Simplified transmit covariance optimization and user ordering algorithm for successive zero-forcing precoding

In this paper, we study duality relations for the fading broadcast channel (BC) under additive white Gaussian noise and a strict ordering of the fading distributions without channel state information at the transmitter and the natural corresponding dual fading multiple-access channel (MAC). We show that if the fading distribution for the weaker user is non-deterministic, the achievable rate region using superposition coding and successive decoding and Gaussian signaling, which is conjectured to be the capacity region, is different from the dual MAC region. Duality holds only in the case of one-sided fading, where the fading distribution for the weaker user is deterministic. Despite this lack of duality, we propose to use the dual MAC in order to approximatively solve a non-convex problem for the BC. Specifically, we consider the problem of weighted sum-rate optimization for the BC and give, under some assumptions, upper bounds on the error incurred using this procedure.

Multiple-input multiple-output (MIMO) wireless communications systems have attracted a lot of attentions, because of their potential for high gain in channel capacity. Recently, attention has shifted to multiuser MIMO (MU-MIMO) systems. In the schemes for downlink MU-MIMO system, dirty paper coding (DPC) and block diagonalization (BD) algorithms can provide higher sum rate capacity of MU-MIMO systems; however, exhaustive user scheduling for them may cause prohibitive computation complexity. The greedy scheduling algorithms were proposed for DPC and for BD; and proportionally fair (PF) scheduling for MU-MIMO was also discussed in the previous works. However, the discussions in where mainly based on the system model with equal average signal to noise power ratio (SNR) users. In this paper, we focus on the user scheduling for the downlink of MU-MIMO systems with DPC transmission scheme, where each user is assumed to have only one receive antenna, which will simplify the analysis and is expected to give more insight of PF scheduling. We also assume each individual user has different average transmit SNR in the system. We modify the conventional user scheduling algorithm for DPC to modified Gram-Schmidt orthogonalization (M-GSO) based algorithm and extend it into PF scheduling. We also propose a modified PF metric corresponding to the unequal SNR users system model, that increases the sum rate capacity of MU-MIMO system.

In this letter, we focus on the signal-to-interference-plus-noise ratio (SINR) enhancement using transmitting waveform covariance matrix optimization in colocated MIMO radars. In our proposed algorithm, transmitted waveform covariance matrix has been optimized to focus the transmit beampattern into the target direction and in the receiver, we try to reject maximum number of interfering objects. In the proposed algorithm, transmitted waveform covariance matrix is able to be synthesized with binary phase shift keying waveforms in closed form. Simulation results show that our proposed method has better SINR performance in comparison with methods in which transmitted covariance matrix is designed independently from the interferences locations.

Multiuser multiple-input multiple-output (MU-MIMO) systems can achieve higher data rates compared to single user (SU-MIMO) by exploiting multi-user diversity. The capacity bound for MU-MIMO systems is given by the MIMO broadcast channel (BC) capacity. Dirty paper coding (DPC) is a well known non-linear algorithm to achieve this bound. Zero forcing DPC (ZF-DPC) is a sub-optimal way to achieve DPC by triagularizing the channel. In our previous work, we had proposed an enhancement of ZF-DPC by introducing additional receiver which was shown to improve the achievable rates over linear schemes such as block diagonalization. In practise Block Diagonalization is implemented by the receiver feeding back quantized information about the channel and the transmitter figuring out the precoders subsequently. To establish a comparison of ZF-DPC to Block Diagonalization for such practical feedback, we first derive the framework for operating ZF-DPC with quantized feedback. Next we compare the performance of ZF-DPC over Block Diagonalization with quantized feedback and demonstrate that the former still performs better.

Summary The primary purpose of this paper is to propose empirical measures of the structural differences between two communities of plants or animals composed of the same species. Structure is defined to consist of; 1) the species in the community, 2) the pattern of interactions as represented by the covariance or correlation matrix of successive observations on each species, and 3) the mean abundances of each species in each of the two communities. Statistical tests are proposed for testing whether the covariance matrices and the vectors of mean densities for each community are equal and empirical measures of the differences between the covariance matrices and mean vectors are proposed. Given unequal covariance or correlation matrices the factor analysis model is used to derive empirical measures of the degree to which each variable of the ecosystem is responsible for the observed defferences in the pattern of interactions in each community. These tests and measures were applied to data gathered by Hunter (1966) on the abundances of six species of Drosophila censused monthly over a period of approximately two and a half years in two adjacent, but different habitats near Bogota, colombia. The two covariance matrices were significantly different indicating different patterns of interactions in the two Drosophila communities.

