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Interleaved training has been studied for single-user and multi-user massive MIMO downlink with either fully-digital or hybrid beamforming. However, the impact of channel correlation on its average training overhead is rarely addressed. In this paper, we explore the channel correlation to improve the interleaved training for single-user massive MIMO downlink. For the beam-domain interleaved training, we propose a modified scheme by optimizing the beam training codebook. The basic antenna-domain interleaved training is also improved by dynamically adjusting the training order of the base station (BS) antennas during the training process based on the values of the already trained channels. Exact and simplified approximate expressions of the average training length are derived in closed-form for the basic and modified beam-domain schemes and the basic antenna-domain scheme in correlated channels. For the modified antenna-domain scheme, a deep neural network (DNN)-based approximation is provided for fast performance evaluation. Analytical results and simulations verify the accuracy of our derived training length expressions and explicitly reveal the impact of system parameters on the average training length. In addition, the modified beam/antenna-domain schemes are shown to have a shorter average training length compared to the basic schemes., Comment: 14 pages (double column), 8 figures. The paper has been accepted by IEEE Transactions on Wireless Communications

In frequency division duplexing (FDD) cell-free massive MIMO, the acquisition of the channel state information (CSI) is very challenging because of the large overhead required for the training and feedback of the downlink channels of multiple cooperating base stations (BSs). In this paper, for systems with partial uplink-downlink channel reciprocity, and a general spatial domain channel model with variations in the average port power and correlation among port coefficients, we propose a joint-port-selection-based CSI acquisition and feedback scheme for the downlink transmission with zero-forcing precoding. The scheme uses an eigenvalue-decomposition-based transformation to reduce the feedback overhead by exploring the port correlation. We derive the sum-rate of the system for any port selection. Based on the sum-rate result, we propose a low-complexity greedy-search-based joint port selection (GS-JPS) algorithm. Moreover, to adapt to fast time-varying scenarios, a supervised deep learning-enhanced joint port selection (DL-JPS) algorithm is proposed. Simulations verify the effectiveness of our proposed schemes and their advantage over existing port-selection channel acquisition schemes., Comment: 15 pages, 11 figures. The paper has been accepted by IEEE TRANSACTIONS ON COMMUNICATIONS

This letter proposes a modified non-orthogonal multiple-access (NOMA) scheme for systems with a multi-antenna base station (BS) and two single-antenna users, where NOMA transmissions are conducted only when the absolute correlation coefficient (CC) between the user channels exceeds a threshold and the BS uses matched-filter (MF) precoding along the user with the stronger average channel gain. We derive the average minimal transmit power to guarantee the signal-to-interference-plus-noise-ratio (SINR) levels of both users. Our results show that the average minimal power grows logarithmically in the reciprocal of the CC threshold and a non-zero threshold is necessary for the modified NOMA scheme to have finite average minimal transmit power. Further, for the massive MIMO scenario, we derive the scaling laws of the average transmit power and outage probability with respect to the antenna numbers, as well as their tradeoff law. Simulation results are shown to validate our theoretical results., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

In this paper, we study a massive multiple-input multiple-output (mMIMO) relay network where multiple source-destination pairs exchange information through a common relay equipped with a massive antenna array. The source users perform simultaneous wireless information and power transfer (SWIPT) and the power-splitting (PS) scheme is used at the relay to first harvest energy from the received signals, and then, to transmit the decoded signals using the harvested energy. Relay performs maximum ratio combining/maximum ratio transmission (MRC/MRT) beam-forming on the received signal. Under the three-dimensional (3D) directional channel model, we derive a closed-form lower bound expression for the average signal-to-interference-plus-noise ratio using results from random matrix theory, which leads to an asymptotic approximation of the achievable sum-rate. Based on that, we study a joint optimization problem over the tilt and PS ratio to maximize the achievable sum-rate. Grid search algorithm is used to solve the non-convex problem. Simulation results verify our theoretical analysis and the efficiency of our optimized design. In particular, our optimized system outperforms a conventional system with $\pi/4$ tilt and PS of $0.5$, by at least $61\%$.

