Precoding Matrices Research Articles

Distributed MIMO Broadcasting: Reverse Compute-and-Forward and Signal-Space Alignment

We study a downlink distributed MIMO system where a central unit (CU) broadcasts messages to $K^{\prime }$ users through $K$ distributed BSs. The CU is connected to the BSs via $K$ independent rate-constrained fronthaul (FH) links. The distributed BSs collectively serve the users through the air. We propose a new network coding based distributed MIMO broadcasting scheme, using reverse compute-and-forward and signal-space alignment. At the CU, a network coding generator matrix is employed for pre network coding of the users’ messages. The network coded messages are forwarded to the BSs, where the FH rate-constraint determines the actual number of network-coded messages forwarded to the BSs. At the BSs, linear precoding matrices are designed to create a number of bins , each containing a bunch of spatial streams with aligned signal-spaces. At each user, post physical-layer network coding is employed to compute linear combinations over the NC messages with respect to the bins, which reverses the prenetwork coding and recovers the desired messages. We derive an achievable rate of the proposed scheme based on the existence of NC generator matrix, signal-space alignment precoding matrices, and nested lattice codes. Improved rate and degrees of freedom over existing interference alignment and compress-and-forward schemes are shown. Numerical results demonstrate the performance improvement, e.g., by as much as 70% increase in throughput over benchmark schemes.

TDD-sparse index multiple access for joint data detection and device identification in MTC

In this paper, we study pre-equalization for sparse index multiple access (SIMA), which was proposed to enable one-shot identification and detection in random access, over frequency-selective fading channels in time division duplexing (TDD) mode. Each device is to decide a transmit vector to adapt to its channel for pre-equalization based on the channel reciprocity. Due to pre-equalization, the receiver does not need to estimate the channel state information (CSI) of active devices. We further modify pre-equalization with multiple precoding matrices for a better performance with a lower transmission power. For low signaling overhead in random access, we also consider one-shot identification and detection to perform active device identification and their signal detection simultaneously with a low-complexity algorithm by exploiting the sparsity of device activity as well as unique identification sequences.

Transceiver Optimization for Two-Hop MIMO Relay Systems With Direct Link and MSE Constraints

In this paper, we investigate the transceiver design in a two-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system with the direct link and quality-of-service (QoS) constraint. The QoS criterion is specified by the upper bound of the mean-squared error of the signal waveform estimation at the destination node. To minimize the total system transmission power, we apply a new AF relay protocol where the source node transmits signals during both time slots. Two iterative algorithms are proposed to jointly optimize the source and relay precoding matrices for the general case with multiple concurrent data streams, and the special case where a single data stream is transmitted, respectively. Simulation results show the effectiveness of both proposed algorithms. Interestingly, for the single data stream case, the second algorithm converges faster than the first algorithm. Compared with conventional two-hop MIMO relay systems where the source node is silent at the second time slot, the new protocol reduces the system transmission power. Under a given system transmission power, the proposed algorithms yield a higher system mutual information thanks to a better utilization of the direct link. Simulation results in this paper shed lights on some fundamental questions in relay system design such as when direct communication between source and destination (without any relay nodes) is optimal, and when the new AF relay protocol provides a larger gain compared with the conventional single phase source power allocation.

Precoding-Based Inter-Relay Interference Cancellation for Amplify-and-Forward Two-Path Successive Relay Networks

In this letter, we consider the inter-relay interference (IRI) problem for amplify-and-forward (AF) two-path successive relay networks. To reduce processing burden for IRI cancelation at the relay nodes, a novel precoding-based interference cancelation scheme based on row-space mapping is proposed, where a pair of orthogonal precoding matrices is alternately utilized to project the source data onto the null space of the received data that is independent of channel state information (CSI). By designing a combined decoding and re-encoding scheme, both the IRI signal and accumulated noise are perfectly suppressed at the relay nodes. Simulation results show that the proposed scheme is significantly better than the channel estimate based interference cancelation schemes.

