Effective Channel Matrix Research Articles

Two stage beamforming and combining scheme for FDD massive MIMO systems with multi‐antenna users

AbstractThis paper proposes a two‐stage beamforming and combining scheme in frequency division duplex (FDD) massive multiple‐input multiple‐output (MIMO) systems with multi‐antenna users. Specifically, the proposed scheme is a two‐stage scheme, where the pre‐beamforming matrix and pre‐combining matrix are designed using the channel covariance matrix (CCM) in the first stage. The problem of the pre‐beamforming matrix and pre‐combining matrix design are formulated as an 0–1 quadratic integer programming problem. To solve this problem, it is further transformed into an 0–1 mixed linear integer programming problem. In the second stage, the sparse code multiple access and multi‐user precoding and combining are adopted to mitigate the inter‐user interference. Different from the previous transmission scheme using CCM, the proposed scheme consider the multi‐antenna user system, and uses the CCM to design both the pre‐beamforming and pre‐combining matrices to sparsify the effective channel matrix, such that the overhead of pilot and feedback can be reduced. Moreover, the sparse code multiple access can help to better reduce the inter‐user interference. Simulation results validate the good performance of the proposed scheme.

AFDM signal detection based on message passing scheme

Affine frequency division multiplexing (AFDM) is a new technology that uses discrete affine Fourier transform (DAFT) for multicarrier modulation. It aims to address the issue of unreliable communication in high-speed mobile scenarios. In this paper, we introduce two signal detection algorithms for AFDM that are low complexity. The first algorithm is a message passing (MP) detection algorithm that handles joint interference cancellation and detection by utilizing the inherent sparsity of the channel. The second algorithm is a matched filtering-based message passing (MF-MP) algorithm that utilizes the sparsity of the effective channel matrix of matched filtering. Simulation results show that the performance of the two detection algorithms is superior to that of the minimum mean square error (MMSE) algorithm and the maximum ratio combination (MRC) algorithm.

Spectral Efficiency of OTFS Based Orthogonal Multiple Access With Rectangular Pulses

In this paper, we consider Orthogonal Time Frequency Space (OTFS) modulation based multiple-access (MA). We specifically consider Orthogonal MA methods (OMA) where the user terminals (UTs) are allocated non-overlapping physical resource in the delay-Doppler (DD) and/or time-frequency (TF) domain. Well known OMA methods include, i) Guard Band (GB) based MA (GBMA), ii) Interleaved Delay Doppler MA (IDDMA), iii) Interleaved Time Frequency MA (ITFMA). The spectral efficiency (SE) performance of these OMA methods has <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">only</i> been studied for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ideal</i> transmit and receive pulses. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">With ideal pulses</i> , IDDMA and ITFMA are free from multi-user interference (MUI) and unlike GBMA they <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">do not</i> use guard bands in the DD/TF domain. Since ideal pulses are not realizable, in this paper we study the SE performance of these OMA methods with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">practical rectangular pulses</i> . For these OMA methods, we derive the expression for the received DD/TF domain symbols at the base station (BS) receiver and the effective DD domain channel matrix when rectangular pulses are used. Study of these expressions reveals the presence of MUI when rectangular pulses are used, although the amount of MUI in IDDMA is observed to be significantly smaller than that in ITFMA. We also derive the expression for the achievable sum SE. Through simulations, for practical values of the received signal-to-noise ratio, we observe that with rectangular pulses the sum SE achieved by the IDDMA method is significantly higher than that achieved by the ITFMA and GBMA methods.

