Linear data-detection algorithms that build on zero forcing (ZF) or linear minimum mean-square error (L-MMSE) equalization achieve near-optimal spectral efficiency in massive multi-user multiple-input multiple-output (MU-MIMO) systems. Such algorithms, however, typically rely on centralized processing at the base-station (BS) which results in (i) excessive interconnect and chip input/output (I/O) data rates and (ii) high computational complexity. Decentralized baseband processing (DBP) partitions the BS antenna array into independent clusters that are associated with separate radio-frequency circuitry and computing fabrics in order to overcome the limitations of centralized processing. In this paper, we investigate decentralized equalization with feedforward architectures that minimize the latency bottlenecks of existing DBP solutions. We propose two distinct architectures with different interconnect and I/O bandwidth requirements that fuse the local equalization results of each cluster in a feedforward network. For both architectures, we consider maximum ratio combining, ZF, L-MMSE, and a nonlinear equalization algorithm that relies on approximate message passing, and we analyze the associated post-equalization signal-to-noise-and-interference-ratio (SINR). We provide reference implementation results on a multi graphics processing unit (GPU) system which demonstrate that decentralized equalization with feedforward architectures enables throughputs in the Gb/s regime and incurs no or only a small performance loss compared to centralized solutions.
We propose equalization-based data detection algorithms for all-digital millimeter-wave (mmWave) massive multiuser multiple-input multiple-out (MU-MIMO) systems that exploit sparsity in the beamspace domain to reduce complexity. We provide a condition on the number of users, basestation antennas, and channel sparsity for which beamspace equalization can be less complex than conventional antenna-domain processing. We evaluate the performance-complexity trade-offs of existing and new beamspace equalization algorithms using simulations with realistic mmWave channel models. Our results reveal that…
Next-generation wireless systems are expected to combine millimeter-wave (mmWave) and massive multi-user multiple-input multiple-output (MU-MIMO) technologies to deliver high data-rates. These technologies require the basestations (BSs) to process high-dimensional data at extreme rates, which results in high power dissipation and system costs. Finite-alphabet equalization has been proposed recently to reduce the power consumption and silicon area of uplink spatial equalization circuitry at the BS by coarsely quantizing the equalization matrix. In this work, we improve upon finite-alphabet equa…
Orthogonal signal-division multiplexing (OSDM) is an attractive alternative to conventional orthogonal frequency-division multiplexing (OFDM) due to its enhanced ability in peak-to-average power ratio (PAPR) reduction. Combining OSDM with multiple-input multiple-output (MIMO) signaling has the potential to achieve high spectral and power efficiency. However, a direct channel equalization in this case incurs a cubic complexity, which may be expensive for practical use. To solve the problem, low-complexity per-vector and block equalization algorithms of MIMO-OSDM are proposed in this paper for t…
We propose finite-alphabet equalization, a new paradigm that restricts the entries of the spatial equalization matrix to low-resolution numbers, enabling high-throughput, low-power, and low-cost hardware equalizers. To minimize the performance loss of this paradigm, we introduce FAME, short for finite-alphabet minimum mean-square error (MMSE) equalization, which is able to significantly outperform a naive quantization of the linear MMSE matrix. We develop efficient algorithms to approximately solve the NP-hard FAME problem and showcase that near-optimal performance can be achieved with equaliz…
Massive multi-user (MU) multiple-input multiple-output (MIMO) promises significant gains in spectral efficiency compared to traditional, small-scale MIMO technology. Linear equalization algorithms, such as zero forcing (ZF) or minimum mean-square error (MMSE)-based methods, typically rely on centralized processing at the base station (BS), which results in (i) excessively high interconnect and chip input/output data rates, and (ii) high computational complexity. In this paper, we investigate the achievable rates of decentralized equalization that mitigates both of these issues. We consider two…