Information Guided Precoding for OFDM

In conventional orthogonal frequency division multiplexing with index modulation (OFDM-IM), the $M$ -ary modulated symbols are transmitted on a subset of subcarriers under the guidance of information bits. In this paper, a novel information guided precoding technique, called precoding aided (P-) OFDM-IM, is proposed to improve the spectral efficiency (SE) of OFDM-IM. In P-OFDM-IM, the information bits are jointly conveyed through the conventional $M$ -ary modulated symbols and the indices of precoding matrices and vectors. The P-OFDM-IM principle is embodied in two different implementations, P-OFDM-IM-I and P-OFDM-IM-II. Specifically, P-OFDM-IM-I divides all subcarriers into $L$ groups and modulates them using $L$ distinguishable constellations. P-OFDM-IM-II partitions the set of all subcarriers into $L$ overlapping layers and performs IM layer by layer, where distinguishable constellations are employed across layers. A practical precoding strategy is designed for P-OFDM-IM under the phase shift keying/quadrature amplitude modulation constraint. A low-complexity log-likelihood ratio detector is proposed to ease the computational burden on the receiver. To evaluate the performance of P-OFDM-IM analytically, an upper bound on the bit error rate and the achievable rate is studied. Computer simulation results show that P-OFDM-IM-I outperforms the existing OFDM-IM-related schemes at high SE, while P-OFDM-IM-II performs the best at low SE.

A Signal-Space Aligned Network Coding Approach to Distributed MIMO

This paper studies an uplink distributed MIMO (DMIMO) system that consists of $K$ users and $K^{\prime }$ distributed base stations (BSs), where the BSs are connected to a central unit (CU) via independent rate-constrained backhaul (BH) links. We propose a new signal-space aligned network coding scheme. First, a network coding generator matrix is selected subject to certain structural properties. Next, distributed linear precoding is employed by the users to create aligned signal-spaces at the BSs, according to the pattern determined by the network coding generator matrix. For each aligned signal-space at a BS, physical-layer network coding is utilized to compute the corresponding network-coded (NC) messages, where the actual number of NC messages forwarded to the CU is determined by the BH rate-constraint. We derive an achievable rate of the proposed scheme based on the existence of the NC generator matrix and signal-space alignment precoding matrices. For DMIMO with two and three BSs, the achievable rates and degrees of freedom (DoF) are evaluated and shown to outperform existing schemes. For example, for DMIMO with two BSs where each user and BS have $N$ and $N^{\prime }$ antennas, respectively, the proposed scheme achieves a DoF of $2\min \left(N,N^{\prime }\right) -1$ , if the BH capacity scales like $\left(2\min \left(N,N^{\prime }\right) -1\right) \log\;{SNR}$ . This leads to greater DoF compared to that utilizes the strategy for interference channel, whose DoF is $\min \left(N,N^{\prime }\right)$ . Numerical results demonstrate the performance advantage of the proposed scheme.

Sum Rate Maximization for Non-Regenerative MIMO Relay Networks

A multiple-antenna amplify-and-forward (AF) two-hop interference network with multiple links and multiple relays is considered. In this paper, we optimize the transmit precoders, the receiver decoders, and the relay AF matrices to maximize the achievable sum rate. First, the total signal to total interference plus noise ratio (TSTINR) maximization approach is proposed to approximate the sum rate maximization problem as a lower bound. Under individual user and individual relay transmit power constraints, an efficient alternating direction algorithm is proposed to maximize the TSTINR. Then, we modify our TSTINR model as well as the algorithm to guarantee multiple data stream transmission, by requiring the precoding matrices to have a certain number of orthogonal columns. We propose the stream selection for preprocessing, and prove that the stream selection problem to maximize the sum rate is NP-hard. Simulation results show that our proposed stream selection TSTINR model achieves much higher sum rate compared to the existing model with the same computational cost; the proposed algorithm solves the problems efficiently, and the computation time is significantly reduced.