A Joint Equalization and Decoding Technique for Multiuser Massive MIMO Uplink System With Transmitter and Receiver RF Impairments Under Doubly Selective Channels

The impairments due to in-phase and quadrature-phase imbalance at the transmitter and/or receiver, carrier frequency offset, and doubly selective channel (DSC) result in multiuser interference (MUI) and self-intercarrier interference (S-ICI) in multiuser massive multiple-input–multiple-output (MIMO) uplink systems. The MUI and S-ICI significantly deteriorate the performance of the receiver and make data detection quite a challenging task. To tackle this issue, we developed a novel crisscross banded effective channel matrix and a joint equalization and detection technique for multiuser massive MIMO single-carrier frequency division multiple access/orthogonal frequency division multiple access uplink systems with RF impairments under DSC. During each iteration of the proposed method, the MUI and S-ICI are calculated using the soft information from the decoder section, and then the interference canceled signal is fed back to the equalizer section for the joint equalization of the mirror subcarrier pairs. Since the proposed method does not put any restriction on the allocation of mirror subcarrier pairs, it is equally applicable to all types of carrier assignment schemes. Further, the extrinsic information transfer chart of the proposed technique is developed for analyzing the convergence. Extensive simulation studies are conducted to validate the performance of the proposed technique.

Low-Complexity Beamforming Algorithms for IRS-Aided Single-User Massive MIMO mmWave Systems

This paper considers intelligent reflecting surface (IRS)-aided single-user (SU) massive multiple-input multiple-output (mMIMO) millimeter wave (mmWave) downlink communication system. We aim to maximize the achievable spectral efficiency by separately designing the passive beamforming and active precoding (combining) through a decoupling strategy to reduce computational complexity. We propose two algorithms for passive beamforming design, which are followed by singular value decomposition (SVD) of the effective channel matrix to generate the active precoding and combining matrices at the bases station (BS) and user equipment (UE), respectively. The first algorithm employs the SVD of the BS-IRS and the IRS-UE channel matrices to generate the unitary matrices. These matrices are used to develop the optimization problem, which is solved via a Riemannian conjugate gradient (RCG)-based algorithm, yielding a passive beamforming vector. In the second algorithm, we propose a greedy-search (GS)-based method to select the array response vectors and their corresponding path gains of the mmWave channels between the BS (IRS) and IRS (UE) required to formulate the optimization problem, which is also solved via the RCG-based algorithm, resulting in a passive beamforming vector. The simulation results show that the proposed schemes achieve an improved trade-off between the spectral efficiency and computational complexity.

A Message Passing-Assisted Iterative Noise Cancellation Method for Clipped OTFS-BFDM Systems.

Compared with orthogonal frequency division multiplexing (OFDM) systems, orthogonal time frequency space systems based on bi-orthogonal frequency division multiplexing (OTFS-BFDM) have lower out-of-band emission (OOBE) and better robustness to high-mobility scenarios, but suffer from a higher peak-to-average ratio (PAPR) in large data packets. In this paper, one-iteration clipping and filtering (OCF) is adopted to reduce the PAPR of OTFS-BFDM signals. However, the extra noise introduced by the clipping process, i.e., clipping noise, will distort the desired signal and increase the bit error rate (BER). We propose a message passing (MP)-assisted iterative cancellation (MP-AIC) method to cancel the clipping noise based on the traditional MP decoding at the receiver, which incorporates with the (OCF) at the transmitter to keep the sparsity of the effective channel matrix. The main idea of MP-AIC is to extract the residual signal fed to the MP detector by iteratively constructing reference clipping noise at the receiver. During each iteration, the variance of residual signal and channel noise are taken as input parameters of MP decoding to improve the BER. Moreover, the convergence probability of the modulation alphabet after MP decoding in the current iteration is used as the initial probability of MP decoding in the next iteration to accelerate the convergence rate of MP decoding. Simulation results show that the proposed MP-AIC method significantly improves MP-decoding accuracy while accelerating the BER convergence in the clipped OTFS-BFDM system. In the clipped OTFS-BFDM system with rectangular pulse shaping, the BER of MP-AIC with two iterations can be reduced by 72% more than that without clipping noise cancellation.