This paper deals with linear equalization in massive multi-user multiple-input multiple-output (MU-MIMO) wireless systems. We first provide simple conditions on the antenna configuration for which the well-known linear minimum mean-square error (L-MMSE) equalizer provides near-optimal spectral efficiency, and we analyze its performance in the presence of parameter mismatches in the signal and/or noise powers. We then propose a novel, optimally-tuned NOnParametric Equalizer (NOPE) for massive MU-MIMO systems, which avoids knowledge of the transmit signal and noise powers altogether. We show tha…
The focus of this letter is on the reduction of the large pilot overhead in orthogonal frequency division multiplexing (OFDM) based massive multiple-input multiple-output (MIMO) systems. We propose a novel joint channel estimation and equalization technique that requires only one pilot subcarrier, reducing the pilot overhead by orders of magnitude. We take advantage of the coherent bandwidth spanning over multiple subcarrier bands. This allows for a band of subcarriers to be equalized with the channel frequency response (CFR) at a single subcarrier. Subsequently, the detected data symbols are …
In diffusion-based communication, as for molecular systems, the achievable data rate is low due to the stochastic nature of diffusion which exhibits a severe inter-symbol-interference (ISI). Multiple-Input Multiple-Output (MIMO) multiplexing improves the data rate at the expense of an inter-link interference (ILI). This paper investigates training-based channel estimation schemes for diffusive MIMO (D-MIMO) systems and corresponding equalization methods. Maximum likelihood and least-squares estimators of mean channel are derived, and the training sequence is designed to minimize the mean squar…
The use of low resolution Analog to Digital Converters (ADCs) can significantly reduce the power consumption for massive Multiple Input Multiple Output (MIMO) systems. The existing literature on quantized massive MIMO systems deals with Cyclic Prefix (CP) transmission schemes in frequency-selective fading channels. In this paper, we propose a block processing Frequency Domain Equalization (FDE) technique in CP-free transmission schemes for massive MIMO systems having low resolution ADCs. The optimal block length for FDE is found by minimizing a computational complexity cost function and taking…
Application of filter bank multicarrier (FBMC) as an effective method for signaling over massive MIMO channels has been recently proposed. This paper further expands the application of FBMC to massive MIMO by applying frequency spreading equalization (FSE) to these channels. FSE allows us to achieve a more accurate equalization. Hence, higher number of bits per symbol can be transmitted and the bandwidth of each subcarrier can be widened. Widening the bandwidth of each subcarrier leads to (i) higher bandwidth efficiency; (ii) lower complexity; (iii) lower sensitivity to carrier frequency offse…
Massive multi-user multiple-input multiple-output (MU-MIMO) enables significant gains in spectral efficiency and link reliability compared to conventional small-scale MIMO technology. Furthermore, linear precoders, e.g., using zero forcing or Wiener filter (WF) precoding, are sufficient to achieve excellent error-rate performance in the massive MU-MIMO downlink. However, these methods necessitate centralized processing at the base-station (BS), which causes (i) excessively high interconnect and chip input/output data rates, and (ii) high implementation complexity. We propose two feedforward ar…
All-digital basestation (BS) architectures for millimeter-wave (mmWave) massive multi-user multiple-input multiple-output (MU-MIMO), which equip each radio-frequency chain with dedicated data converters, have advantages in spectral efficiency, flexibility, and baseband-processing simplicity over hybrid analog-digital solutions. For all-digital architectures to be competitive with hybrid solutions in terms of power consumption, novel signal-processing methods and baseband architectures are necessary. In this paper, we demonstrate that adapting the resolution of the analog-to-digital converters …