Sum-Rate Maximization for Multiuser MIMO Wireless Powered Communication Networks

This paper investigates multiuser multiple-input–multiple-output (MIMO) wireless powered communication networks where a multiantenna hybrid access point (H-AP) transfers wireless energy to multiantenna users in a downlink phase, and the users utilize the harvested energy for their information transmission to the H-AP in an uplink phase. By employing space-division multiple-access techniques, we propose an optimal algorithm that jointly computes the downlink energy precoding matrices, the uplink information precoding matrices, and time allocation between the downlink and the uplink phases for maximizing the uplink sum-rate performance. To this end, we first obtain the optimal energy and information transmit covariance matrices with given time allocation. Then, the optimal time allocation can be efficiently identified by a simple line search method. Simulation results verify that the proposed joint optimal algorithm significantly improves the average sum-rate performance, compared with a conventional scheme that determines time allocation and precoding matrices separately.

MRT precoding in downlink multi-user MIMO systems

This paper focuses on the design of maximum ratio transmission (MRT) precoding for multi-user multiple-input multiple-output (MU-MIMO) downlink transmission. Exiting block diagonalization (BD) precoding studies on MU-MIMO systems have the high complexity, because the transmitter precoding matrices constructed by singular value decomposition (SVD) are successively calculated twice. The MRT scheme construct precoding vectors aimed at each received antennas, respectively, so the signals of every antenna are independent. More spatial diversity gain can be obtained compared with BD precoding when MRT precoding and maximum ratio combining are employed. Simulations show that the proposed algorithm has many gains over the conventional BD precoding in various MU-MIMO systems.

Destination-Aided Cooperative Jamming for Dual-Hop Amplify-and-Forward MIMO Untrusted Relay Systems

In this paper, we consider a dual-hop amplify-and-forward (AF) multiple-input–multiple-output (MIMO) relay network, where the source, relay, and destination are each equipped with multiple antennas. The relay is untrusted if it is willing to forward the signal to the destination and, at the same time, acts as a potential eavesdropper to interpret the message from the source. Since there exists no direct link between the source and the destination, a positive secrecy rate cannot be obtained. Addressing this issue, we propose a joint destination-aided cooperative jamming and precoding at both the source and the relay scheme: joint source, relay, and destination precoding (JP). We target at maximizing the secrecy rate by jointly designing the source, relay, and destination precoding matrices and propose an alternating iterative optimization algorithm to tackle the nonconvex problem. Then, a comprehensive study on the asymptotic performance is conducted in a high signal-to-noise ratio (SNR) regime. In particular, we present simple closed-form expressions for the two key performance parameters in the asymptotic secrecy rate, i.e., the high-SNR slope and the high-SNR power offset. Finally, numerical results are conducted to demonstrate the validity of the proposed secure scheme and its performance analysis.

Perfect Secrecy in Physical-Layer Network Coding Systems From Structured Interference

Physical-layer network coding (PNC) has been proposed for next generation networks. In this paper, we investigate PNC schemes with embedded perfect secrecy by exploiting structured interference in relay networks with two users and a single relay. In a practical scenario where both users employ finite and uniform signal input distributions, we establish upper bounds (UBs) on the achievable perfect secrecy rates and make these explicit when pulse amplitude modulation modems are used. We then describe two simple, explicit encoders that can achieve perfect secrecy rates close to these UBs with respect to an untrustworthy relay in the single antenna and single relay setting. Last, we generalize our system to a multiple-input multiple-output relay channel, where the relay has more antennas than the users and study optimal precoding matrices, which maintain a required secrecy constraint. Our results establish that the design of PNC transmission schemes with enhanced throughput and guaranteed data confidentiality is feasible in next generation systems.

Fronthaul Compression and Precoding Design for C-RANs Over Ergodic Fading Channels

This work investigates the joint design of fronthaul compression and precoding for the downlink of Cloud Radio Access Networks (C-RANs). In a C-RAN, a central unit (CU) performs the baseband processing for a cluster of radio units (RUs) that receive compressed baseband samples from the CU through low-latency fronthaul links. Most previous works on the design of fronthaul compression and precoding assume constant channels and instantaneous channel state information (CSI) at the CU. This work, in contrast, concentrates on a more practical scenario with block-ergodic channels and considers either instantaneous or stochastic CSI at the CU. Moreover, the analysis encompasses both the Compression-After-Precoding (CAP) and the Compression-Before-Precoding (CBP) schemes. With the CAP approach, which is the standard C-RAN solution, the CU performs channel coding and precoding and then the CU compresses and forwards the resulting baseband signals on the fronthaul links to the RUs. With the CBP scheme, instead, the CU does not perform precoding but rather forwards separately the information messages of a subset of mobile stations (MSs) along with the compressed precoding matrices to the each RU, which then performs precoding. Optimization algorithms over fronthaul compression and precoding for both CAP and CBP are proposed that are based on a stochastic successive upper-bound minimization approach. Via numerical results, the relative merits of the two strategies under either instantaneous or stochastic CSI are evaluated as a function of system parameters such as fronthaul capacity and channel coherence time.