Two numerical approaches, the Robust-Generalized Iterative Approach (R-GIA) and the Robust-Transmit Covariance Optimization Approach (R-TCOA), are proposed for jointly designing the minimum mean square error (MMSE) precoders and decoders of uplink multiuser multiple-input-multiple-output (MIMO) systems with arbitrary linear equality power constraints and possibly imperfect channel state information (CSI). The R-TCOA always gives optimum solutions but is only applicable when the rank constraints on the precoders are relaxed, the spatial correlation matrix for the transmit antennas of each user is an identity matrix, and there exists a scalar such that squaring the source covariance matrices is the same as multiplying them by it. The statistics of the CSI error also need to be the same for all users if the power constraints of the users are interdependent. The R-GIA, on the other hand, has no such restrictions. But whenever the R-TCOA is applicable, both approaches converge, and all the transmit covariance matrices are full rank, the two solutions are actually equivalent (i.e. the R-GIA is also optimum)! Numerical results show that these two robust approaches, for the most part, outperform their non-robust counterparts in various different channel correlation scenarios.

Wireless communication paradigm has evolved from single-user single-input single-output (SISO) and multiple-input multiple-output (MIMO) systems to multi-user (MU) MIMO counterparts, which are shown greatly improving the rate performance by transmitting to multiple users simultaneously. The sum-capacity and the capacity region of a single-cell MU MIMO downlink system or the so-called MIMO broadcast channel (MIMO-BC) can be attained by the nonlinear “Dirty Paper Coding (DPC)” scheme [1] [2] [3]. However, DPC requires a high implementation complexity due to the non-linear successive encoding/decoding at the transmitter/receiver, and is thus not suitable for real-time applications. Other studies have proposed to use alternative linear precoding schemes for the MIMO-BC, e.g., the block-diagonalization scheme [4], to reduce the complexity. More information on the key developments of single-cell MIMO communication can be found in, for example, [5] [6] [7].

The knowledge of channel covariance matrices is of paramount importance to the estimation of instantaneous channels and the design of beamforming vectors in multi-antenna systems. In practice, an abrupt change in channel covariance matrices may occur due to the change in the environment and the user location. Although several works have proposed efficient algorithms to estimate the channel covariance matrices after any change occurs, how to detect such a change accurately and quickly is still an open problem in the literature. In this paper, we focus on channel covariance change detection between a multi-antenna base station (BS) and a single-antenna user equipment (UE). To provide theoretical performance limit, we first propose a genie-aided change detector based on the log-likelihood ratio (LLR) test assuming the channel covariance matrix after change is known, and characterize the corresponding missed detection and false alarm probabilities. Then, this paper considers the practical case where the channel covariance matrix after change is unknown. The maximum likelihood (ML) estimation technique is used to predict the covariance matrix based on the received pilot signals over a certain number of coherence blocks, building upon which the LLR-based change detector is employed. Numerical results show that our proposed scheme can detect the change with low error probability even when the number of channel samples is small such that the estimation of the covariance matrix is not that accurate. This result verifies the possibility to detect the channel covariance change both accurately and quickly in practice.

In this paper, we propose a new downlink multi-user multiple-input multiple-output (MIMO) precoding scheme based on maximizing the successive signal to leakage plus noise ratio (SSLNR). The work is motivated by the precoding scheme developed by Sadek, Tarighat and Sayed by maximizing the signal to leakage plus noise ratio (SLNR), which does not impose any restriction on the number of antennas at the transmitter and receiver. In our proposed scheme, dirty paper coding (DPC) is applied to cancel the known leakages, so SLNR can be calculated only using the unknown leakages. The proposed scheme has no restriction of the number of antennas as the conventional SLNR scheme. In addition, the proposed scheme decreases the complexity of the receivers compared with the conventional SLNR scheme. Simulations show that the proposed scheme has superior bit error rate (BER) performance over the conventional SLNR scheme.

An analytical lower bound on uplink channel capacity of a user in a massive multiple-input multiple-output system where the channel vector and the covariance matrices of the users in that cell are unknown is derived in this paper. This analytical bound enables us to choose appropriate sample size for covariance matrix estimation to meet the spectral efficiency requirements. The accurate agreement between the derived bound and the simulated bound based on random samples of channel vectors and covariance matrices is shown.

Estimating large covariance and precision (inverse covariance) matrices has become increasingly important in high dimensional statistics because of its wide applications. The estimation problem is challenging not only theoretically due to the constraint of its positive definiteness, but also computationally because of the curse of dimensionality. Many types of estimators have been proposed such as thresholding under the sparsity assumption of the target matrix, banding and tapering the sample covariance matrix. However, these estimators are not always guaranteed to be positive-definite, especially, for finite samples, and the sparsity assumption is rather restrictive. We propose a novel two-stage adaptive method based on the Cholesky decomposition of a general covariance matrix. By banding the precision matrix in the first stage and adapting the estimates to the second stage estimation, we develop a computationally efficient and statistically accurate method for estimating high dimensional precision matrices. We demonstrate the finite-sample performance of the proposed method by simulations from autoregressive, moving average, and long-range dependent processes. We illustrate its wide applicability by analyzing financial data such S&P 500 index and IBM stock returns, and electric power consumption of individual households. The theoretical properties of the proposed method are also investigated within a large class of covariance matrices.