We consider the use of deep neural network (DNN) to develop a decision-directed (DD)-channel estimation (CE) algorithm for multiple-input multiple-output (MIMO)-space-time block coded systems in highly dynamic vehicular environments. We propose the use of DNN for k-step channel prediction for space-time block code (STBC)s, and show that deep learning (DL)-based DD-CE can removes the need for Doppler spread estimation in fast time-varying quasi stationary channels, where the Doppler spread varies from one packet to another. Doppler spread estimation in this kind of vehicular channels is remarkably challenging and requires a large number of pilots and preambles, leading to lower power and spectral efficiency. We train two DNNs which learn real and imaginary parts of the MIMO fading channels over a wide range of Doppler spreads. We demonstrate that by those DNNs, DD-CE can be realized with only rough priori knowledge about Doppler spread range. For the proposed DD-CE algorithm, we also analytically derive the maximum likelihood (ML) decoding algorithm for STBC transmission. The proposed DL-based DD-CE is a promising solution for reliable communication over the vehicular MIMO fading channels without accurate mathematical models. This is because DNN can intelligently learn the statistics of the fading channels. Our simulation results show that the proposed DL-based DD-CE algorithm exhibits lower propagation error compared to existing DD-CE algorithms while the latters require perfect knowledge of the Doppler rate.

Water-filling solutions play an important role in the designs for wireless communications, e.g., transmit covariance matrix design. A traditional physical understanding is to use the analogy of pouring water over a pool with fluctuating bottom. Numerous variants of water-filling solutions have been discovered during the evolution of wireless networks. To obtain the solution values, iterative computations are required, even for simple cases with compact mathematical formulations. Thus, algorithm design is a key issue for the practical use of water-filling solutions, which however has been given marginal attention in the literature. Many existing algorithms are designed on a case-by-case basis for the variations of water-filling solutions and/or with complex logics. In this paper, a new viewpoint for water-filling solutions is proposed to understand the problem dynamically by considering changes in the increasing rates on different subchannels. This fresh viewpoint provides useful mechanism and fundamental information in finding the optimization solution values. Based on the new understanding, a novel and comprehensive method for practical water-filling algorithm design is proposed, which can be used for systems with various performance metrics and power constraints, even for systems with imperfect channel state information (CSI)., Comment: 16 pages, 3 figures. This manuscript is submitted to IEEE Transactions on Signal Processing

In this paper, a deep learning (DL)-based sphere decoding algorithm is proposed, where the radius of the decoding hypersphere is learned by a deep neural network (DNN). The performance achieved by the proposed algorithm is very close to the optimal maximum likelihood decoding (MLD) over a wide range of signal-to-noise ratios (SNRs), while the computational complexity, compared to existing sphere decoding variants, is significantly reduced. This improvement is attributed to DNN's ability of intelligently learning the radius of the hypersphere used in decoding. The expected complexity of the proposed DL-based algorithm is analytically derived and compared with existing ones. It is shown that the number of lattice points inside the decoding hypersphere drastically reduces in the DL-based algorithm in both the average and worst-case senses. The effectiveness of the proposed algorithm is shown through simulation for high-dimensional multiple-input multiple-output (MIMO) systems, using high-order modulations.

High power consumption and hardware cost are two barriers for practical massive multiple-input multiple-output (mMIMO) systems. A promising solution is to employ low-resolution analog-to-digital converters (ADCs). In this paper, we consider a general mMIMO multi-way relaying system with a multi-level mixed-ADC architecture, in which each antenna is connected to an ADC pair of an arbitrary resolution. By leveraging on Bussgang's decomposition theorem and Lloyd-Max algorithm for quantization, tight closed-form approximations are derived for the average achievable rates of zero-forcing (ZF) relaying considering both perfect and imperfect channel state information (CSI). To conquer the challenges caused by multi-way relaying, the complicated ZF beam-forming matrix, and the general mixed-ADC structure, we develop a novel method for the achievable rate analysis using the singular-value decomposition (SVD) for Gaussian matrices, distributions of the singular values of Gaussian matrices, and properties of Haar matrices. The results explicitly show the achievable rate behavior in terms of the user and relay transmit powers and the numbers of relay antennas and users. Most importantly, it quantifies the performance degradation caused by low-resolution ADCs and channel estimation error. We demonstrate that the average achievable rate has an almost linear relation with the square of the average of quantization coefficients pertaining to the ADC resolution profile., Comment: Part of this work on the performance analysis of mMIMO multi-way relay networks with low-resolution uniform-ADC structures has been presented at the IEEE International Conference on Communications (ICC) 2019 [1]