Clustered linear precoding for downlink network MIMO systems with partial CSI

AbstractWe propose two novel clustered linear precoding schemes applicable to network multi‐input multi‐output systems using only partial channel state information to enhance the sum‐rate of the system. Using a channel model that decomposes a multi‐input multi‐output channel matrix into transmit and receive steering vectors and assuming that only transmit steering vectors are available at the base transmit stations, we, first, propose a regularized channel inversion precoding scheme to enhance the sum‐rate assuming only single‐antenna users are available in the system. Next, because of the limitation of regularized channel inversion to handle users with multiple receive antennas, a novel block diagonalization method is proposed. We construct the precoding matrices that jointly eliminate inter‐cell interference and maximize the sum‐rate for a given input covariance matrix. Assuming total power constraint and per‐base‐station power constraints, optimal power allocation schemes are further developed to optimize the sum‐rate. We analytically show that the sum‐rate increases linearly with the number of users when only single‐antenna users are present in the system. Numerical results show that at low signal‐to‐noise ratios, the block diagonalization precoding outperforms the regularized channel inversion in terms of the bit error rate; while at high signal‐to‐noise ratios, the regularized channel inversion provides a better performance. Copyright © 2016 John Wiley & Sons, Ltd.

Secure Multiuser MIMO Downlink Transmission Via Precoding-Aided Spatial Modulation

This letter generalizes the precoding-aided spatial modulation (PSM) to a multiuser (MU) downlink scenario. With precoding vectors elaborately designed, a proposed MU-PSM scheme has the capability to resist a multiple antenna eavesdropper. Specifically, signal precoding matrices (SPMs) are designed to cancel the MU interference and modulate partial information bits on the indices of receive antennas. To improve physical layer security, scrambling on SPMs is conceived to construct a fast-varying precoding matrix, which contributes to the degradation at Eve’s blind estimation and detection. Moreover, issues of detection algorithms and a lower bound of secrecy rate are addressed to verify security enhancement in the proposed scheme.

Transceiver optimization for multi-antenna device-to-device communications

It has been shown that the deployment of device-to-device (D2D) communication in cellular systems can provide better support for local services. However, improper design of the hybrid system may cause severe interference between cellular and D2D links. In this paper, we consider transceiver design for the system employing multiple antennas to mitigate the interference. The precoder and decoder matrices are optimized in terms of sum mean squared error (MSE) and capacity, respectively. For the MSE minimization problem, we present an alternative transceiver optimization algorithm. While for the non-convex capacity maximization problem, we decompose the primal problem into a sequence of standard convex quadratic programs for efficient optimization. The evaluation of our proposed algorithms for performance enhancement of the entire D2D integrated cellular system is carried out through simulations.

Robust Transceiver Design for Two-User MIMO Interference Channel With Simultaneous Wireless Information and Power Transfer

For two-user multiple-input–multiple-output interference channels with simultaneous wireless information and power transfer, we investigate robust transceiver design problem where channel uncertainties are modeled by worst case model. Our objective is to minimize worst case sum mean square error under individual transmit power constraints and worst case energy harvesting (EH) constraints. We propose to transform the quadratic EH constraints into linear matrix inequalities combined with two equality constraints. Furthermore, we propose to employ an algorithm based on constrained concave–convex procedure to alternatively optimize precoding matrices and postprocessing matrices. Simulation results demonstrate that our proposed robust transceiver design has significant performance gain over the nonrobust one.