We perform an asymptotic study of the performance of filter bank multicarrier (FBMC) in the context of massive multi-input multi-output (MIMO). We show that the effects of channel distortions, i.e., intersymbol interference and intercarrier interference, do not vanish as the base station (BS) array size increases. As a result, the signal-to-interference-plus-noise ratio (SINR) cannot grow unboundedly by increasing the number of BS antennas, and is upper bounded by a certain deterministic value. We show that this phenomenon is a result of the correlation between the multi-antenna combining tap …
This paper addresses channel estimation and data equalization on frequency-selective 1-bit quantized Multiple Input-Multiple Output (MIMO) systems. No joint processing or Channel State Information is assumed at the transmitter, and therefore our findings are also applicable to the uplink of Multi-User MIMO systems. System models for both Orthogonal Division Frequency Multiplexing (OFDM) and single-carrier schemes are developed. A Cramér-Rao Lower Bound for the estimation problems is derived. The two nonlinear algorithms Expectation Maximization (EM) and Generalized Approximate Message Passing …
We consider joint transceiver design for general Multiple-Input Multiple-Output communication systems that implement interference (pre-)subtraction, such as those based on Decision Feedback Equalization (DFE) or Tomlinson-Harashima precoding (THP). We develop a unified framework for joint transceiver design by considering design criteria that are expressed as functions of the Mean Square Error (MSE) of the individual data streams. By deriving two inequalities that involve the logarithms of the individual MSEs, we obtain optimal designs for two classes of communication objectives, namely those …
This paper addresses the problem of data detection for a massive Multiple-Input-Multiple-Output (MIMO) base station which utilizes 1-bit Analog-to-Digital Converters (ADCs) for quantizing the uplink signal. The existing literature on quantized massive MIMO systems deals with Cyclic Prefix (CP) transmission over frequency-selective channels. In this paper, we propose a computationally efficient block processing equalizer based on the Expectation Maximization (EM) algorithm in CP-free transmission for 1-bit quantized systems. We investigate the optimal block length and overlapping factor in rela…
In this paper, we deal with low-complexity near-optimal detection/equalization in large-dimension multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels using message passing on graphical models. A key contribution in the paper is the demonstration that near-optimal performance in MIMO-ISI channels with large dimensions can be achieved at low complexities through simple yet effective simplifications/approximations, although the graphical models that represent MIMO-ISI channels are fully/densely connected (loopy graphs). These include 1) use of Markov Random Field (MRF) ba…
This paper presents a novel adaptive reduced-rank multi-input-multi-output (MIMO) decision feedback equalization structure based on joint iterative optimization of adaptive estimators. The novel reduced-rank equalization structure consists of a joint iterative optimization of two equalization stages, namely, a projection matrix that performs dimensionality reduction and a reduced-rank estimator that retrieves the desired transmitted symbol. The proposed reduced-rank structure is followed by a decision feedback scheme that is responsible for cancelling the inter-antenna interference caused by t…
This paper presents results on the achievable spectral efficiency and on the energy efficiency for a wireless multiple-input-multiple-output (MIMO) link operating at millimeter wave frequencies (mmWave) in a typical 5G scenario. Two different single-carrier modem schemes are considered, i.e., a traditional modulation scheme with linear equalization at the receiver, and a single-carrier modulation with cyclic prefix, frequency-domain equalization and FFT-based processing at the receiver; these two schemes are compared with a conventional MIMO-OFDM transceiver structure. Our analysis jointly tak…
Linear minimum mean-square error (L-MMSE) equalization is among the most popular methods for data detection in massive multi-user multiple-input multiple-output (MU-MIMO) wireless systems. While L-MMSE equalization enables near-optimal spectral efficiency, accurate knowledge of the signal and noise powers is necessary. Furthermore, corresponding VLSI designs must solve linear systems of equations, which requires high arithmetic precision, exhibits stringent data dependencies, and results in high circuit complexity. This paper proposes the first VLSI design of the NOnParametric Equalizer (NOPE)…
