Multiple-input Multiple-output Broadcast Research Articles

Identification Over Compound Multiple-Input Multiple-Output Broadcast Channels

The identification capacity region of the compound broadcast channel is determined under an average error criterion, where the sender has no channel state information. We give single-letter identification capacity formulas for discrete channels and multiple-input multiple-output Gaussian channels under an average input constraint. The capacity theorems apply to general discrete memoryless broadcast channels. This is in contrast to the transmission setting, where the capacity is only known for special cases, notably the degraded broadcast channel and the multiple-input multiple-output broadcast channel with private messages. Furthermore, the identification capacity region of the compound multiple-input multiple-output broadcast channel can be larger than the transmission capacity region. This is a departure from the single-user behavior of identification, since the identification capacity of a single-user channel equals the transmission capacity.

Secure Degrees of Freedom of the Three-User MIMO Broadcast Channel With Delayed CSIT

This paper investigates the sum-secure degrees-of-freedom (SDoF) of three-user multiple-input multiple-output (MIMO) broadcast channel with confidential messages (BCCM) and delayed channel state information at the transmitter (CSIT). Specifically, we obtain non-trivial sum-SDoF upper and lower bounds. Firstly, we derive the sum-SDoF upper bound by means of statistical equivalence property, security constraints, and permutations. Then, for the sum-SDoF lower bound, we leverage the artificial noise transmission and interference re-transmission to design two transmission schemes, which have holistic and sequential higher-order symbol generation, respectively. For these two schemes, we propose the redundancy reduction approach for security analysis, by which the minimal duration of artificial noise transmission phase of the scheme is obtained. To eliminate the redundant equations in security analysis, this approach first identifies the constituent equations, and then analyzes the rank of assemble of them. As a result, both the proposed sum-SDoF upper and lower bounds are tighter than the existing sum-SDoF upper and lower bounds, respectively. Furthermore, the proposed lower bound showcases a three-user coding gain.

The DoF region of two‐user MIMO broadcast channel with delayed imperfect‐quality CSIT

The channel state information at the transmitter (CSIT) play an important role in the performance of wireless networks. The CSIT model can be delayed and imperfect-quality, since the feedback link has a delay and the channel state information (CSI) feedback has distortion. In this paper, we thus characterize the degrees-of-freedom (DoF) region of the two-user multiple-input multiple-output (MIMO) broadcast channel with delayed imperfect-quality CSIT, where the antenna configurations can be arbitrary. The converse proof of DoF region is based on the enhancement of physically degraded channel. The achievability proof of DoF region is through a novel transmission scheme design, where the duration of each phase and the amount of transmitted symbols are configured based on the imperfect-quality of delayed CSIT. As a result, we show that the DoF region with delayed imperfect-quality CSIT is located between the DoF region with no CSIT and the DoF region with delayed CSIT.

Joint Optimization of Received Signal Power and Signal Space Dimensions for MIMO Broadcast Channels

In Multiple-input multiple-output (MIMO) broadcast channels (BCs), the transmitter simultaneously broadcasts signals to multiple receivers at same frequency band, resulting in that the communication capacity is affected by both interference, channel fading and random noise. Although channel fading can be mitigated by transceivers, the signal-to-noise-ratio (SNR) of the practical communication system is still dynamically changing due to the randomly changing noise. Traditional MIMO transceiver optimization algorithms can not flexibly adapt to the dynamic changes of SNR, resulting in large performance degradation. In this paper, we comprehensively consider signal power and signal space dimensions of the received signal in MIMO BCs, and propose two transceiver optimization algorithms which can dynamically adapt to the variance of SNRs. In the proposed algorithms, SNR is adopted to be an adjustment factor to cope with its variance. When SNR is low, i.e, large noise, the algorithm parameters are automatically adjusted so that the signal power is preserved as much as possible to combat the loss of communication capacity caused by large random noise. Correspondingly, under the condition of high SNR environment, the algorithm parameters are adjusted automatically to effectively compress the inter-user-interference (IUI) and intra-user-inter-stream-interference (ISI) by optimizing signal space dimensions. Simulation results show that in different SNR environments, the proposed algorithms can automatically adjust the focus of optimization, so that the optimization of signal power and signal space dimensions can automatically adapt to different SNRs. Compared with traditional transceiver optimization algorithms, the proposed algorithms can improve the communication capacity within a large dynamic range of SNR.

