Linear Minimum Mean Square Error Receiver Research Articles

Deep Learning OFDM Receivers for Improved Power Efficiency and Coverage

In this article, we propose multiple machine learning (ML) based physical-layer receiver solutions for demodulating orthogonal frequency-division multiplexing (OFDM) signals that are subject to high level of nonlinear distortion. Specifically, three novel deep learning based convolutional neural network receivers are devised, containing layers in time- and/or frequency-domains, allowing to demodulate and decode the transmitted bits reliably despite the high error vector magnitude (EVM) in the transmit signal. Applicable training procedures are also described, such that the learned layers in the receiver processing properly generalize over different nonlinear distortion and multipath channel characteristics. Extensive set of numerical results is provided, in the context of 5G NR uplink (UL) incorporating also measured terminal power amplifier (PA) characteristics. The obtained results show that the proposed receiver systems are able to clearly outperform the classical linear minimum mean-squared error (LMMSE) receiver as well as the existing ML receiver approaches, especially when the EVM is high compared to modulation order. This is particularly so when the devised ML receiver is of hybrid nature with layers both in time and frequency. The proposed ML receivers can thus facilitate pushing the terminal PA systems deeper into saturation, and thereon improve the terminal power-efficiency, radiated power and network coverage. Through combining the obtained radio link performance results with link budget calculations, all carried out at the 28 GHz mmWave band, it is shown that the proposed ML receivers can enhance the network coverage in terms of maximum UL link distances by close to 100%, when compared to classical LMMSE receiver based networks.

Spectral Efficiency of Massive MIMO With LMMSE Receivers Under Finite Dimensional Channels

This letter investigates the uplink achievable spectral efficiency (SE) of massive MIMO systems, where the base station (BS) utilizes the linear minimum mean square error (LMMSE) detector and is deployed with the uniform rectangular array (URA). The novel expressions on the achievable SE have been derived by considering a finite dimensional physical channels model and assuming the BS has perfect channel state information (CSI). Based on the derived analytical expression, we further derive the closed-form expression on the total achievable SE for a purely line-of-sight (LoS) channel and explore the effect of the physical parameters on the total achievable SE. Results show that the total achievable SE tends to a saturation rate as the number of BS antennas and/or the average transmit power increases under a purely LoS channel. For a finite dimensional channels, the total achievable SE can not be improved by increasing the number of the paths. Instead, we take advantage of the sparsity characteristics of the finite dimensional channels and propose a beam selection scheme by select the dominant eigenvalues of steering matrix. Results show that the proposed scheme can achieve near-optimal performance with massive MIMO system.

LMMSE-Based SIMO Receiver for Ultraviolet Scattering Communication With Nonlinear Conversion

Linear minimum mean square error (LMMSE) receivers are often applied in practical communication scenarios for single-input-multiple-output (SIMO) systems owing to their low computational complexity and competitive performance. However, their performance is only the best among all the linear receivers, as they minimize the bit mean square error (MSE) alone in linear space. To overcome this limitation, in this study, we propose an LMMSE receiver based on the measurements augmented by their nonlinear conversion for a photon-counting receiver, a photomultiplier tube, and an avalanche photodetector. The performance of the proposed LMMSE receiver is studied for different nonlinear conversions, numbers of receivers, and receiver types. The simulation results indicate that the Monte Carlo results are consistent with the analytical results and that the proposed LMMSE receiver outperforms the conventional one in terms of bit MSE and bit error rate. Accordingly, it can be concluded that to achieve a desired bit MSE, the proposed LMMSE-based nonlinear receiver not only reduces the need to increase the number of receivers but also reduces the bandwidth requirements.

Correlation-Aided Nonlinear Spectrum Detection

It is shown that a higher spectral efficiency (SE) can be achieved in a narrow-bandwidth b-modulated NFDM subsystem than a moderate-bandwidth one. Exploiting the statistical correlation between the noise in the sub-carriers-which is shown to be stronger in narrow-bandwidth b-modulated NFDM subsystems than in moderate or wide-bandwidth ones-a linear minimum mean-squared error receiver improves signal detection. The achievable SE is increased by 0.94 b/s/Hz compared to that achieved by the matched filter receiver in a 5 GHz b-modulated NFDM subsystem.