On the Number of RF Chains and Phase Shifters, and Scheduling Design With Hybrid Analog–Digital Beamforming

This paper considers hybrid beamforming (HB) for downlink multiuser massive multiple input multiple output (MIMO) systems with frequency selective channels. For this system, first we determine the required number of radio frequency (RF) chains and phase shifters (PSs) such that the proposed HB achieves the same performance as that of the digital beamforming (DB) which utilizes $N$ (number of transmitter antennas) RF chains. We show that the performance of the DB can be achieved with our HB just by utilizing $r_t$ RF chains and $2r_t(N-r_t + 1)$ PSs, where $r_t \leq N$ is the rank of the combined digital precoder matrices of all sub-carriers. Second, we provide a simple and novel approach to reduce the number of PSs with only a negligible performance degradation. Numerical results reveal that only $20-40$ PSs per RF chain are sufficient for practically relevant parameter settings. Finally, for the scenario where the deployed number of RF chains $(N_a)$ is less than $r_t$, we propose a simple user scheduling algorithm to select the best set of users in each sub-carrier. Simulation results validate theoretical expressions, and demonstrate the superiority of the proposed HB design over the existing HB designs in both flat fading and frequency selective channels.

Throughput optimisation for energy harvesting transmitter with partial instantaneous channel state information and finite‐alphabet inputs

Wireless communication systems with energy harvester are attracting much attention due to their ability to improve the system operation time. Extensive research has been carried out on how to maximise the sum of mutual information over multiple time slots (i.e. the throughput). However, most research focuses on the energy harvesting transmitter with Gaussian inputs and single antenna. This study considers the throughput maximisation problem for an energy harvesting transmitter with causal energy constraint over multiple-input multiple-output (MIMO) channels. Different from existing works, the authors consider the MIMO system with finite-alphabet inputs and partial instantaneous channel state information (CSI). Specifically, the transmitter knows the statistical CSI of the entire channel frame as well as the instantaneous CSI of current time slot. The precoder design in this scenario is an intractable optimisation problem with respect to multiple precoding matrices. The authors’ analysis shows that this difficult precoding problem can be equivalently transformed into a set of scalar optimisation subproblems with respect to the transmit power. To solve these subproblems, an efficient algorithm based on the dynamic programming is proposed. The authors analyse the performance of the proposed algorithm, and simulation results validate its effectiveness.

Transceiver Design in Full-Duplex MIMO Cognitive Radios Under Channel Uncertainties

In this paper, the operation of a full-duplex (FD) multiple-input multiple-output (MIMO) underlay cognitive radio (CR) network is studied. Each pair of secondary users (SUs) operate in FD mode, and each SU communicates with its peer within the coverage area of multiple primary users (PUs). Each SU suffers from self-interference, along with interference created by all other SUs and, in its turn, generates interference towards the PU. We assume that the channel-state-information (CSI) of the interference links between the SUs and the PU is imperfectly known and the channel estimation errors are norm bounded. Under such channel uncertainties, we address the problem of robust minimization of the aggregate mean-squared-error (MSE) of all estimated symbols, subject to a set of transmit power constraints, as well as interference constraints, with the aim of protecting PU communication. It is shown that the problem can be cast as a semidefinite programming problem and the optimal precoding matrices can be obtained via an iterative algorithm. By means of simulation, the proposed FD precoding scheme is shown to outperform the standard half-duplex scheme.

Improving Wireless Physical Layer Security via Exploiting Co-Channel Interference

This paper considers a scenario in which a source-destination pair needs to establish a confidential connection against an external eavesdropper, aided by the interference generated by another source-destination pair that exchanges public messages. The goal is to compute the maximum achievable secrecy degrees of freedom (S.D.o.F) region of a MIMO two-user wiretap network. First, a cooperative secrecy transmission scheme is proposed, whose feasible set is shown to achieve all S.D.o.F. pairs on the S.D.o.F. region boundary. In this way, the determination of the S.D.o.F. region is reduced to a problem of maximizing the S.D.o.F. pair over the proposed transmission scheme. The maximum achievable S.D.o.F. region boundary points are obtained in closed form, and the construction of the precoding matrices achieving the maximum S.D.o.F. region boundary is provided. The obtained analytical expressions clearly show the relation between the maximum achievable S.D.o.F. region and the number of antennas at each terminal.