On Linearly Precoded Rate Splitting for Gaussian MIMO Broadcast Channels

In this paper, we consider a general $K$ -user Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). We assume that the channel state is deterministic and known to all the nodes. While the private-message capacity region is well known to be achievable with dirty paper coding (DPC), we are interested in the simpler linearly precoded transmission schemes. In particular, we focus on linear precoding schemes combined with rate-splitting (RS). First, we derive an achievable rate region with minimum mean square error (MMSE) precoding at the transmitter and joint decoding of the sub-messages at the receivers. Then, we study the achievable sum rate of this scheme and obtain two findings: 1) an analytically tractable upper bound on the sum rate that is shown numerically to be a close approximation, and 2) how to reduce the number of active streams – crucial to the overall complexity – while preserving the sum rate to within a constant loss. The latter results in two practical algorithms: a stream elimination algorithm and a stream ordering algorithm. Finally, we investigate the constant-gap optimality of linearly precoded RS with respect to the capacity. Our result reveals that, while the achievable rate of linear precoding alone can be arbitrarily far from the capacity, the introduction of RS can help achieve the capacity region to within a constant gap in the two-user case. Nevertheless, we prove that the RS scheme’s constant-gap optimality does not extend to the three-user case. Specifically, we show, through a pathological example, that the gap between the sum rate and the sum capacity can be unbounded.

Distributed Adaptive Cooperative Bandwidth Spectrum Sensing for Cognitive MIMO Radios

To allow secondary and primary concurrent transmissions achieving optimal spectrum utilization in cognitive radio networks (CRNs), this paper proposes an innovative distributed cooperative spectrum sensing methodology using adaptive sensing bandwidth entitled distributed adaptive cooperative bandwidth spectrum sensing (DACB-SS) scheme when multiple secondary users (SUs) use part of the bandwidth to collaboratively perform spectrum sensing throughout the whole frame to detect the primary user (PU)'s reappearance in time. The SU’s spectrum efficiency is maximized by jointly optimizing the sensing bandwidth proportion, the number of cooperative SUs, and the detection probability, subject to the constraints on the SUs’ interference and the false alarm probability. A gripping slant of DACB-SS regime is provided to maintain overall maximum spectral efficiency. Another contribution of DACB-SS algorithm is the benefit to make great improvement on the sum capacity to obtain better performance of spectrum coexistence. Simulation results illustrate that the proposed analytical model investigates characteristic changes of the spectrum usage affected by the outage probability of PR and the coexisting secondary transmission bandwidth in terms of overall spectral efficiency as well as the outage capacity which can be characterized by the outage probability of SR and the interference from ST to PR in multiuser multiple-input multiple-output broadcast channel (MU-MIMO-BC). Besides, the sum capacity is impacted by channel gains, primary transmit power and secondary transmit power in Gaussian cognitive inference channel (G-CIFC).

Achievable DoF Regions of Three-User MIMO Broadcast Channel With Delayed CSIT

For the two-user multiple-input multiple-output (MIMO) broadcast channel with delayed channel state information at the transmitter (CSIT) and arbitrary antenna configurations, all the degrees-of-freedom (DoF) regions are obtained. However, for the three-user MIMO broadcast channel with delayed CSIT and arbitrary antenna configurations, the DoF region of order-2 messages is still unclear and only a partial achievable DoF region of order-1 messages is obtained, where the order-2 messages and order-1 messages are desired by two receivers and one receiver, respectively. In this paper, for the three-user MIMO broadcast channel with delayed CSIT and arbitrary antenna configurations, we first design transmission schemes for order-2 messages and order-1 messages. Next, we propose to analyze the achievable DoF region of transmission scheme by transformation approach. In particular, we transform the decoding condition of transmission scheme w.r.t. phase duration into the achievable DoF region w.r.t. achievable DoF, through achievable DoF tuple expression connecting phase duration and achievable DoF. As a result, the DoF region of order-2 messages is characterized and an achievable DoF region of order-1 messages is completely expressed. Besides, for order-1 messages, we derive the sufficient condition, under which the proposed achievable DoF region is the DoF region.

Spectral and energy efficient power allocation for MIMO broadcast channels with individual delay and QoS constraints

In this paper, we propose a novel power allocation algorithm to maximize the spectral efficiency (SE) and energy efficiency (EE) of multiple-input multiple-output (MIMO) broadcast channels under individual quality of service (QoS) constraints. In several wireless applications, one of the most important factors for QoS guarantee is delay outage. To address the impact of delay outage occurring in the link layer, effective capacity (EC) that means the maximum constant arrival rate satisfying statistical delay-QoS constraint is considered. Using a novel performance metric, effective-EE, which is defined as EC divided by total power consumption, we formulate an EC and effective-EE maximization problem with QoS constraints as an adaptive power allocation problem. By applying Lagrangian method, we solve optimization problem and propose an optimal power allocation algorithm. Simulation results demonstrate that our proposed algorithm can improve the EC and effective-EE performance.