Machine Learning for MU-MIMO Receive Processing in OFDM Systems

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 conventional linear minimum mean squared error (LMMSE) architecture. It preserves the interpretability and scalability of the LMMSE receiver, while improving its accuracy in two ways. First, convolutional neural networks (CNNs) are used to compute an approximation of the second-order statistics of the channel estimation error which are required for accurate equalization. Second, a CNN-based demapper jointly processes a large number of orthogonal frequency-division multiplexing (OFDM) symbols and subcarriers, which allows it to compute better log likelihood ratios (LLRs) by compensating for channel aging. The resulting architecture can be used in the up- and downlink and is trained in an end-to-end manner, removing the need for hard-to-get perfect channel state information (CSI) during the training phase. Simulation results demonstrate consistent performance improvements over the baseline which are especially pronounced in high mobility scenarios.

Maximizing the spectral efficiency of finite dimensional multiuser massive MIMO

In this paper, we derive a closed-form approximation for the achievable uplink ergodic rate of the users in a single-cell multi-user multiple-input multiple-output (MIMO) system, where the angular domain in the physical channel model is divided into a finite number of separate directions and the base station (BS) is equipped with a large number of antenna elements. Then, we develop an approximation for the spectral efficiency of various detectors such as maximum-ratio combining (MRC), zero-forcing (ZF), and linear minimum mean square error (LMMSE). We also propose a resource allocation scheme in which the pilot power, data power, and training duration are optimally chosen in order to maximize the spectral efficiency in a given total power budget. By employing the proposed power allocation scheme, the simulation results illustrate a notable improvement in the achievable spectral efficiency. Moreover, the results show that the performance of the proposed method is much superior when the number of channel directions or the number of antennas at BS increases. Furthermore, while the advantage of the proposed method is more notable in the case of ZF and LMMSE receivers, it still outperforms the equal power allocation method for the MRC receiver in terms of spectral efficiency.

Performance Analysis of a Linear MMSE Receiver in Time-Variant Rayleigh Fading Channels

The performance of the uplink of single and multiuser multiple input multiple output (MIMO) systems depends crucially on the receiver architecture and the quality of channel state information at the receiver. Therefore, several previous works have developed minimum mean squared error (MMSE) receivers and proposed balancing the resources spent on acquiring channel state information and transmitting the payload of data packets. Somewhat surprisingly, the most popular MIMO linear MMSE receivers do not exploit the correlation structure that is present in autoregressive Rayleigh fading environments. Therefore, in this article we first develop a new linear receiver that not only takes channel state information errors into account in minimizing the MSE of the received data symbols, but it also utilizes that the subsequent noisy channel coefficients are correlated. For this new linear MMSE receiver, we derive the achieved MSE as a function of the number of receive antennas and the pilot-to-data power ratio. Interestingly, we find that the pilot power that minimizes the MSE of the data symbols does not depend on the number of antennas and that the new linear MMSE receiver outperforms previously proposed MIMO receivers when the autocorrelation coefficient of the channel is high.

Massive MIMO Channel Estimation With Low-Resolution Spatial Sigma-Delta ADCs

We consider channel estimation for an uplink massive multiple-input multiple-output (MIMO) system where the base station (BS) uses an array with low-resolution (1-2 bit) analog-to-digital converters and a spatial Sigma-Delta ( ΣΔ) architecture to shape the quantization noise away from users in some angular sector. We develop a linear minimum mean squared error (LMMSE) channel estimator based on the Bussgang decomposition that reformulates the nonlinear quantizer model using an equivalent linear model plus quantization noise. We also analyze the uplink achievable rate with maximal ratio combining (MRC), zero-forcing (ZF) and LMMSE receivers and provide a lower bound for the achievable rate with the MRC receiver. Numerical results show superior channel estimation and sum spectral efficiency performance using the ΣΔ architecture compared to conventional 1- or 2-bit quantized massive MIMO systems.