A cellular multiple-input multiple-output (MIMO) downlink system is studied in which each base station (BS) transmits to some of the users, so that each user receives its intended signal from a subset of the BSs. This scenario is referred to as network MIMO with partial cooperation, since only a subset of the BSs are able to coordinate their transmission towards any user. The focus of this paper is on the optimization of linear beamforming strategies at the BSs and at the users for network MIMO with partial cooperation. Individual power constraints at the BSs are enforced, along with constrain…
This paper presents a novel adaptive reduced-rank {multi-input multi-output} (MIMO) equalization scheme and algorithms based on alternating optimization design techniques for MIMO spatial multiplexing systems. The proposed reduced-rank equalization structure consists of a joint iterative optimization of two equalization stages, namely, a transformation matrix that performs dimensionality reduction and a reduced-rank estimator that retrieves the desired transmitted symbol. The proposed reduced-rank architecture is incorporated into an equalization structure that allows both decision feedback an…
This paper studies the possibility of eliminating the redundant cyclic prefix (CP) of orthogonal frequency division multiplexing (OFDM) in massive multiple-input multiple-output systems. The absence of CP increases the bandwidth efficiency in expense of intersymbol interference (ISI) and intercarrier interference (ICI). It is known that in massive MIMO, different types of interference fade away as the number of base station (BS) antennas tends to infinity. In this paper, we investigate if the channel distortions in the absence of CP are averaged out in the large antenna regime. To this end, we…
Pilot contamination problem in massive MIMO networks operating in time-division duplex (TDD) mode can limit their expected capacity to a great extent. This paper addresses this problem in cosine modulated multitone (CMT) based massive MIMO networks; taking advantage of their so-called blind equalization property. We extend and apply the blind equalization technique from single antenna case to multi-cellular massive MIMO systems and show that it can remove the channel estimation errors (due to pilot contamination effect) without any need for cooperation between different cells or transmission o…
Link-adaptation (LA) is one of the most important aspects of wireless communications where the modulation and coding scheme (MCS) used by the transmitter is adapted to the channel conditions in order to meet a certain target error-rate. In a single-user SISO (SU-SISO) system with out-of-cell interference, LA is performed by computing the post-equalization signal-to-interference-noise ratio (SINR) at the receiver. The same technique can be employed in multi-user MIMO (MU-MIMO) receivers that use linear detectors. Another important use of post-equalization SINR is for physical layer (PHY) abstra…
For single-carrier systems with frequency domain equalization, decision feedback equalization (DFE) performs better than linear equalization and has much lower computational complexity than sequence maximum likelihood detection. The main challenge in DFE is the feedback symbol selection rule. In this paper, we give a theoretical framework for a simple, sparsity based thresholding algorithm. We feed back multiple symbols in each iteration, so the algorithm converges fast and has a low computational cost. We show how the initial solution can be obtained via convex relaxation instead of linear eq…
In this theoretical work, the DSP-perceived channel in optical coherent communications is first simplified, based on which we categorize linear MIMO equalizers into four classes according to their reference locations. The entire channel inverse can be represented by a complex conjugate-dependent system, coinciding with the widely linear equalization theory. Suboptimally removing FO dynamics, relatively static channel inverses parameterized with common device and channel parameters are presented for monitoring or calibration purposes.