Secure Degrees of Freedom of Rank-Deficient BCCM and Rank-Deficient ICCM

The secure degrees of freedom (SDoF) of two-user rank-deficient multiple-input multiple-output (MIMO) broadcast channel with confidential messages (BCCM) and two-user rank- deficient MIMO interference channel with confidential messages (ICCM) are studied respectively in this paper. In the systems, each transmitter has $M$ antennas, and each receiver has $N$ antennas. We consider that each transmitter intends to send secure messages to the corresponding receiver, and another receiver can receive the messages but cannot decode them, which ensures that the messages are confidential. Comparing with previous studies on two-user broadcast channel and interference channel, we explore the case that channel matrices are rank-deficient, and the rank of channel matrices can take arbitrary value, $D \leq \text{min} (M,N)$ . For the two rank-deficient channels, BCCM and ICCM, we divide the problem into several regimes according to the different configurations of the rank of channel matrices and the number of antennas at each node. The outer bound of rank-deficient BCCM is inferred from information theoretic methods and the achievable schemes are given by zero forcing techniques. We derive the outer bound of rank-deficient ICCM by taking the minimum region of the three outer bounds, where the first outer bound is the result of rank-deficient interference channel model without secrecy constraints, the second outer bound is obtained by considering secrecy constraints, and the third outer bound is achieved by transmitters cooperation. Then we present the achievable schemes by combining zero-forcing, real interference alignment, and spatial alignment. Finally, we determine the exact SDoF of the rank-deficient BCCM and the rank-deficient ICCM.

On the Accuracy of Quantization Cell Approximation in MIMO Broadcast Systems Based on Limited Feedback

This study investigates the accuracy of quantization cell approximation (QCA) in a multiple-input multiple-output (MIMO) broadcast channel. QCA is an analytical quantization model used to approximate the quantized channel state information (CSI) in limited-feedback-based MIMO systems. It has been widely used in important studies for analytical tractability because it approximates the quantized CSI as a simple beta random variable multiplied by a deterministic value. Moreover, the effect of quantization is solely concentrated on the deterministic value such that the corresponding performance analysis is stochastically independent of the quantization process. Nevertheless, the accuracy of QCA has not been carefully demonstrated in previous studies. In this study, a generalized version of QCA is proposed with a complete analysis. Because the proposed QCA requires the use of a specific distance measure, the validity of the distance measure is first investigated. Based on the proposed distance measure, the accuracy of QCA is estimated by analyzing the difference between the spectral efficiencies achieved using QCA and random matrix quantization (RMQ). The corresponding results show that the difference gradually decreases and converges to zero as the number of feedback bits increases. As QCA and RMQ provide performance upper and lower bounds, respectively, in terms of codebook construction, these results prove the asymptotic validity of QCA with respect to the number of feedback bits. Both analysis and simulation results demonstrate that the difference in spectral efficiencies is also small for a moderate number of feedback bits. In addition, this study also demonstrates an asymptotic difference in spectral efficiencies with respect to the signal-to-noise-ratio (SNR). The difference increases with the SNR, but it is bounded by a finite value. Thus, the difference in the worst case SNR can also be suppressed by increasing the number of feedback bits.

On Achievable Multiuser Diversity Gain of Limited-Feedback-Based Block Diagonalization in Interference-Limited MIMO Broadcast Channels

The scaling law of sum spectral efficiency achieved by limited-feedback-based block diagonalization with semi-orthogonal user selection in an interference-limited multiple-input–multiple-output broadcast channel is investigated. An interference-limited regime is realized by assuming a large transmit power. An analysis of the distribution of the channel quality indicator of scheduling makes it possible to characterize the limiting behavior of the spectral efficiency. From the limiting behavior, it is shown that the achievable multiuser diversity gain can be significantly increased as the system approaches the interference-limited regime from large user regimes.

Treating Content Delivery in Multi-Antenna Coded Caching as General Message Sets Transmission: A DoF Region Perspective

Coded caching can create coded multicasting thus significantly accelerates content delivery in broadcast channels with receiver caches. While the original delivery scheme in coded caching multicasts each coded message sequentially, it is not optimal for multiple-input multiple-output (MIMO) broadcast channels. This work aims to investigate the full spatial multiplexing gain in multi-antenna coded caching by transmitting all coded messages concurrently. In specific, we propose to treat the content delivery as the transmission problem with general message sets where all possible messages are present, each with different length and intended for different user set. We first obtain inner and outer bounds of the degrees of freedom (DoF) region of a $K$-user $(M,N)$ broadcast channel with general message sets, with $M$ and $N$ being the number of transmit and receive antennas, respectively. Then for any given set of coded messages, we find its minimum normalized delivery time (NDT) by searching the optimal DoF tuple in the DoF regions. The obtained minimum NDT is optimal at antenna configuration $\frac{M}{N} \in (0,1]\cup[K, \infty)$ and is within a multiplicative gap of $\frac{M}{N}$ to optimum at $\frac{M}{N} \in (1,K)$. Our NDT results can be evaluated for any user demand with both centralized and decentralized cache placement.