Phase Noise in Modular Millimeter Wave Massive MIMO

This paper investigates the effect of oscillator phase noise on a multiuser millimeter wave (mmWave) massive MIMO uplink as we scale up the number of base station antennas, fixing the load factor, defined as the ratio of the number of simultaneous users to the number of base station antennas. We consider a modular approach in which the base station employs an array of subarrays, or “tiles.” Each tile supports a fixed number of antennas, and can therefore be implemented using a separate radio frequency integrated circuit (RFIC), with synchronization across tiles accomplished by employing a phased locked loop in each tile to synthesize an on-chip oscillator at the carrier frequency by locking on to a common lower frequency reference clock. Assuming linear minimum mean squared error (LMMSE) multiuser detection, we provide an analytical framework that can be used to specify the required power spectral density (PSD) mask for phase noise for a target system performance. Our analysis for the phase noise at the output of the LMMSE receiver indicates two distinct effects: self-noise for each user which is inversely proportional to the number of tiles, and cross-talk between users which is insensitive to the number of tiles, and is proportional to the load factor. These analytical predictions, verified by simulations for a 140 GHz system targeting a per-user data rate of 10 Gbps, show that tiling is a robust approach for scaling. Numerical results for our proposed design approach yield relatively relaxed specifications for phase noise PSD masks.

Effect of Pilot Contamination Over Diversity Gain in Multi-cell MU-MIMO Systems

In this paper, we investigate the diversity performance of multi-cell multi-user multiple-input multiple-output wireless system with linear minimum mean-squared error receiver. We consider imperfect channel state information at the receiver, and in particular we focus on the effect of pilot contamination. With the equivalent channel model, we study the outage probability of the uplink transmission, and mathematically analyze the diversity performance. We successfully derive the closed-form expression of the outage probability in finite signal to noise ratio (SNR) regime, and then the optimal pilot-to-data power ratio is studied. It is proved that due to pilot contamination, diversity gain approaches to zero with the SNR growing to positive infinite.

A New Turbo Equalizer Conditioned on Estimated Channel for MIMO MMSE Receiver

In this letter, we propose a new equalization scheme based on minimum mean-square error (MMSE) criteria with a channel estimation error. Different from the existing work on linear MMSE receivers, we consider both the a priori information and channel estimation error in the equalizer design, and re-derive the soft output extrinsic information used for the channel decoder. Conditioned on the estimated channel, we developed the new autocorrelation and covariance matrix of the received vector, which are used to derive the equalizer coefficients. One of our major contributions of this letter is a general expression of the MMSE-based turbo equalization to account for both the channel estimation error and the a priori information, which is not presented in the literature. Simulation results show that significant performance improvement can be achieved with the proposed turbo equalizer.

A Low-Complexity Graph-Based LMMSE Receiver for MIMO ISI Channels With $M$ -QAM Modulation

In this paper, we propose a low complexity graph-based linear minimum mean square error (LMMSE) equalizer in order to remove inter-symbol and inter-stream interference in multiple input multiple output (MIMO) communication. The proposed state space representation inflicted on the graph provides linearly increasing computational complexity with block length. Also, owing to the Gaussian assumption used in the presented cycle-free factor graph, the complexity of the suggested equalizer structure is not affected by the size of the signalling space. In addition, we introduce an efficient way of computing extrinsic bit log-likelihood ratio (LLR) values for LMMSE estimation compatible with higher order alphabets which is shown to perform better than the other methods in the literature. Overall, we provide an efficient receiver structure reaching high data rates in frequency selective MIMO systems whose performance is shown to be very close to a genie-aided matched filter bound through extensive simulations.

Soft‐output MMSE MIMO detector under different channel estimation models

This study considers the effect of channel estimation error (CEE) on the soft-output bit log-likelihood ratio (LLR) in a multiple-input–multiple-output detection system which the source sends their quadrature amplitude modulation to the detector through Rayleigh fading channels. The new expressions of LLR with maximum-likelihood CE for deterministic channel model and minimum mean square error (MMSE) CE for random channel model are obtained separately for linear MMSE receiver using known pilot-symbol-aided CE. Meanwhile, the optimal power allocation between training and data transmissions for these two different LLR expressions, which attends to get the maximum ratio of signal and interference plus noise ratio, are obtained under the total transmitting power constraints. Numerical results show that the power allocation ratio sets to be ∼0.5 is optimal for two new different LLRs at the same total power and system noise. Moreover, the derived LLR expressions match the simulation result and outperform the conventional system without the consideration of CEE and optimal power allocation. Meanwhile, the system performance is better than the existing research with the consideration of CE.