Channel estimation for reconfigurable intelligent surface‐assisted multiuser mmWave MIMO system in the presence of array blockage

AbstractIn this article, we focus on the channel estimation problem for reconfigurable intelligent surface (RIS)‐assisted multiuser mmWave MIMO system. The main challenge for channel estimation of this system lies in that all elements of the RIS are passive reflecting antennas incapable of processing signals, which are designed to reflect the incident signals by a certain phase shift. Meanwhile, considering that array blockage is often present at the RIS working in mmWave band, the channel estimation problem becomes more challenging. By introducing the effective channel model derived from the cascaded channel model among the base station (BS), the RIS, and the user equipment, we formulate the original problem to estimate the effective channel and array blockage matrix jointly. For the single‐user scenario, we propose the orthogonal matching pursuit‐array blockage calibration (OMPABC) algorithm to complete this estimation problem. In the multiuser scenario, with the aid of channel estimation scheme based on feedback, all the channel matrices of UEs and array blockage matrix are estimated at the BS jointly. Furthermore, in the small number of UEs case, we introduce the common support among the different UEs and extend this property to the effective channel. Utilizing the property, we propose the joint OMPABC algorithm to estimate the effective channel of all UEs and array blockage matrix jointly. Finally, in the large number of UEs case, we propose the two‐space‐scale OMPABC algorithm with a low computational complexity. The simulation results illustrate our proposed algorithms can effectively improve the estimation performance.

A Bipartite Graph Approach for FDD V2V Underlay Massive MIMO Transmission

Utilizing the inherent sparsity of massive multiple-input multiple-output (MIMO) channels in the beam domain, we propose a bipartite graph approach for frequency-division duplexing (FDD) vehicle-to-vehicle (V2V) underlay massive MIMO transmission. First, the physically motivated constraints are introduced to schedule the users with channel dimension no larger than the pilot dimension and beam directions with strong channel power as well as weak interference. We then develop an optimization problem which is formulated as a mixed-integer linear program (MILP) to maximize the rank of the effective channel matrix subject to the introduced constraints. We further provide a channel estimation and precoding scheme for the base station and each V2V transmitter over the equivalent reduced-dimensional channels based on the solution of MILP. Numerical results show the superiority of the proposed bipartite graph approach in terms of pilot overhead and spectral efficiency over the conventional baseline.

Reconfigurable Intelligent Surface: Reflection Design Against Passive Eavesdropping

The reconfigurable intelligent surface (RIS) is envisioned to create ultra-secure wireless networks. Previous works on the RIS-assisted security provisioning techniques assumed wiretap channel information at the transmitter, which is practically unavailable in a passive eavesdropping scenario. In this article, we consider a point-to-point anti-eavesdropping system in which a RIS is used to enable the secure transmission from a multi-antenna transmitter to a multi-antenna legitimate receiver. A passive eavesdropper, whose channel state information is completely unknown, attempts to decode the secret messages. We propose a security approach by using the reflection at the RIS as multiplicative randomness against the wiretapper. Specifically, the reflection coefficients in terms of amplitude and phase are updated in each transmission and kept private at the RIS. Through the reflection designs, the effective channel matrix is diagonalized at the legitimate receiver. In contrast, the eavesdropper receives coupled signals with the weights of the randomness at RIS. The main contributions of this article are three reflection designs and correspondingly three secure transmission schemes, which fulfills diverse requirements of the balance amongst performance metrics including the degrees of randomness, spectral efficiency, and reliability. The main benefits of the proposed secure transmission schemes are four-fold. First, the transmitter does not need to know the eavesdropper's channel states. Second, closed-form solutions for the reflection coefficients are provided. Third, the legitimate receiver has a linear decoding complexity. Fourth, the unauthorized wiretapper is unable to cancel out the multiplicative randomness and thus cannot extract much useful information. Numerical results show that exploiting the RIS as a source of multiplicative randomness provides a new perspective to improve the security of the wireless networks.

Multimode Integer-Forcing Receivers for Block Fading Channels

Integer-forcing (IF) receivers are a class of linear multiple-input multiple-output (MIMO) receivers to achieve near-optimal performance under quasi-static channels, with almost the same complexity as that of conventional linear receivers. Instead of trying to recover the transmitted messages directly, an IF receiver recovers their integer-linear combinations corresponding to a chosen integer-valued effective channel matrix, and then obtains them. Recently, the IF strategy has been extended to a block fading scenario. In this paper, we propose a novel IF receiver for block fading channels, called a multimode IF (M-IF) receiver. Unlike conventional IF receivers, the proposed M-IF receiver employs several integer-valued effective channel matrices for IF decoding. We also propose an efficient search algorithm for selecting such matrices with the aid of Gaussian elimination. We then show that for any channel realizations, the proposed M-IF receiver has better performance in terms of the effective noise variance than conventional IF receivers. Simulation results demonstrate that it works really well in various environments.