Data detection in massive multi-user (MU) multiple-input multiple-output (MIMO) wireless systems is among the most critical tasks due to the excessively high implementation complexity. In this paper, we propose a novel, equalization-based soft-output data-detection algorithm and corresponding reference FPGA designs for wideband massive MU-MIMO systems that use orthogonal frequency-division multiplexing (OFDM). Our data-detection algorithm performs approximate minimum mean-square error (MMSE) or box-constrained equalization using coordinate descent. We deploy a variety of algorithm-level optimi…
We propose a novel user equipment (UE) scheduling framework for millimeter-wave (mmWave) massive multiuser (MU) multiple-input multiple-output (MIMO) wireless systems. Our framework determines (sub)sets of UEs that should transmit simultaneously in a given time slot by approximately solving a nonconvex optimization problem using forward-backward splitting. Our UE scheduling framework is flexible in the sense that it (i) supports a variety of cost functions, including post-equalization mean square error and sum rate, and (ii) enables precise control over the minimum and maximum number of resour…
This paper introduces filter bank multicarrier (FBMC) as a potential candidate in the application of massive MIMO communication. It also points out the advantages of FBMC over OFDM (orthogonal frequency division multiplexing) in the application of massive MIMO. The absence of cyclic prefix in FBMC increases the bandwidth efficiency. In addition, FBMC allows carrier aggregation straightforwardly. Self-equalization, a property of FBMC in massive MIMO that is introduced in this paper, has the impact of reducing (i) complexity; (ii) sensitivity to carrier frequency offset (CFO); (iii) peak-to-aver…
This article reviews existing related work and identifies the main challenges in the key 5G area at the intersection of waveform design and large-scale multiple antenna systems, also known as Massive MIMO. The property of self-equalization is introduced for Filter Bank Multicarrier (FBMC)-based Massive MIMO, which can reduce the number of subcarriers required by the system. It is also shown that the blind channel tracking property of FBMC can be used to address pilot contamination -- one of the main limiting factors of Massive MIMO systems. Our findings shed light into and motivate for an enti…
Delay alignment modulation (DAM) is a novel wideband communication technique, which exploits the high spatial resolution and multi-path sparsity of millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems to mitigate inter-symbol interference (ISI), without relying on conventional techniques like channel equalization or multi-carrier transmission. In this paper, we extend the DAM technique to multi-user mmWave massive MIMO communication systems. We first provide asymptotic analysis by showing that when the number of base station (BS) antennas is much larger than the total…
An open-loop single-user multiple-input multiple-output communication scheme is considered where a transmitter, equipped with multiple antennas, encodes the data into independent streams all taken from the same linear code. The coded streams are then linearly precoded using the encoding matrix of a perfect linear dispersion space-time code. At the receiver side, integer-forcing equalization is applied, followed by standard single-stream decoding. It is shown that this communication architecture achieves the capacity of any Gaussian multiple-input multiple-output channel up to a gap that depend…
In this paper, we resort to the graph neural network (GNN) and propose the new channel tracking method for the massive multiple-input multiple-output networks under the high mobility scenario. We first utilize a small number of pilots to achieve the initial channel estimation. Then, we represent the obtained channel data in the form of graphs and describe the channel spatial correlation by the weights along the edges of the graph. Furthermore, we introduce the computation steps of the main unit for the GNN and design a GNN-based channel tracking framework, which includes an encoder, a core net…
Massive multiple-input multiple-output (MIMO) promises improved spectral efficiency, coverage, and range, compared to conventional (small-scale) MIMO wireless systems. Unfortunately, these benefits come at the cost of significantly increased computational complexity, especially for systems with realistic antenna configurations. To reduce the complexity of data detection (in the uplink) and precoding (in the downlink) in massive MIMO systems, we propose to use conjugate gradient (CG) methods. While precoding using CG is rather straightforward, soft-output minimum mean-square error (MMSE) detect…
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…
This is the second part of a two-part paper that focuses on link-adaptation (LA) and physical layer (PHY) abstraction for multi-user MIMO (MU-MIMO) systems with non-linear receivers. The first part proposes a new metric, called bit-metric decoding rate (BMDR) for a detector, as being the equivalent of post-equalization signal-to-interference-noise ratio (SINR) for non-linear receivers. Since this BMDR does not have a closed form expression, a machine-learning based approach to estimate it effectively is presented. In this part, the concepts developed in the first part are utilized to develop n…