Low-complexity distributed algorithms for uplink CoMP in heterogeneous LTE networks

Coordinated multi-point transmission (CoMP) techniques are being touted as enabling technologies for interference mitigation in next generation heterogeneous wireless networks (HetNets). In this paper, we present a comparative performance study of uplink (UL) CoMP algorithms for the 3GPP LTE HetNets. Focusing on a distributed and functionally-split architecture, we consider six distinct UL-CoMP algorithms: 1. Joint reception in the frequency-domain (JRFD) 2. Two-stage equalization (TSEQ) 3. Log-likelihood ratio exchange (LLR-E) 4. Symmetric TSEQ (S-TSEQ) 5. Transport block selection diversity (TBSD) 6. Coordinated scheduling with adaptive interference mitigation (CS-AIM) where JRFD, TSEQ, S-TSEQ, TBSD and CS-AIM are our main contributions in this paper, and quantify their relative performances via the post-processing signal-to-interference-plus-noise ratio distributions. We also compare the CoMP-specific front-haul rate requirements for all the schemes considered in this paper. Our results indicate that, with a linear minimum mean-square error receiver, the JRFD and TSEQ have identical performances, whereas S-TSEQ relaxes the front-haul latency requirements while approaching the performance of TSEQ. Furthermore, in a HetNet environment, we find that CS-AIM provides an attractive alternative to TBSD and LLR-E with a significantly reduced CoMP-specific front-haul rate requirement.

LMMSE SIMO Receiver for Short-Range Non-Line-of-Sight Scattering Communication

We propose linear minimum mean square error (LMMSE) receivers for optical wireless scattering communications with single transmitter and multiple receivers, namely the single-input multiple-output (SIMO) system, where the received signals exhibit the characteristics of discrete photons. We first propose an LMMSE receiver scheme based on photon-counting detection, and then generalize to other type of receivers with amplification gains such as photomultiplier tube (PMT) and avalanche photodetector (APD). The proposed LMMSE receiver is designed for both on-off key (OOK) modulation and pulse-position modulation (PPM), and estimated bit mean square error performance is analyzed in detail. Simulation results are provided to show the bit estimation performance of the proposed LMMSE receivers. It is concluded that OOK incurs larger estimation error at smaller required bandwidth, while $M$ -PPM with $M > 4$ leads to smaller estimation error with more bandwidth requirements.

Properties, performance and practical interest of the widely linear MMSE beamformer for nonrectilinear signals

Widely Linear (WL) Minimum Mean Square Error (MMSE) estimation has received a great interest these last 20 years for second order (SO) noncircular signals. In the context of radio communications networks, it has been shown in particular that WL MMSE receivers allow to implement Single Antenna Interference Cancellation (SAIC) of one rectilinear interference, such as Binary Phase Shift Keying (BPSK) or Amplitude Shift Keying (ASK) interference, or of quasi-rectilinear interference, such as Minimum Shift keying (MSK), Gaussian MSK (GMSK) or Offset Quadrature Amplitude Modulation (OQAM) interference, hence their great interest for Global System for Mobile Communications (GSM) cellular networks in particular. However, one may wonder whether WL MMSE receivers remain attractive for SO noncircular nonrectilinear interferences, not so scarce in practice. The purpose of this paper is mainly to answer to this important question by giving, in a self-contained and unified way, some new insights into the behavior, properties and performance of the WL MMSE beamformer in the presence of arbitrary noncircular signals and interference which are not necessarily rectilinear. It is shown in particular that, surprisingly, WL MMSE receivers lose their practical interest for strong interferences which are not rectilinear. This breakthrough thus generates a new open problem for the choice between linear and WL MMSE receiver corresponding to the detection of rectilinearity (and/or quasi-rectilinearity), instead of noncircularity, in a given noisy observation. Although this question is out of the scope of this paper, we finally propose preliminary tools based on blind source separation methods to solve this problem.