Joint Spatial Division and Multiplexing in Massive MIMO: A Neighbor-Based Approach

In this paper, we propose a joint spatial division and multiplexing (JSDM) beamforming based on a neighbor scheme for frequency division duplex (FDD) massive multi-input multi-output (MIMO) systems. The neighbor-based JSDM (N-JSDM) can fully utilize signal space, leading to higher spectral efficiency over the conventional JSDMs. The reason is that for the neighbor scheme, neighbors and non-neighbors are classified adaptively by the angles of departure (AoD), and the prebeamformer is designed to mitigate the non-neighbors' interference by the statistical channel state information. The effective channel matrix after the prebeamformer then becomes a band matrix, from which the downlink training length (DTL) and the channel feedback length are much smaller than the number of antennas. Moreover, an optimal prebeamformer which is proved to be able to achieve the same system capacity as the full CSI system is proposed, followed by a suboptimal prebeamformer with constrained DTL, and a DFT-based prebeamformer. On the other hand, the neighbors' interference is mitigated using the banded channel state information. Simulation results validate the good performance of the proposed N-JSDM.

Hybrid Beamforming in MU-MIMO Using Partial Interfering Beam Feedback

We propose a hybrid beamforming scheme with partial interfering beam feedback for a codebook-based multi-user multiple-input multiple-output (MU-MIMO) system, where users feed back information only about the top- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> transmit beams. For the analog part of the precoding, we consider two codebooks, the conventional Discrete Fourier Transform (DFT) codebook with uniform amplitude beamforming vectors and the Taylor codebook with non-uniform amplitude beamforming vectors. For the digital precoding part, the effective channel matrix is approximated and used for zero-forcing (ZF). We also propose a beam pairing algorithm that results in reduced inter-beam interference and simplifies beam and user selection in MU-MIMO. When <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> is equal to the number of beams in the transmit codebook, the proposed scheme includes an existing scheme with full effective channel matrix feedback as a special case. Numerical results show that the proposed hybrid beamforming performs better than an existing hybrid precoding scheme based on channel reconstruction.

Low-Complexity Linear Equalization for OTFS Modulation

In this letter, we propose low-complexity linear equalizers for orthogonal time frequency space (OTFS) modulation that exploit the structure of the effective channel matrix in OTFS. The proposed approach exploits the block circulant nature of the OTFS channel matrix to achieve significant complexity reduction. For an $N\times M$ OTFS system, where $N$ and $M$ are the number of Doppler and delay bins, respectively, the proposed approach gives exact minimum mean square error (MMSE) and zero-forcing (ZF) solutions with just $\mathcal {O}(MN \log MN)$ complexity, while MMSE and ZF solutions using the traditional matrix inversion approach require $\mathcal {O}(M^{3}N^{3})$ complexity. The proposed approach can provide low complexity initial solutions for local search techniques to achieve enhanced bit error performance.

FDD Massive MIMO via UL/DL Channel Covariance Extrapolation and Active Channel Sparsification

