Filter Precoding Research Articles

Millimeter Wave Massive MIMO Downlink Per-Group Communications With Hybrid Linear Precoding

We address the problem of analyzing and classifying into groups the downlink channel environment in a dense millimeter-wavelength cell, accounting for path loss, multipath fading, and User Equipment (UE) blocking, by employing a hybrid propagation and multipath fading model, thus using accurate inter-group interference modeling. The base station (BS) employs a large Uniform Planar Array (UPA) to facilitate massive Multiple-Input, Multiple-Output (MIMO) communications with high efficiency. UEs are equipped with a single antenna and are distributed uniformly within the cell. The key problem is analyzing and defining groups toward efficient precoding. Because balanced throughput is desired between groups, up to four separate frequency sub-carriers are employed in an Orthogonal Frequency Division Multiple Access (OFDMA) system. We show that by employing three or four OFDMA subcarriers, depending on the number of UEs in the cell and the cell range, the UEs can be efficiently separated into <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">high-throughput</i> groups, with each group employing Virtual Channel Model Beams (VCMB) based inner precoding, followed by efficient Multi-User Multiple-Input Multiple-Output (MU-MIMO) outer precoders. For each group, we study two different sub-grouping methods offering different advantages. We show that the improvement offered by Zero-Forcing Per-Group Precoding (ZF-PGP) over Matched Filter Precoding (MFP) and Zero-Forcing Precoding (ZFP) is very high when finite-alphabet inputs are used. We also show ZF-PGP with finite-alphabet inputs significantly outperforms MFP with Gaussian inputs in certain realistic setups. Finally, a new technique for power allocation among different UEs is proposed, called Optimized Per-Group Power Allocation (OPGPA), which achieves much higher power efficiency jointly with equal throughput among all UEs in each group.

Efficient Low-Complexity Antenna Selection Algorithms in Multi-User Massive MIMO Systems With Matched Filter Precoding

In this work, two efficient low complexity Antenna Selection (AS) algorithms are proposed for downlink Multi-User (MU) Massive Multiple-Input Multiple-Output (M-MIMO) systems with Matched Filter (MF) precoding. Both algorithms avoid vector multiplications during the iterative selection procedure to reduce complexity. Considering a system with N antennas at the Base Station (BS) serving K single-antenna users in the same time-frequency resources, the first algorithm divides the available antennas into K groups, with the kth group containing the N/K antennas that have the maximum channel norms for the kth user. Therefore, the Signal-to-Interference plus Noise Ratio (SINR) for the kth user can be maximized by selecting a subset of the antennas from only the kth group, thereby resulting in a search space reduction by a factor of K. The second algorithm is a semiblind interference rejection method that relies only on the signs of the interference terms, and at each iteration the antenna that rejects the maximum number of interference terms will be selected. The performance of our proposed methods is evaluated under perfect and imperfect Channel State Information (CSI) and compared with other low complexity AS schemes in terms of the achievable sum rate as well as the energy efficiency. In particular, when the Signal-to-Noise Ratio (SNR) is 10 dB, and for a system with 20 MHz of bandwidth, the proposed methods outperform the case where all the antennas are employed by 108.8 and 49.2 Mbps for the first and second proposed algorithms, respectively, given that the BS has perfect CSI knowledge and is equipped with 256 antennas, out of which 64 are selected to serve 8 single-antenna users.

Per-Tone Precoding and Per-Tone Equalization for OFDM and DMT Transmission Systems: Duality, Filter Optimization, and Resource Allocation

OFDM and DMT transmission systems add a cyclic prefix (CP) or zero pad (ZP) to the transmitted signal. Interference-free transmission requires this CP/ZP to be similarly long as the channel impulse response (CIR), reducing the achievable data rate in highly dispersive channels. A first strategy for dealing with long CIRs without increasing the CP/ZP overhead consists of applying a channel shortening filter to the received signal. A second strategy consists of spectral resource allocation, i.e. bit and power allocation to reduce interference. As little effort has been made towards joint channel shortening and resource allocation, a new algorithm to simultaneously optimize the channel shortening per-tone equalization (PTEQ) filters and the resource allocation is presented. In addition, transmitter-side channel shortening filters are considered, more specifically so-called per-tone precoding (PTPC) filters which apply the channel shortening filter before the IDFT modulation of the ODFM/DMT transmitter. At first glance, the FIR filter optimization for PTPC seems much more involved than the relatively straightforward FIR filter optimization for PTEQ. However, it will be demonstrated that any OFDM/DMT system with PTPC is - after time-reversing the CIR - equivalent to an OFDM/DMT system employing PTEQ. With this result in hand, systems with PTPC can take full advantage of the straightforward FIR filter optimization in systems with PTEQ, as well as of the aforementioned resource allocation algorithm. Simulation results show that the performance obtained for systems with PTPC is nearly indistinguishable from that obtained for systems with PTEQ, making PTPC an interesting alternative channel shortening strategy.