Non-orthogonal multiple access (NOMA), as the newest member of the multiple access family, is envisioned to be an essential component of 5G mobile networks. The combination of NOMA and multi-antenna multi-input multi-output (MIMO) technologies exhibits a significant potential in improving spectral efficiency and providing better wireless services to more users. In this article, we introduce the basic concepts of MIMO-NOMA and summarize the key technical problems in MIMO-NOMA systems. Then, we explore the problem formulation, beamforming, user clustering, and power allocation of single/multi-cluster MIMO-NOMA in the literature along with their limitations. Furthermore, we point out an important issue of the stability of successive interference cancellation (SIC) that arises using achievable rates as performance metrics in practical NOMA/MIMO-NOMA systems. Finally, we discuss incorporating NOMA with massive/millimeter wave MIMO, and identify the main challenges and possible future research directions in this area., Comment: 14 pages (single column), 4 figures. This work has been accepted by the IEEE Wireless Communications, the special issue of non-orthogonal multiple access for 5G

For multi-input multi-output (MIMO) communication systems, many transceiver design problems involve the optimization of the covariance matrices of the transmitted signals. The derivation of the optimal solutions based on Karush-Kuhn-Tucker (KKT) conditions is a most popular method, and many results have been reported for different scenarios of MIMO systems. In this overview paper, we propose a unified framework in formulating the KKT conditions for general MIMO systems. Based on this framework, the optimal water-filling structures of the transmission covariance matrices are derived rigorously, which are applicable to a wide range of MIMO systems. Our results show that for seemingly different MIMO systems with various power constraints and objective functions, the derivations and water-filling structures for the optimal covariance matrix solutions are fundamentally the same. Thus, our unified framework and solution reveal the underlying relationships among the different water-filling structures of the covariance matrices. Furthermore, our results provide new solutions to the covariance matrix optimization of many complicated MIMO systems with multiple users and imperfect channel state information which were unknown before., Comment: Multi-input multi-output communications, covariance matrix optimization, matrix variate optimization, Karush-Kuhn-Tucker conditions, water-filling structure

Zero-forcing (ZF) precoding plays an important role for massive MIMO downlink due to its near optimal performance. However, the high computation cost of the involved matrix inversion hinders its application. In this paper, we adopt the first order Neumann series (NS) for a low-complexity approximation. By introducing a relaxation parameter jointly with one selected user's interference to others into the precondition matrix, we propose the identity-plus-column NS (ICNS) method. By further exploiting the multi-user diversity gain via choosing the user with the largest interference to others, the ordered ICNS method is also proposed. Moreover, the sum-rate approximations of the proposed ICNS method and the competitive existing identity matrix based NS (INS) method are derived in closed-form, based on which the performance loss of ICNS due to inversion approximation compared with ideal ZF and its performance gain over INS are explicitly analyzed for three typical massive MIMO scenarios. Finally, simulations verify our analytical results and also show that the proposed two designs achieve better performance-complexity tradeoff than ideal ZF and existing low-complexity ZF precodings for practical large antenna number, correlated channels and not-so-small loading factor., Comment: 30 Pages, 9 figures, submitted to IEEE Transactions on Communications

In this paper, we study the beam-based training design jointly with the transmission design for hybrid massive antenna single-user (SU) and multiple-user (MU) systems where outage probability is adopted as the performance measure. For SU systems, we propose an interleaved training design to concatenate the feedback and training procedures, thus making the training length adaptive to the channel realization. Exact analytical expressions are derived for the average training length and the outage probability of the proposed interleaved training. For MU systems, we propose a joint design for the beam-based interleaved training, beam assignment, and MU data transmissions. Two solutions for the beam assignment are provided with different complexity-performance tradeoff. Analytical results and simulations show that for both SU and MU systems, the proposed joint training and transmission designs achieve the same outage performance as the traditional full-training scheme but with significant saving in the training overhead., Comment: 16 Pages (double column), 11 figures. This work has been accepted by the IEEE Journal of Selected Topics in Signal Processing (JSTSP), Special Issue on Hybrid Analog - Digital Signal Processing for Hardware-Efficient Large Scale Antenna Arrays. This version is different from the former one due to the revisions made for the comments of 1st and 2nd round review