We propose a novel method for massive multiple-input multiple-output (massive MIMO) in frequency division duplexing (FDD) systems. Due to the large frequency separation between uplink (UL) and downlink (DL) in FDD systems, channel reciprocity does not hold. Hence, in order to provide DL channel state information to the base station (BS), closed-loop DL channel probing, and channel state information (CSI) feedback is needed. In massive MIMO, this typically incurs a large training overhead. For example, in a typical configuration with M ≃200 BS antennas and fading coherence block of T ≃ 200 symbols, the resulting rate penalty factor due to the DL training overhead, given by max{0, 1 - M/T }, is close to 0. To reduce this overhead, we build upon the well-known fact that the angular scattering function of the user channels is invariant over frequency intervals whose size is small with respect to the carrier frequency (as in current FDD cellular standards). This allows us to estimate the users' DL channel covariance matrix from UL pilots without additional overhead. Based on this covariance information, we propose a novel sparsifying precoder in order to maximize the rank of the effective sparsified channel matrix subject to the condition that each effective user channel has sparsity not larger than some desired DL pilot dimension T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dl</sub> , resulting in the DL training overhead factor max{0, 1 - T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dl</sub> /T } and CSI feedback cost of Tdl pilot measurements. The optimization of the sparsifying precoder is formulated as a mixed integer linear program, that can be efficiently solved. Extensive simulation results demonstrate the superiority of the proposed approach with respect to the concurrent state-of-the-art schemes based on compressed sensing or UL/DL dictionary learning.

Matrix Completion-Based Channel Estimation for MmWave Communication Systems With Array-Inherent Impairments

Hybrid massive MIMO structures with reduced hardware complexity and power consumption have been widely studied as a potential candidate for millimeter wave (mmWave) communications. Channel estimators that require knowledge of the array response, such as those using compressive sensing (CS) methods, may suffer from performance degradation when array-inherent impairments bring unknown phase errors and gain errors to the antenna elements. In this paper, we design matrix completion (MC)-based channel estimation schemes which are robust against the array-inherent impairments. We first design an open-loop training scheme that can sample entries from the effective channel matrix randomly and is compatible with the phase shifter-based hybrid system. Leveraging the low-rank property of the effective channel matrix, we then design a channel estimator based on the generalized conditional gradient (GCG) framework and the alternating minimization (AltMin) approach. The resulting estimator is immune to array-inherent impairments and can be implemented to systems with any array shapes for its independence of the array response. In addition, we extend our design to sample a transformed channel matrix following the concept of inductive matrix completion (IMC), which can be solved efficiently using our proposed estimator and achieve similar performance with a lower requirement of the dynamic range of the transmission power per antenna. Numerical results demonstrate the advantages of our proposed MC-based channel estimators in terms of estimation performance, computational complexity and robustness against array-inherent impairments over the orthogonal matching pursuit (OMP)-based CS channel estimator.

Hybrid Beamforming Based on Implicit Channel State Information for Millimeter Wave Links

Hybrid beamforming provides a promising solution to achieve high data rate transmission at millimeter waves. Implementing hybrid beamforming at a transceiver based on available channel state information is a common solution. However, many reference methods ignore the complexity of channel estimation for large antenna arrays or subsequent steps, such as the singular value decomposition of a channel matrix. To this end, we present a low-complexity scheme that exploits implicit channel knowledge to facilitate the design of hybrid beamforming for frequency-selective fading channels. The implicit channel knowledge can be interpreted as couplings between all possible pairs of analog beamforming vectors at the transmitter and receiver over the surrounding channel. Instead of calculating mutual information between large antenna arrays, we focus on small-size coupling matrices between beam patterns selected by using appropriate key parameters as performance indicators. This converts the complicated hybrid beamforming problem to a much simpler one: it amounts to collecting different sets of the large-power coupling coefficients to construct multiple alternatives for an effective channel matrix. Then, the set yielding the largest Frobenius norm (or the largest absolute value of the determinant) of the effective channel provides the solution to the hybrid beamforming problem. It turns out that the proposed method does not require information on MIMO channel and can be simply implemented by the received correlated pilot signals that are supposed to be used for channel estimation.