Multi-Agent Distributed Beamforming With Improper Gaussian Signaling for MIMO Interference Broadcast Channels

For rate optimization in interference limited networks, improper Gaussian signaling has shown its ability to outperform conventional proper Gaussian signaling. In this paper, we study a weighted sum-rate maximization problem with improper Gaussian signaling for the multiple-input multiple-output interference broadcast channel. To solve this nonconvex and NP-hard problem, we propose an effective separate covariance and pseudo-covariance matrices optimization algorithm. In the covariance optimization, a weighted minimum mean square error algorithm is adopted, and in the pseudo-covariance optimization, an alternating optimization (AO) algorithm is proposed, which guarantees convergence to a stationary solution and ensures a sum-rate improvement over proper Gaussian signaling. An alternating direction method of multipliers-based multi-agent distributed algorithm is proposed to solve an AO subproblem with the globally optimal solution in a parallel and scalable fashion. The proposed scheme exhibits favorable convergence, optimality, and complexity properties for future large-scale networks. The simulation results demonstrate the superior sum-rate performance of the proposed algorithm as compared with the existing schemes with proper as well as improper Gaussian signaling under various network configurations.

Unsupervised Learning-Based Fast Beamforming Design for Downlink MIMO

In the downlink transmission scenario, power allocation and beamforming design at the transmitter are essential when using multiple antenna arrays. This paper considers a multiple input–multiple output broadcast channel to maximize the weighted sum-rate under the total power constraint. The classical weighted minimum mean-square error (WMMSE) algorithm can obtain suboptimal solutions but involves high computational complexity. To reduce this complexity, we propose a fast beamforming design method using unsupervised learning, which trains the deep neural network (DNN) offline and provides real-time service online only with simple neural network operations. The training process is based on an end-to-end method without labeled samples avoiding the complicated process of obtaining labels. Moreover, we use the “APoZ”-based pruning algorithm to compress the network volume, which further reduces the computational complexity and volume of the DNN, making it more suitable for low computation-capacity devices. Finally, the experimental results demonstrate that the proposed method improves computational speed significantly with performance close to the WMMSE algorithm.

Efficient Optimization Algorithms for Multi-User Beamforming With Superposition Coding

Channel asymmetry and channel correlation are frequently encountered in wireless communication systems. Orthogonal transmission schemes are usually inefficient in dealing with these problems. In this paper, in order to boost the throughput performance for multiple-input multiple-output broadcast communications in the presence of channel asymmetry and/or channel correlation, we study optimization algorithms for multi-user superposition coding beamforming (SCBF). Starting with solving the minimum power optimization problem for the two-user case, we derive the optimal solution structure of the problem and two types of dedicated algorithms that could efficiently find the optimal solutions with all parameter setups. Extensions are then made to the same problem with the signals of more than two users multiplexed in the power domain as well as to the rate region computation problem. Finally, to adapt our algorithms to more general cases, novel hybrid precoding schemes are proposed, where certain user grouping strategy is used to combine zero-forcing beamforming and SCBF. Numerical simulations are provided to show that with our algorithms, a considerable performance gain is achieved by SCBF compared to the other orthogonal transmission methods.

On Linearly Precoded Rate Splitting for Gaussian MIMO Broadcast Channels

In this paper, we consider a general K-user Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). We assume that the channel state is deterministic and known to all the nodes. While the private-message capacity region is well known to be achievable with dirty paper coding (DPC), we are interested in the simpler linearly precoded transmission schemes. In particular, we focus on linear precoding schemes combined with rate-splitting (RS). First, we derive an achievable rate region with minimum mean square error (MMSE) precoding at the transmitter and joint decoding of the sub-messages at the receivers. Then, we study the achievable sum rate of this scheme and obtain two findings: 1) an analytically tractable upper bound on the sum rate that is shown numerically to be a close approximation, and 2) how to reduce the number of active streams -- crucial to the overall complexity -- while preserving the sum rate to within a constant loss. The latter results in two practical algorithms: a stream elimination algorithm and a stream ordering algorithm. Finally, we investigate the constant-gap optimality of linearly precoded RS with respect to the capacity. Our result reveals that, while the achievable rate of linear precoding alone can be arbitrarily far from the capacity, the introduction of RS can help achieve the capacity region to within a constant gap in the two-user case. Nevertheless, we prove that the RS scheme's constant-gap optimality does not extend to the three-user case. Specifically, we show, through a pathological example, that the gap between the sum rate and the sum capacity can be unbounded.

