Subspace Tracking and Least Squares Approaches to Channel Estimation in Millimeter Wave Multiuser MIMO

The problem of MIMO channel estimation at millimeter wave frequencies, both in a single-user and in a multi-user setting, is tackled in this paper. Using a subspace approach, we develop a protocol enabling the estimation of the right (resp. left) singular vectors at the transmitter (resp. receiver) side; then, we adapt the projection approximation subspace tracking with deflation and the orthogonal Oja algorithms to our framework and obtain two channel estimation algorithms. We also present an alternative algorithm based on the least squares approach. The hybrid analog/digital nature of the beamformer is also explicitly taken into account at the algorithm design stage. In order to limit the system complexity, a fixed analog beamformer is used at both sides of the communication links. The obtained numerical results, showing the accuracy in the estimation of the channel matrix dominant singular vectors, the system achievable spectral efficiency, and the system bit-error-rate, prove that the proposed algorithms are effective, and that they compare favorably, in terms of the performance-complexity trade-off, with respect to several competing alternatives.Comment: To appear on the IEEE Transactions on Communication

An Overview of Signal Processing Techniques for Millimeter Wave MIMO Systems

Communication at millimeter wave (mmWave) frequencies is defining a new era of wireless communication. The mmWave band offers higher bandwidth communication channels versus those presently used in commercial wireless systems. The applications of mmWave are immense: wireless local and personal area networks in the unlicensed band, 5G cellular systems, not to mention vehicular area networks, ad hoc networks, and wearables. Signal processing is critical for enabling the next generation of mmWave communication. Due to the use of large antenna arrays at the transmitter and receiver, combined with radio frequency and mixed signal power constraints, new multiple-input multiple-output (MIMO) communication signal processing techniques are needed. Because of the wide bandwidths, low complexity transceiver algorithms become important. There are opportunities to exploit techniques like compressed sensing for channel estimation and beamforming. This article provides an overview of signal processing challenges in mmWave wireless systems, with an emphasis on those faced by using MIMO communication at higher carrier frequencies.Comment: Submitted to IEEE Journal of Selected Topics in Signal Processin

Interference-Nulling Time-Reversal Beamforming for mm-Wave Massive MIMO in Multi-User Frequency-Selective Indoor Channels

Millimeter wave (mm-wave) and massive MIMO have been proposed for next generation wireless systems. However, there are many open problems for the implementation of those technologies. In particular, beamforming is necessary in mm-wave systems in order to counter high propagation losses. However, conventional beamsteering is not always appropriate in rich scattering multipath channels with frequency selective fading, such as those found in indoor environments. In this context, time-reversal (TR) is considered a promising beamforming technique for such mm-wave massive MIMO systems. In this paper, we analyze a baseband TR beamforming system for mm-wave multi-user massive MIMO. We verify that, as the number of antennas increases, TR yields good equalization and interference mitigation properties, but inter-user interference (IUI) remains a main impairment. Thus, we propose a novel technique called interference-nulling TR (INTR) to minimize IUI. We evaluate numerically the performance of INTR and compare it with conventional TR and equalized TR beamforming. We use a 60 GHz MIMO channel model with spatial correlation based on the IEEE 802.11ad SISO NLoS model. We demonstrate that INTR outperforms conventional TR with respect to average BER per user and achievable sum rate under diverse conditions, providing both diversity and multiplexing gains simultaneously.Comment: 25 pages, 9 figures, 2 table

Channel Estimation for Millimeter Wave Multiuser MIMO Systems via PARAFAC Decomposition

We consider the problem of uplink channel estimation for millimeter wave (mmWave) systems, where the base station (BS) and mobile stations (MSs) are equipped with large antenna arrays to provide sufficient beamforming gain for outdoor wireless communications. Hybrid analog and digital beamforming structures are employed by both the BS and the MS due to hardware constraints. We propose a layered pilot transmission scheme and a CANDECOMP/PARAFAC (CP) decomposition-based method for joint estimation of the channels from multiple users (i.e. MSs) to the BS. The proposed method exploits the sparse scattering nature of the mmWave channel and the intrinsic multi-dimensional structure of the multiway data collected from multiple modes. The uniqueness of the CP decomposition is studied and sufficient conditions for essential uniqueness are obtained. The conditions shed light on the design of the beamforming matrix, the combining matrix and the pilot sequences, and meanwhile provide general guidelines for choosing system parameters. Our analysis reveals that our proposed method can achieve a substantial training overhead reduction by employing the layered pilot transmission scheme. Simulation results show that the proposed method presents a clear advantage over a compressed sensing-based method in terms of both estimation accuracy and computational complexity