On Integer-Forcing Precoding for the Gaussian MIMO Broadcast Channel

Integer-forcing (IF) precoding, also known as downlink IF, is a promising new approach for communication over multiple-input multiple-output (MIMO) broadcast channels. Inspired by the integer-forcing linear receiver for multiple-access channels, it generalizes linear precoding by inducing an effective channel matrix that is approximately integer, rather than approximately identity. Combined with lattice encoding and a pre-inversion of the channel matrix at the transmitter, the scheme has the potential to outperform any linear precoding scheme, despite enjoying similar low complexity. In this paper, a specific IF precoding scheme, called diagonally-scaled exact IF (DIF), is proposed and shown to achieve maximum spatial multiplexing gain. For the special case of two receivers, in the high SNR regime, an optimal choice of parameters is derived analytically, leading to an almost closed-form expression for the achievable sum rate. In particular, it is shown that the gap to the sum capacity is upper bounded by 0.27 bits for any channel realization. For general SNR, a regularized version of DIF (RDIF) is proposed. Numerical results for two receivers under Rayleigh fading show that RDIF can achieve performance superior to optimal linear precoding and very close to the sum capacity.

Downlink MU-MIMO With THP Combined With Pre- and Post-processing and Selection of the Processing Vectors for Maximization of Per-Stream SNR

In this paper, we consider a downlink multiuser multiple-input–multiple-output (MU-MIMO) system with multiple antennas at the transmitter and multiple antennas at each user, where the transmitter can send one or more data streams to each user. We propose a non-iterative method by combining Tomlinson–Harashima precoding (THP) with pre- and post-processing and selecting processing vectors based on the maximization of instantaneous signal-to-noise ratio (SNR) of the data stream at the input of the detector of each user. The postprocessing vectors for all users are found to be eigenvectors corresponding to the maximum eigenvalue of a certain matrix involving the channel matrix of the user. The transmitter computes the vectors of the linear processing matrix through an orthonormalization procedure in a single step. The feedback matrix at the transmitter is then obtained from the effective channel matrix and the linear processing matrix. We express the instantaneous SNR of all data streams in terms of eigenvalues of a Wishart matrix, obtained from the channel matrix of the user, and find the diversity order for each data stream. Considering multiple scenarios, we find the outage probability of the instantaneous SNR for all data streams and the cumulative distribution function (cdf) of the sum-rate capacity for all users using the proposed method and compare the results with those of recently proposed methods that provide a closed-form solution and with that of block diagonalization, channel inversion, and THP in scenarios where they are applicable.

Impact of CSI Knowledge on the Codebook-Based Hybrid Beamforming in Massive MIMO

Hybrid beamforming, which consists of an RF precoder and a baseband precoder, has been proposed to reduce the number of RF chains at the massive multiple input multiple output (MIMO) base station (BS). This paper studies the impact of channel state information (CSI) on the capacity of massive MIMO systems with codebook-based hybrid beamforming , where the RF precoder is selected from a finite size codebook. Two types of CSI at the BS (CSIT) are commonly assumed: full instantaneous CSIT and hybrid CSIT (channel statistics plus the low-dimensional effective channel matrix). With full instantaneous CSIT, both the RF and baseband precoders are adaptive to the full instantaneous CSI at the fast timescale. With hybrid CSIT, the RF precoder is adaptive to channel statistics only, and the baseband precoder is adaptive to the instantaneous effective channel, yielding lower implementation complexity by sacrificing some capacity. We derive asymptotic sum capacity expressions under these two types of CSIT. We find that, in codebook-based hybrid beamforming systems, exploiting the full instantaneous CSIT can only achieve a marginal SNR gain and hybrid CSIT is sufficient to achieve the first-order gain provided by the massive MIMO for most of the cases. We also propose fast and slow timescale RF precoding algorithms, which asymptotically achieve the capacity under full instantaneous CSIT and hybrid CSIT, respectively.

Interference cancellation method based on space-time code for MIMO interference channel

We investigate how to cancel interference by using space time code and codeword space alignment for multiple-input multiple-output (MIMO) Y channel consisting of three users and a relay. All the nodes adopt Alamouti code. During the multiple access (MA) stage, two codewords within each reciprocal codeword pair are aligned through pre-coding. The relay decodes the elements of each codeword pair using the orthogonal property of effective channel matrix of Alamouti codeword. During the broadcast (BC) stage, the interference between codeword pairs at each user is eliminated by the orthogonal property of effective channel matrix of Alamouti codeword, instead of the interference alignment (IA) pre-coding. Thus, channel state information (CSI) is not required during the BC stage, which greatly reduce the amount of feedback.