Consider a Gaussian multiple-input multiple-output (MIMO) multiple-access channel (MAC) with channel matrix $\mathbf{H}$ and a Gaussian MIMO broadcast channel (BC) with channel matrix $\mathbf{H}^{\mathsf{T}}$. For the MIMO MAC, the integer-forcing architecture consists of first decoding integer-linear combinations of the transmitted codewords, which are then solved for the original messages. For the MIMO BC, the integer-forcing architecture consists of pre-inverting the integer-linear combinations at the transmitter so that each receiver can obtain its desired codeword by decoding an integer-…
We study the possibility of removing the cyclic prefix (CP) overhead from orthogonal frequency division multiplexing (OFDM) in massive multiple-input multiple-output (MIMO) systems. We consider the uplink transmission while our results are applicable to the downlink as well. The absence of CP increases the spectral efficiency in expense of intersymbol interference (ISI) and intercarrier interference (ICI). It is known that in massive MIMO, the effects of uncorrelated noise and multiuser interference vanish as the number of base station (BS) antennas tends to infinity. To investigate if the cha…
This paper considers the joint impact of non-linear hardware impairments at the base station (BS) and user equipments (UEs) on the uplink performance of single-cell massive MIMO (multiple-input multiple-output) in practical Rician fading environments. First, Bussgang decomposition-based effective channels and distortion characteristics are analytically derived and the spectral efficiency (SE) achieved by several receivers are explored for third-order non-linearities. Next, two deep feedforward neural networks are designed and trained to estimate the effective channels and the distortion varian…
Nokia Bell Labs（诺基亚贝尔实验室）；Univ. Lyon（里昂大学）；INSA Lyon（里昂国立应用科学学院）；Inria（法国国家信息与自动化研究所）
Machine learning (ML) starts to be widely used to enhance the performance of multi-user multiple-input multiple-output (MU-MIMO) receivers. However, it is still unclear if such methods are truly competitive with respect to conventional methods in realistic scenarios and under practical constraints. In addition to enabling accurate signal reconstruction on realistic channel models, MU-MIMO receive algorithms must allow for easy adaptation to a varying number of users without the need for retraining. In contrast to existing work, we propose an ML-enhanced MU-MIMO receiver that builds on top of a…
Iterative information processing, either based on heuristics or analytical frameworks, has been shown to be a very powerful tool for the design of efficient, yet feasible, wireless receiver architectures. Within this context, algorithms performing message-passing on a probabilistic graph, such as the sum-product (SP) and variational message passing (VMP) algorithms, have become increasingly popular. In this contribution, we apply a combined VMP-SP message-passing technique to the design of receivers for MIMO-ODFM systems. The message-passing equations of the combined scheme can be obtained fro…
We consider the downlink of a massive multiuser (MU) multiple-input multiple-output (MIMO) system in which the base station (BS) is equipped with low-resolution digital-to-analog converters (DACs). In contrast to most existing results, we assume that the system operates over a frequency-selective wideband channel and uses orthogonal frequency division multiplexing (OFDM) to simplify equalization at the user equipments (UEs). Furthermore, we consider the practically relevant case of oversampling DACs. We theoretically analyze the uncoded bit error rate (BER) performance with linear precoders (e…
Linear precoding is a relatively simple method of MIMO signaling that can also be optimal in certain special cases. This paper is dedicated to high-SNR analysis of MIMO linear precoding. The Diversity-Multiplexing Tradeoff (DMT) of a number of linear precoders is analyzed. Furthermore, since the diversity at finite rate (also known as the fixed-rate regime, corresponding to multiplexing gain of zero) does not always follow from the DMT, linear precoders are also analyzed for their diversity at fixed rates. In several cases, the diversity at multiplexing gain of zero is found not to be unique, …
This paper investigates downlink channel estimation in frequency-division duplex (FDD)-based massive multiple-input multiple-output (MIMO) systems. To reduce the overhead of downlink channel estimation and uplink feedback in FDD systems, cascaded precoding has been used in massive MIMO such that only a low-dimensional effective channel needs to be estimated and fed back. On the other hand, traditional channel estimations can hardly achieve the minimum mean-square-error (MMSE) performance due to lack of the a priori knowledge of the channels. In this paper, we design and analyze a strategy for …