The ever increasing demands for mobile network access have resulted in a significant increase in bandwidth usage. By improving the system spectral efficiency, multi-way relay networks (MWRNs) provide promising approaches to address this challenge. In this paper, we propose a novel linear beamforming design, namely partial zero-forcing (PZF), for MWRNs with a multiple-input-multiple-output (MIMO) relay. Compared to zero-forcing (ZF), PZF relaxes the constraints on the relay beamforming matrix such that only partial user-interference, instead of all, is canceled at the relay. The users eliminate the remaining interferences through self-interference and successive interference cancellation. A sum-rate maximization problem is formulated and solved to exploit the extra degrees-of-freedom resulted from PZF. Simulation results show that the proposed PZF relay beamforming design achieves significantly higher network sum-rates than the existing linear beamforming designs.

For massive MIMO public channel with any sector size in either microwave or millimeter wave (mmwave) band, this paper studies the beamforming design to minimize the transmit power while guaranteeing the quality of service (QoS) for randomly deployed users. First the ideal beampattern is derived via Parseval Identity, based on which a beamforming design problem is formulated to minimize the gap with the idea beampattern. The problem is transformable to a multiconvex one and an iterative optimization algorithm is used to obtain the full-digital beamformer. In addition, with the help of same beampattern theorem, the power amplifier (PA) efficiency of the beamformer is improved with unchanged beampattern. Finally, the practical hybrid implementation is obtained that achieves the full-digital beamformer solution. Simulations verify the advantages of the proposed scheme over existing ones., Comment: Accepted by IEEE Transactions on Vehicular Technology

This work provides a comprehensive scaling law based performance analysis for multi-cell multi-user massive multiple-input-multiple-output (MIMO) downlink systems. Imperfect channel state information (CSI), pilot contamination, and channel spatial correlation are all considered. First, a sum- rate lower bound is derived by exploiting the asymptotically deterministic property of the received signal power, while keeping the random nature of other components in the signal-to-interference-plus-noise-ratio (SINR) intact. Via a general scaling model on important network parameters, including the number of users, the channel training energy and the data transmission power, with respect to the number of base station antennas, the asymptotic scaling law of the effective SINR is obtained, which reveals quantitatively the tradeoff of the network parameters. More importantly, pilot contamination and pilot contamination elimination (PCE) are considered in the analytical framework. In addition, the applicability of the derived asymptotic scaling law in practical systems with large but finite antenna numbers are discussed. Finally, sufficient conditions on the parameter scalings for the SINR to be asymptotically deterministic in the sense of mean square convergence are provided, which covers existing results on such analysis as special cases and shows the effect of PCE explicitly., Comment: 14 pages, 7 figures, accepted by IEEE Transactions on Vehicular Technology

Mean-squared-error (MSE) is one of the most widely used performance metrics for the designs and analysis of multi-input-multiple-output (MIMO) communications. Weighted MSE minimization, a more general formulation of MSE minimization, plays an important role in MIMO transceiver optimization. While this topic has a long history and has been extensively studied, existing treatments on the methods in solving the weighted MSE optimization are more or less sporadic and non-systematic. In this paper, we firstly review the two major methodologies, Lagrange multiplier method and majorization theory based method, and their common procedures in solving the weighted MSE minimization. Then some problems and limitations of the methods that were usually neglected or glossed over in existing literature are provided. These problems are fundamental and of critical importance for the corresponding MIMO transceiver optimizations. In addition, a new extended matrix-field weighted MSE model is proposed. Its solutions and applications are discussed in details. Compared with existing models, this new model has wider applications, e.g., nonlinear MIMO transceiver designs and capacity-maximization transceiver designs for general MIMO networks., Comment: 34 Pages, 4 figures