Diversity Analysis of Randomized Linear Dispersion Codes in a Half-Duplex Amplify-and-Forward Multiple-Relay System

A point-to-point multiple-relay communication system with half-duplex constraints is considered. The relays operate under the amplify-and-forward paradigm and implement a linear dispersion distributed space-time code with randomized dispersion matrices of independent and identically distributed entries. The large-signal-to-noise-ratio behavior of the asymptotically large deterministic system is studied for both the optimum (maximum likelihood) receiver and the linear minimum mean squared error (LMMSE) receiver. The diversity order of the system is shown to have a strong dependence on the aspect ratio of the linear dispersion matrices. More specifically, when the linear dispersion matrices are sufficiently tall, both receivers achieve the maximum diversity order, i.e., the total number of relays plus one. Conversely, when the linear dispersion matrices are fat (in the sense that relays linearly compress the information received from the source), the optimum receiver is shown to achieve an asymptotic diversity order of two, whereas the LMMSE receiver is totally unable to exploit the available spatial diversity.

Single Stream HSDPA MIMO 시스템에서 Precoding Weight 적용에 따른 LMMSE 수신기 성능 고찰

최근 들어 CDMA 기반 시스템에서 고속 데이터 서비스 지원을 위한 수신 성능 개선 방법의 하나로 칩 단위에서 동작하는 선형 최소 평균 제곱 오차(LMMSE: linear minimum mean-squared error) 수신기에 대한 연구가 활발히 진행되고 있다. 본 논문에서는 D-TxAA (dual stream transmit antenna array) 방식을 사용하는 단일 스트림(single stream) HSDPA MIMO 시스템에서 선부호화 계수(precoding weight) 적용이 LMMSE 수신기의 성능에 미치는 영향을 분석하고자 한다. 우선 D-TxAA 기반 2x2 다중입력 다중출력(MIMO: multiple input multiple output) 시스템에서 수신 신호 순간 파워 (instantaneous power)의 총 합이 최대가 되도록 하는 선부호화 계수 결정 방식을 유도할 것이다. 또한 선부호화 계수의 적용 지연 시간과 단말의 이동 속도가 LMMSE 수신기의 성능에 미치는 영향을 분석하고, 컴퓨터 모의실험을 통해 검증하고자 한다.

무선 애드혹 네트워크에서의 간섭 제어 수신 기법

근래 애드혹 네트워크에서 송신 노드가 하나의 안테나만을 가지고 있을 지라도 다수의 수신 안테나로 선형적인 네트워크 throughput에 근접한 값을 얻을 수 있음이 보여졌다. 본 논문에서는 수신 노드에서 채널 상태 정보 (channel state information at reciever, CSIR)가 주어지지 않았을 때, 비모수 기반 선형 평균 제곱오차 (MMSE) 수신기를 사용하여 안테나 수에 비례하는 선형 이득을 얻는 수신 기법을 제안한다. 제안하는 방법에서는 간섭과 노이즈의 공분산에 관심 있는 채널 정보를 포함하여 전송률의 손실 없이 최적의 MMSE 전송 용량에 근접한 결과를 얻는다. 네트워크 전송 용량에 대한 분석과 모의실험을 통해 제안하는 비모수 기반의 선형 MMSE 수신 기법이 기존의 알고리즘들보다 우수한 성능을 가질 수 있음을 확인할 수 있다.

Adaptive BER-constraint-based power allocation for downlink MC-CDMA systems with linear MMSE receiver

To facilitate the efficient allocation of limited transmit power, a bit error rate (BER) constraint based power allocation scheme is proposed in this paper for the downlink of multi-carrier code division multiple access (MC-CDMA) systems with linear minimum mean square error (MMSE) receiver. According to the instantaneous channel conditions, the proposed scheme can adaptively allocate the required minimum transmit power on each channel to meet the BER constraint. The simulation results show that the proposed scheme is efficient in reducing the transmit power while meeting BER constraint, and thereby improve the system performance.