In this article, we investigate achievable sum-rates of a multiuser multiple-input multiple-output (MU-MIMO) network with maximal ratio transmission (MRT) and zero-forcing (ZF) precoders for downlink cellular scenarios. We use Gamma distribution to derive tight lower and upper bounds of the achievable sum-rates. From the analytical results, the sum-rates of the MRT and ZF precoders are increased with the number of the transmit antennas and transmit power, and there exists an optimal number of served users for the highest achievable sum-rates when using the ZF precoder.

Reconfigurable intelligent surface (RIS) stands out as a promising technology by enhancing the electromagnetic wave propagation environment with its passive reflecting elements. In this paper, we focus on the ergodic sum-rate analysis and maximization of the RIS-assisted uplink multiuser multiple-input multiple-output (MIMO) multiple-access channel (MAC) under Rician fading by exploiting full statistical channel state information (CSI). The spatial correlations at the base station, the users, and the RIS are also considered. By using the replica method originated in statistical physics, the closed-form asymptotic ergodic sum-rate of the system is first derived in the large-system regime on the account of the unique channel structure of the RIS-assisted MIMO-MAC system. Then, based on the derived asymptotic ergodic sum-rate, we propose an alternating optimization (AO) algorithm to jointly design the transmit covariance matrix of users and the phase-shifting matrix of RIS with full statistical CSI. Simulation results are also demonstrated to verify the accuracy of the derived asymptotic ergodic sum-rate and the superiority of the proposed AO algorithm. The results reveal that the derived closed-form asymptotic ergodic sum-rate matches very well with the Monte Carlo results even for a small number of antennas, and the proposed AO algorithm can achieve up to 10 bps/Hz gain at high signal-to-noise (SNR) regime, which is therefore valuable for future RIS-assisted MIMO-MAC system designs.

In this paper, we consider the precoder design for an under-loaded or critically loaded downlink multi-user multiple-input multiple-output (MU-MIMO) communication system. We propose novel precoding and decoding schemes which enhance system performance based on rate splitting at the transmitter and single-stage successive interference cancellation at the receivers. The proposed successive null-space (SNS) precoding scheme utilizes linear combinations of the null-space basis vectors of the successively augmented MIMO channel matrices of the users as precoding vectors to adjust the inter-user-interference experienced by the receivers. We formulate a non-convex weighted sum rate (WSR) optimization problem, and solve it via successive convex approximation to obtain a suboptimal solution for the precoding vectors and the associated power allocation. Our simulation results reveal that the proposed SNS precoders outperform block diagonalization based linear and rate splitting designs, and in many cases, have a relatively small gap to the maximum sum rate achieved by dirty paper coding.

Channel state information (CSI) is important for achieving large rates in MIMO channels. However, in time-varying MIMO channels, there is a tradeoff between the time/energy spent acquiring channel state information (CSI) and the time/energy remaining for data transmission. This tradeoff is accentuated in the MIMO multiple access channel (MAC), since the number of channel vectors to be estimated increases with the number of users. Furthermore, the problem of acquiring CSI is tightly coupled with the problem of exploiting CSI through multiuser scheduling. This paper considers a block-fading MAC with coherence time <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> , n uncoordinated users-each with one transmit antenna and the same average power constraint, and a base station with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> receive antennas and no a priori CSI. For this scenario, a training-based communication scheme is proposed and the training and multiuser-scheduling aspects of the scheme are jointly optimized. In the high-SNR regime, the sum capacity of the non-coherent SIMO MAC is characterized and used to establish the SNR-scaling-law optimality of the proposed scheme. In the low-SNR regime, the sum-rate of the proposed scheme is found to decay linearly with vanishing SNR when flash signaling is incorporated. Furthermore, this linear decay is shown to be order-optimal through comparison to the low-SNR sum capacity of the non-coherent SIMO MAC. A by product of these SNR-asymptotic analyses is the observation that non-trivial scheduling (i.e., scheduling a strict subset of trained users) is advantageous at low SNR, but not at high SNR. The sum-rate and per-user throughput are also explored in the large- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> and large- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> regimes. Non-coherent capacity, training, multiple access channel, multiuser scheduling, opportunistic scheduling.