This paper investigated the uplink of multi-user massive multi-input multi-output (MIMO) systems with a mixed analog-to-digital converter (ADC) receiver architecture, in which some antennas are equipped with costly full-resolution ADCs and others with less expensive low-resolution ADCs. A closed-form approximation of the achievable spectral efficiency (SE) with the maximum-ratio combining (MRC) detector is derived. Based on this approximated result, the effects of the number of base station antennas, the transmit power, the proportion of full-resolution ADCs in the mixed-ADC structure, and the number of quantization bits of the low-resolution ADCs are revealed. Results showcase that the achievable SE increases with the number of BS antennas and quantization bits, and it converges to a saturated value in the high user power regime or the full ADC resolution case. Most important, this work efficiency verifies that for massive MIMO, the mixed-ADC receiver with a small fraction of full-resolution ADCs can have comparable SE performance with the receiver with all full-resolution ADCs but at a considerably lower hardware cost., Comment: 11 pages, 3 figures

This work provides a comprehensive scaling law and performance analysis for multi-user massive MIMO relay networks, where the relay is equipped with massive antennas and uses MRC/MRT for low-complexity processing. CSI error is considered. First, a sum-rate lower bound is derived which manifests the effect of system parameters including the numbers of relay antennas and users, the CSI quality, and the transmit powers of the sources and the relay. Via a general scaling model on the system parameters with respect to the relay antenna number, the asymptotic scaling law of the SINR as a function of the parameter scalings is obtained, which shows quantitatively the tradeoff between the network parameters and their effect on the network performance. In addition, a sufficient condition on the parameter scalings for the SINR to be asymptotically deterministic is given, which covers existing studies on such analysis as special cases. Then, the scenario where the SINR increases linearly with the relay antenna number is studied. The sufficient and necessary condition on the parameter scaling for this scenario is proved. It is shown that in this case, the interference power is not asymptotically deterministic, then its distribution is derived, based on which the outage probability and average bit error rate of the relay network are analysed., Comment: 30 pages, 5 figures, submitted to IEEE Trans. Wireless Commun

In this paper, we analyze the achievable rate of the uplink of a single-cell multi-user distributed massive multiple-input-multiple-output (MIMO) system. The multiple users are equipped with single antenna and the base station (BS) is equipped with a large number of distributed antennas. We derive an analytical expression for the asymptotic ergodic achievable rate of the system under zero-forcing (ZF) detector. In particular, we consider circular antenna array, where the distributed BS antennas are located evenly on a circle, and derive an analytical expression and closed-form tight bounds for the achievable rate of an arbitrarily located user. Subsequently, closed-form bounds on the average achievable rate per user are obtained under the assumption that the users are uniformly located in the cell. Based on the bounds, we can understand the behavior of the system rate with respect to different parameters and find the optimal location of the circular BS antenna array that maximizes the average rate. Numerical results are provided to assess our analytical results and examine the impact of the number and the location of the BS antennas, the transmit power, and the path-loss exponent on system performance. It is shown that circularly distributed massive MIMO system largely outperforms centralized massive MIMO system., Comment: Single column, 30 pages, 8 figures. Submitted to IEEE Transactions on Wireless Communications

This paper considers a multi-user single-relay wireless network, where the relay gets paid for helping the users forward signals, and the users pay to receive the relay service. We study the relay power allocation and pricing problems, and model the interaction between the users and the relay as a two-level Stackelberg game. In this game, the relay, modeled as the service provider and the leader of the game, sets the relay price to maximize its revenue; while the users are modeled as customers and the followers who buy power from the relay for higher transmission rates. We use a bargaining game to model the negotiation among users to achieve a fair allocation of the relay power. Based on the proposed fair relay power allocation rule, the optimal relay power price that maximizes the relay revenue is derived analytically. Simulation shows that the proposed power allocation scheme achieves higher network sum-rate and relay revenue than the even power allocation. Furthermore, compared with the sum-rate-optimal solution, simulation shows that the proposed scheme achieves better fairness with comparable network sum-rate for a wide range of network scenarios. The proposed pricing and power allocation solutions are also shown to be consistent with the laws of supply and demand.