A Framework on Hybrid MIMO Transceiver Design based on Matrix-Monotonic Optimization

Hybrid transceiver can strike a balance between complexity and performance of multiple-input multiple-output (MIMO) systems. In this paper, we develop a unified framework on hybrid MIMO transceiver design using matrix-monotonic optimization. The proposed framework addresses general hybrid transceiver design, rather than just limiting to certain high frequency bands, such as millimeter wave (mmWave) or terahertz bands or relying on the sparsity of some specific wireless channels. In the proposed framework, analog and digital parts of a transceiver, either linear or nonlinear, are jointly optimized. Based on matrix-monotonic optimization, we demonstrate that the combination of the optimal analog precoders and processors are equivalent to eigenchannel selection for various optimal hybrid MIMO transceivers. From the optimal structure, several effective algorithms are derived to compute the analog transceivers under unit modulus constraints. Furthermore, in order to reduce computation complexity, a simple random algorithm is introduced for analog transceiver optimization. Once the analog part of a transceiver is determined, the closed-form digital part can be obtained. Numerical results verify the advantages of the proposed design.Comment: 13 pages,7 figures, IEEE Signal Processing 201

Fully-Connected vs. Sub-Connected Hybrid Precoding Architectures for mmWave MU-MIMO

Hybrid digital analog (HDA) beamforming has attracted considerable attention in practical implementation of millimeter wave (mmWave) multiuser multiple-input multiple-output (MU-MIMO) systems due to its low power consumption with respect to its digital baseband counterpart. The implementation cost, performance, and power efficiency of HDA beamforming depends on the level of connectivity and reconfigurability of the analog beamforming network. In this paper, we investigate the performance of two typical architectures for HDA MU-MIMO, i.e., the fully-connected (FC) architecture where each RF antenna port is connected to all antenna elements of the array, and the one-stream-per-subarray (OSPS) architecture where the RF antenna ports are connected to disjoint subarrays. We jointly consider the initial beam acquisition phase and data communication phase, such that the latter takes place by using the beam direction information obtained in the former phase. For each phase, we propose our own BA and precoding schemes that outperform the counterparts in the literature. We also evaluate the power efficiency of the two HDA architectures taking into account the practical hardware impairments, e.g., the power dissipation at different hardware components as well as the potential power backoff under typical power amplifier (PA) constraints. Numerical results show that the two architectures achieve similar sum spectral efficiency, but the OSPS architecture outperforms the FC case in terms of hardware complexity and power efficiency, only at the cost of a slightly longer time of initial beam acquisition

A Survey on MIMO Transmission with Discrete Input Signals: Technical Challenges, Advances, and Future Trends

Multiple antennas have been exploited for spatial multiplexing and diversity transmission in a wide range of communication applications. However, most of the advances in the design of high speed wireless multiple-input multiple output (MIMO) systems are based on information-theoretic principles that demonstrate how to efficiently transmit signals conforming to Gaussian distribution. Although the Gaussian signal is capacity-achieving, signals conforming to discrete constellations are transmitted in practical communication systems. As a result, this paper is motivated to provide a comprehensive overview on MIMO transmission design with discrete input signals. We first summarize the existing fundamental results for MIMO systems with discrete input signals. Then, focusing on the basic point-to-point MIMO systems, we examine transmission schemes based on three most important criteria for communication systems: the mutual information driven designs, the mean square error driven designs, and the diversity driven designs. Particularly, a unified framework which designs low complexity transmission schemes applicable to massive MIMO systems in upcoming 5G wireless networks is provided in the first time. Moreover, adaptive transmission designs which switch among these criteria based on the channel conditions to formulate the best transmission strategy are discussed. Then, we provide a survey of the transmission designs with discrete input signals for multiuser MIMO scenarios, including MIMO uplink transmission, MIMO downlink transmission, MIMO interference channel, and MIMO wiretap channel. Additionally, we discuss the transmission designs with discrete input signals for other systems using MIMO technology. Finally, technical challenges which remain unresolved at the time of writing are summarized and the future trends of transmission designs with discrete input signals are addressed.Comment: 110 pages, 512 references, submit to Proceedings of the IEE