Energy Efficiency Optimization With SWIPT in MIMO Broadcast Channels for Internet of Things

Simultaneous wireless information and power transfer (SWIPT) is anticipated to have great applications in 5G communication systems and the Internet of Things. In this paper, we address the energy efficiency (EE) optimization problem for SWIPT multiple-input multiple-output broadcast channel (BC) with time-switching (TS) receiver design. Our aim is to maximize the EE of the system whilst satisfying certain constraints in terms of maximum transmit power and minimum harvested energy per user. The coupling of the optimization variables, namely transmit covariance matrices and TS ratios, leads to an EE problem which is nonconvex, and hence very difficult to solve directly. Hence, we transform the original maximization problem with multiple constraints into a suboptimal min–max problem with a single constraint and multiple auxiliary variables. We propose a dual inner/outer layer resource allocation framework to tackle the problem. For the inner-layer, we invoke an extended SWIPT-based BC-multiple access channel (MAC) duality approach and provide two iterative resource allocation schemes under fixed auxiliary variables for solving the dual MAC problem. A subgradient searching scheme is then proposed for the outer-layer in order to obtain the optimal auxiliary variables. Numerical results confirm the effectiveness of the proposed algorithms and illustrate that significant performance gain in terms of EE can be achieved by adopting the proposed extended BC-MAC duality-based algorithm.

Joint Interference and Phase Alignment among Data Streams in Multicell MIMO Broadcasting

For the problem of channel state information (CSI) delay and error, this paper proposes a joint interference and phase alignment algorithm based on Bayesian estimation and power allocation among data streams for multicell, multiple-input multiple-output broadcast channels (MIMO-BC). Firstly, the sender obtains the best estimate of the current CSI through Bayesian estimation. Secondly, the interference suppression matrix is designed by maximizing the ratio of the desired signal power to the intercell interference plus noise ratio (SINR) in the forward link, and in the reverse communication, by maximizing the SINR design precoding. Further, the water-filling algorithm is combined to optimize power allocation among data streams. Finally, the phase alignment is used to rotate the interference between data streams into the signal space of the target receive data stream, thereby enhancing the received power of the target data stream. Simulation results show that the proposed algorithm has certain performance advantages over other algorithms, whether it is ideal CSI or delay and error CSI.

Weighted sum-throughput maximization for MIMO broadcast channel: Energy harvesting with hybrid energy storage

In this work, a multiple-input multiple-output (MIMO) broadcast channel under the energy harvesting (EH) constraint and the peak power constraint is investigated. The transmitter is equipped with a hybrid energy storage system consisting of a perfect super capacitor (SC) and an inefficient battery, where both elements are with limited energy storage capacities. In addition, the effect of data processing circuit power consumption is also addressed. To be specific, two extreme cases are studied here, where the first assumes ideal/zero circuit power consumption and the second considers a positive constant circuit power consumption where the circuit is always operating at its highest power level. The performance of these two extreme cases hence serve as the upper bound and the lower bound of the system performance in practice, respectively. In this setting, the offline scheduling with ideal and maximum circuit power consumption models are investigated. Their corresponding optimization problems are formulated and solved in terms of weighted sum-throughput. Further, we extend to a general circuit power consumption model. To complement this work, some intuitive online policies are presented for all cases. Interestingly, for the case with maximum circuit power consumption, a close-to-optimal online policy is presented and its performance is shown to be comparable to its offline counterpart in the numerical results.

On the Feasibility of Interference Alignment in Compounded MIMO Broadcast Channels With Antenna Correlation and Mixed User Classes

This paper presents a generalized closed-form beamforming technique that can achieve the maximum degrees of freedom in compounded multiple-input multiple-output (MIMO) broadcast channels with mixed classes of multiple-antenna users. The contribution is firstly described within the context of a three-cell network and later extended to the general multi-cell scenario where we also show how to determine the conditions required to align the interference in a subspace that is orthogonal to the one reserved for the desired signals. This is then followed by an analysis of the impact of antenna correlation for different channel state information acquisition models. The proposed scheme is examined under both conventional and Large-scale MIMO systems. It will be shown that the proposed technique enables networks with any combination of user classes to achieve superior performance even under significant antenna correlation, particularly in the case of the Large-scale MIMO systems.