Data-Aided Secure Massive MIMO Transmission Under the Pilot Contamination Attack

In this paper, we study the design of secure communication for time division duplex multi-cell multi-user massive multiple-input multiple-output (MIMO) systems with active eavesdropping. We assume that the eavesdropper actively attacks the uplink pilot transmission and the uplink data transmission before eavesdropping the downlink data transmission of the users. We exploit both the received pilots and the received data signals for uplink channel estimation. We show analytically that when the number of transmit antennas and the length of the data vector both tend to infinity, the signals of the desired user and the eavesdropper lie in different eigenspaces of the received signal matrix at the base station provided that their signal powers are different. This finding reveals that decreasing (instead of increasing) the desired user's signal power might be an effective approach to combat a strong active attack from an eavesdropper. Inspired by this observation, we propose a data-aided secure downlink transmission scheme and derive an asymptotic achievable secrecy sum-rate expression for the proposed design. For the special case of a single-cell single-user system with independent and identically distributed fading, the obtained expression reveals that the secrecy rate scales logarithmically with the number of transmit antennas. This is the same scaling law as for the achievable rate of a single-user massive MIMO system in the absence of eavesdroppers. Numerical results indicate that the proposed scheme achieves significant secrecy rate gains compared to alternative approaches based on matched filter precoding with artificial noise generation and null space transmission.

Nonlinear Equalization Approaches for Physical Layer Network Coding

We consider a two-way relaying system employing physical layer network coding in channels suffering from frequency-selective fading. We study decision-feedback equalization (DFE), a technique based on delayed decision-feedback sequence estimation (DDFSE), and Tomlinson-Harashima precoding (THP) approaches for mitigating the distortions introduced by the channel. For DFE, we introduce transmit filtering schemes that generate identical overall source-to-relay channel impulse responses for both source nodes, while achieving the maximum signal-to-noise ratio after equalization for the zero-forcing and the minimum mean-squared error criterion, respectively. The advocated DDFSE approach also relies on transmit filtering at the source nodes. For the THP scheme, we derive the optimal precoding filters that guarantee an intersymbol interference free source-to-relay transmission. In order to obtain a two-way relaying system, which uses the same equalization techniques in both transmission directions, we design a THP-based compromise precoding scheme for the relay-to-destination transmission. The performance of the proposed techniques is compared with that of benchmark schemes with simpler filtering/precoding, where identical overall source-to-relay channel impulse responses are enforced by straightforward but suboptimum choices for the transmit filters. Our results reveal that the developed schemes enable significant gains compared with the benchmark schemes.

Three-Dimension Massive MIMO for Air-to-Ground Transmission: Location-Assisted Precoding and Impact of AoD Uncertainty

This paper investigates the 3-D massive multiple-input multiple-output (MIMO) for air-to-ground transmission, where an air platform (AP) is equipped with a 2-D rectangular antenna array and communicates with a number of user equipments (UEs) on the ground. By exploiting the slow time-varying parameters, such as channel correlation and angles of departure (AoDs) of UEs, we first propose a location-assisted two-layer precoding scheme for downlink transmission. The first-layer precoding aims to decompose the original massive MIMO system into several low-dimension MIMO systems, with each operating on the orthogonal subspace. Through proper UE clustering, we show that the first-layer precoding matrix can be approximated using a constant-envelope matrix, which results in significant reduction on hardware complexity of AP. The second-layer precoding is designed to eliminate the multi-UE interference within each low-dimension MIMO system. Since the AoD information is usually not perfectly known at AP, we then investigate the effect of AoD uncertainty on the performance of the proposed precoding scheme. In particular, we propose a new analytic method to fast estimate approximately the power loss due to AoD error. Numerical simulations are presented to evaluate the performance of location-assisted precoding under different system parameters, including Rician factor, altitude of AP, and AoD uncertainty. The results show that the location-assisted precoding outperforms match filter precoding and basis expansion-based precoding in the air-to-ground transmission scenarios significantly.

A Framework for Joint Design of Pilot Sequence and Linear Precoder

Most performance measures of pilot-assisted multiple-input multiple-output (MIMO) systems are functions that depend on both the linear precoding filter and the pilot sequence. A framework for the optimization of these two parameters is proposed, based on a matrix-valued generalization of the concept of effective signal-to-noise ratio (SNR) introduced in a famous work by Hassibi and Hochwald. The framework applies to a wide class of utility functions of said effective SNR matrix, most notably a well-known mutual information expression for Gaussian inputs, an upper bound on the minimum mean-square error (MMSE), as well as approximations thereof. The approach consists in decomposing the joint optimization problem into three subproblems: first, we describe how to reformulate the optimization of the linear precoder subject to a fixed pilot sequence as a convex problem. Second, we do likewise for the optimization of the pilot sequence subject to a fixed precoder. Third, we describe how to generate pairs of precoders and pilot sequences that are Pareto optimal in the sense that they attain the Pareto boundary of the set of feasible effective SNR matrices. By combining these three optimization problems into an iteration, we obtain an algorithm which allows to compute jointly optimal pairs of precoders and pilot sequences with respect to some generic utility function of the effective SNR.