Efficient Beam Alignment for mmWave Single-Carrier Systems with Hybrid MIMO Transceivers

Communication at millimeter wave (mmWave) bands is expected to become a key ingredient of next generation (5G) wireless networks. Effective mmWave communications require fast and reliable methods for beamforming at both the User Equipment (UE) and the Base Station (BS) sides, in order to achieve a sufficiently large Signal-to-Noise Ratio (SNR) after beamforming. We refer to the problem of finding a pair of strongly coupled narrow beams at the transmitter and receiver as the Beam Alignment (BA) problem. In this paper, we propose an efficient BA scheme for single-carrier mmWave communications. In the proposed scheme, the BS periodically probes the channel in the downlink via a pre-specified pseudo-random beamforming codebook and pseudo-random spreading codes, letting each UE estimate the Angle-of-Arrival / Angle-of-Departure (AoA-AoD) pair of the multipath channel for which the energy transfer is maximum. We leverage the sparse nature of mmWave channels in the AoA-AoD domain to formulate the BA problem as the estimation of a sparse non-negative vector. Based on the recently developed Non-Negative Least Squares (NNLS) technique, we efficiently find the strongest AoA-AoD pair connecting each UE to the BS. We evaluate the performance of the proposed scheme under a realistic channel model, where the propagation channel consists of a few multipath scattering components each having different delays, AoAs-AoDs, and Doppler shifts.The channel model parameters are consistent with experimental channel measurements. Simulation results indicate that the proposed method is highly robust to fast channel variations caused by the large Doppler spread between the multipath components. Furthermore, we also show that after achieving BA the beamformed channel is essentially frequency-flat, such that single-carrier communication needs no equalization in the time domain

Beam Acquisition and Training in Millimeter Wave Networks with Narrowband Pilots

This paper studies initial beam acquisition in a millimeter wave network consisting of multiple access points (APs) and mobile devices. A training protocol for joint estimation of transmit and receive beams is presented with a general frame structure consisting of an initial access sub-frame followed by data transmission sub-frames. During the initial subframe, APs and mobiles sweep through a set of beams and determine the best transmit and receive beams via a handshake. All pilot signals are narrowband (tones), and the mobiles are distinguished by their assigned pilot frequencies. Both non-coherent and coherent beam estimation methods based on, respectively, power detection and maximum likelihood (ML) are presented. To avoid exchanging information about beamforming vectors between APs and mobiles, a local maximum likelihood (LML) algorithm is also presented. An efficient fast Fourier transform implementation is proposed for ML and LML to achieve high-resolution. A system-level optimization is performed in which the frame length, training time, and training bandwidth are selected to maximize a rate objective taking into account blockage and mobility. Simulation results based on a realistic network topology are presented to compare the performance of different estimation methods and training codebooks, and demonstrate the effectiveness of the proposed protocol.Comment: 28 pages, 11 figure

Joint Spatial Division and Multiplexing for mm-Wave Channels

Massive MIMO systems are well-suited for mm-Wave communications, as large arrays can be built with reasonable form factors, and the high array gains enable reasonable coverage even for outdoor communications. One of the main obstacles for using such systems in frequency-division duplex mode, namely the high overhead for the feedback of channel state information (CSI) to the transmitter, can be mitigated by the recently proposed JSDM (Joint Spatial Division and Multiplexing) algorithm. In this paper we analyze the performance of this algorithm in some realistic propagation channels that take into account the partial overlap of the angular spectra from different users, as well as the sparsity of mm-Wave channels. We formulate the problem of user grouping for two different objectives, namely maximizing spatial multiplexing, and maximizing total received power, in a graph-theoretic framework. As the resulting problems are numerically difficult, we proposed (sub optimum) greedy algorithms as efficient solution methods. Numerical examples show that the different algorithms may be superior in different settings.We furthermore develop a new, "degenerate" version of JSDM that only requires average CSI at the transmitter, and thus greatly reduces the computational burden. Evaluations in propagation channels obtained from ray tracing results, as well as in measured outdoor channels show that this low-complexity version performs surprisingly well in mm-Wave channels.Comment: Accepted for publication in "JSAC Special Issue in 5G Communication Systems