This paper investigates the relay selection (RS) problem in networks with multiple users and multiple common amplify-and-forward (AF) relays. Considering the overall quality-of-service of the network, we first specify our definition of optimal RS for multiple-user relay networks. Then an optimal RS (ORS) algorithm is provided, which is a straightforward extension of an RS scheme in the literature that maximizes the minimum end-to-end receive signal-to-noise ratio (SNR) of all users. The complexity of the ORS is quadratic in both the number of users and the number of relays. Then a suboptimal RS (SRS) scheme is proposed, which has linear complexity in the number of relays and quadratic complexity in the number of users. Furthermore, diversity orders of both the ORS and the proposed SRS are theoretically derived and compared with those of a naive RS scheme and the single-user RS network. It is shown that the ORS achieves full diversity; while the diversity order of the SRS decreases with the the number of users. For two-user networks, the outage probabilities and array gains corresponding to the minimum SNR of the RS schemes are derived in closed forms. It is proved that the advantage of the SRS over the naive RS scheme increases as the number of relays in the network increases. Simulation results are provided to corroborate the analytical results.

This paper considers transmission schemes in multi-access relay networks (MARNs) where $J$ single-antenna sources send independent information to one $N$-antenna destination through one $M$-antenna relay. For complexity considerations, we propose a linear framework, where the relay linearly transforms its received signals to generate the forwarded signals without decoding and the destination uses its multi-antennas to fully decouple signals from different sources before decoding, by which the decoding complexity is linear in the number of sources. To achieve a high symbol rate, we first propose a scheme called DSTC-ICRec in which all sources' information streams are concurrently transmitted in both the source-relay link and the relay-destination link. In this scheme, distributed space-time coding (DSTC) is applied at the relay, which satisfies the linear constraint. DSTC also allows the destination to conduct the zero-forcing interference cancellation (IC) scheme originally proposed for multi-antenna systems to fully decouple signals from different sources. Our analysis shows that the symbol rate of DSTC-ICRec is $1/2$ symbols/source/channel use and the diversity gain of the scheme is upperbounded by $M-J+1$. To achieve a higher diversity gain, we propose another scheme called TDMA-ICRec in which the sources time-share the source-relay link. The relay coherently combines the signals on its antennas to maximize the signal-to-noise ratio (SNR) of each source, then concurrently forwards all sources' information. The destination performs zero-forcing IC. It is shown through both analysis and simulation that when $N \ge 2J-1$, TDMA-ICRec achieves the same maximum diversity gain as the full TDMA scheme in which the information stream from each source is assigned to an orthogonal channel in both links, but with a higher symbol rate., Comment: submitted to IEEE Transaction on Signal Processing

We study multi-user transmission and detection schemes for a multi-access relay network (MARN) with linear constraints at all nodes. In a $(J, J_a, R_a, M)$ MARN, $J$ sources, each equipped with $J_a$ antennas, communicate to one $M$-antenna destination through one $R_a$-antenna relay. A new protocol called IC-Relay-TDMA is proposed which takes two phases. During the first phase, symbols of different sources are transmitted concurrently to the relay. At the relay, interference cancellation (IC) techniques, previously proposed for systems with direct transmission, are applied to decouple the information of different sources without decoding. During the second phase, symbols of different sources are forwarded to the destination in a time division multi-access (TDMA) fashion. At the destination, the maximum-likelihood (ML) decoding is performed source-by-source. The protocol of IC-Relay-TDMA requires the number of relay antennas no less than the number of sources, i.e., $R_a\ge J$. Through outage analysis, the achievable diversity gain of the proposed scheme is shown to be $\min\{J_a(R_a-J+1),R_aM\}$. When {\small$M\le J_a\left(1-\frac{J-1}{R_a}\right)$}, the proposed scheme achieves the maximum interference-free (int-free) diversity gain $R_aM$. Since concurrent transmission is allowed during the first phase, compared to full TDMA transmission, the proposed scheme achieves the same diversity, but with a higher symbol rate., Comment: submitted to IEEE Transaction on Wireless Communication