Secure Massive MIMO Transmission With an Active Eavesdropper

In this paper, we investigate secure and reliable transmission strategies for multi-cell multi-user massive multiple-input multiple-output (MIMO) systems with a multi-antenna active eavesdropper. We consider a time-division duplex system where uplink training is required and an active eavesdropper can attack the training phase to cause pilot contamination at the transmitter. This forces the precoder used in the subsequent downlink transmission phase to implicitly beamform towards the eavesdropper, thus increasing its received signal power. Assuming matched filter precoding and artificial noise (AN) generation at the transmitter, we derive an asymptotic achievable secrecy rate when the number of transmit antennas approaches infinity. For the case of a single-antenna active eavesdropper, we obtain a closed-form expression for the optimal power allocation policy for the transmit signal and the AN, and find the minimum transmit power required to ensure reliable secure communication. Furthermore, we show that the transmit antenna correlation diversity of the intended users and the eavesdropper can be exploited in order to improve the secrecy rate. In fact, under certain orthogonality conditions of the channel covariance matrices, the secrecy rate loss introduced by the eavesdropper can be completely mitigated.

Power-Reductive Precoding for the Transmission of Correlated Information Sequences

In communication theory, the conventional role of precoding is to reshape a spectrally flat sequence of data symbols in favor of a particular inter-symbol interference (ISI) channel such that signal-to-noise power ratio (SNR) is maximized. In contrast, in this paper a novel precoding technique is devised to exploit a particular property of the information source rather than the channel. Specifically, we focus on the scenario where the source sequence has an inherent correlation that is known a priori, and design a precoding filter that attempts to reduce the average power of the resulting transmit symbol sequences. The proposed precoding technique is thus termed power-reductive precoding (PRP). This reduction of average transmit power accrues without changing the amplitude of the original sequence and thus can be treated as a system gain. An apparent drawback of this approach is the intentional ISI introduced by the precoding filter, which may lessen the minimum distance among legitimate sequences. Nevertheless, we show that even if the loss associated with the minimum distance penalty is properly taken into account, the achievable error rate versus SNR can be made superior to the case without precoding.

Feasibility Condition for Interference Alignment With Diversity

This paper studies the diversity benefit of different interference alignment solutions. While most research about interference alignment was aiming at deriving or realizing the maximum achievable multiplexing gain, the symbol error rate performance, which can be characterized by the diversity gain is of equal importance. Different interference alignment solutions are classified into two categories called diversity interference alignment and zero-forcing interference alignment. Although these two types of solutions are not distinguishable in terms of the multiplexing gain, this paper will show their difference lies in the fact that they have different diversity gains. In this paper, a K-user (M × N) interference channel is used, with each user sending 1 degree of freedom of information by using interference alignment precoding and receiving filters but without space-time codes. The feasibility conditions for diversity interference alignment to be achieved are analyzed and the diversity orders different solutions can provide are compared. The results imply that diversity interference alignment solutions offer both multiplexing and diversity gains simultaneously. It also tells us two important rules about the interference alignment precoding filters design: an optimal design has to take both desired and interference channel matrices into consideration and the separation of interference alignment precoding filters design and space-time codes design may not be optimal in general.

Finite-Length MMSE Tomlinson–Harashima Precoding for Frequency Selective Vector Channels

We design Tomlinson-Harashima precoding for decentralized receivers and frequency-selective channels based on the minimum mean square error criterion, where the feedforward filter is restricted to have finite length. Contrary to most other publications on Tomlinson-Harashima precoding which rely on solutions for decision feedback equalization to find the corresponding precoding filters in a heuristic manner, we deduce the optimization for Tomlinson-Harashima precoding from the optimization for the linear minimum mean square error transmit filter. Thereby, we include the precoding order explicitly in the problem formulation and thus obtain the precoding filter solutions, together with the algorithms to compute the latency time, i.e., the time difference between application of the precoder at the transmitter and detection at the receiver and the precoding order from a single optimization. Since the algorithm for THP filter computation resulting from the optimization has a high computational complexity, we present an alternative algorithm to compute the Tomlinson-Harashima precoding filters based on a Cholesky factorization with symmetric permutation, resulting in an order of complexity that is the same as for the computation of the linear transmit filters. The simulations reveal that the latency time optimization can be omitted without performance degradation for most practical channel models, i.e., the latency time can be chosen to be the order of the feedforward filter