.

A robust joint multiuser scheduling and precoding design is proposed for uplink multiuser MIMO systems with imperfect channel state information (CSI). The effect of the antenna correlations is involved in the channel model. The multiuser scheduling and the precoding that avail the total mean square error (TMSE) minimization criteria under individual power constraint are firstly deduced and the combination of the two parts is designed in the following. The proposed design is compared with the robust precoding with random scheduling scheme and the non-robust scheme. The simulation results show that the joint design helps achieving larger system throughput and the robust algorithm mitigates the performance loss due to the imperfect CSI.

In this study, we consider the downlink beamforming problem in millimeter wave (mmWave) systems subjected to both path blockages and imperfect channel state information (CSI), and propose a new robust hybrid sum-outage minimizing design as a solution. We first formulate the problem as an empirical risk minimization (ERM) stochastic learning problem, whose solution can be obtained by the alternate iteration of a baseband digital and a radio frequency (RF) analog Riemann manifold-constrained beamforming updates through a mini-batch stochastic gradient descent (MSGD) approach, with gradient minimizing update rules given in closed-form, and learning rates optimized based on the lower-bounds of the corresponding Lipschitz constants. Unlike existing solutions to the path blockage-robust mmWave beamforming problem, wherein out-of-band side information is required or perfect CSI is assumed, our method relies only on the estimates and statistical knowledge of the channel's angles of departure (AoD) and complex gains, which are simultaneously captured in a Bernoulli-Gaussian model and used to generate the training data for the MSGD-based optimizer. Further, unlike preceding fully-digital or fully-connected hybrid contributions, the proposed scheme assumes a virtually-configured partially-connected setup; therefore, it is compatible with coordinated multipoint (CoMP) architectures, which are known to be crucial in terms of exploiting the full potential of mmWave systems. Simulation results confirm the effectiveness of our MSGD-based robust hybrid CoMP mmWave beamformer in mitigating the effects of path blockage and CSI error, demonstrating its superiority to state-of-the-art (SotA) alternatives.

Millimeter wave (mmWave) communication systems are considered to be a promising technology enabling gigabit-per-second data rates, as the mmWave band offers large transmission bandwidth. However, precoding in mmWave systems cannot be performed in digital domain, due to the large number of radio frequency chains required. Deploying a hybrid precoding transceiver architecture, where mmWave precoding is divided among digital and analog processing domains, is an attractive and cost-efficient alternative. Yet, the design of near-optimal hybrid precoders is a non-trivial optimization problem. In this paper, we consider transmit precoding and receive combining in mmWave systems with large antenna arrays in a partially-connected structure, then we make use of projection algorithms to greatly simplify the design problem of digital baseband and analog radio frequency precoders into two sub-optimization problems whose optimal solutions can be found. We also develop a channel estimation algorithm to estimate mmWave channel parameters via a codebook of beamforming vectors obtained through the discrete Fourier transform design. The results illustrate that the system using the proposed projection hybrid precoding and channel estimation algorithms approaches the spectral efficiency achievable when perfect channel knowledge is available.

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.

The provision for spectrally efficient multicast broadcast services (MBS) is one of the key functional requirements for next generation wireless communication systems. The challenge inherent to MBS is to ensure that all MBS users can be served, and one effective solution to this problem is to employ MIMO multicast transmit precoding. In previous works on MIMO multicast transmit precoding design, the authors either assumed (1) perfect transmitter-side channel state information (CSIT) or (2) special channel conditions that facilitate precoder design with imperfect CSIT. In this paper, we focus on transmit precoding design for MBS where the CSIT is obtained via limited feedback. In addition, we analyze the average minimum receive signal-noise-ratio (RxSNR) among the MBS users and study the order of growth with respect to the number of MBS users, the number of feedback bits, and the number of transmit antennas. Finally, we propose a threshold based feedback reduction scheme and study the tradeoff between feedback cost and performance loss.