Minimum Mean Square Error Detector Research Articles

Dual-Driven Learning-Based Multiple-Input Multiple-Output Signal Detection for Unmanned Aerial Vehicle Air-to-Ground Communications

Unmanned aerial vehicle (UAV) air-to-ground (AG) communication plays a critical role in the evolving space–air–ground integrated network of the upcoming sixth-generation cellular network (6G). The integration of massive multiple-input multiple-output (MIMO) systems has become essential for ensuring optimal performing communication technologies. This article presents a novel dual-driven learning-based network for millimeter-wave (mm-wave) massive MIMO symbol detection of UAV AG communications. Our main contribution is that the proposed approach combines a data-driven symbol-correction network with a model-driven orthogonal approximate message passing network (OAMP-Net). Through joint training, the dual-driven network reduces symbol detection errors propagated through each iteration of the model-driven OAMP-Net. The numerical results demonstrate the superiority of the dual-driven detector over the conventional minimum mean square error (MMSE), orthogonal approximate message passing (OAMP), and OAMP-Net detectors at various noise powers and channel estimation errors. The dual-driven MIMO detector exhibits a 2–3 dB lower signal-to-noise ratio (SNR) requirement compared to the MMSE and OAMP-Net detectors to achieve a bit error rate (BER) of 1×10−2 when the channel estimation error is −30 dB. Moreover, the dual-driven MIMO detector exhibits an increased tolerance to channel estimation errors by 2–3 dB to achieve a BER of 1×10−3.

Developing analytical models for the post‐detection SINR of TSVD‐based techniques with imperfect CSI

SummaryIn massive multiple input multiple output (m‐MIMO) uplink, the performance gap between zero forcing (ZF) or direct pseudo‐inverse and minimum mean square error (MMSE) detection schemes increases with an increase in the load factor. To report this issue, truncated singular value decomposition (TSVD) is used in both ZF and direct pseudo‐inverse detection techniques using dynamic threshold. Moreover, the analytical models for the post‐detection signal‐to‐interference‐plus‐noise ratio (PDSINR) of TSVD‐based detection schemes are derived with imperfect channel state information (CSI), and subsequently, bit error rate (BER) is evaluated. Later, an optimum hard threshold for the TSVD‐based detection schemes is deduced from the empirical analysis. Further, the tightness of the analysis is verified through Monte Carlo trails. The simulation result shows that at lower values of average signal‐to‐noise ratio (SNR), TSVD‐based detection schemes with imperfect CSI offer comparable performance and low complexity when compared with the MMSE technique. However, the BER of TSVD‐based detection schemes decreases and gets saturated with an increase in the average SNR, whereas the BER of the MMSE detection scheme increases and approaches the BER of ZF or direct pseudo‐inverse detection schemes.

Low-Complexity BFGS-Based Soft-Output MMSE Detector for Massive MIMO Uplink

For the massive multiple-input multiple-output (MIMO) uplink, the linear minimum mean square error (MMSE) detector is near-optimal but involves undesirable matrix inversion. In this paper, we propose a low-complexity soft-output detector based on the simplified Broyden–Fletcher–Goldfarb–Shanno method to realize the matrix-inversion-free MMSE detection iteratively. To accelerate convergence with minimal computational overhead, an appropriate initial solution is presented leveraging the channel-hardening property of massive MIMO. Moreover, we employ a low-complexity approximated approach to calculating the log-likelihood ratios with negligible performance losses. Simulation results finally verify that the proposed detector can achieve the near-MMSE performance with a few iterations and outperforms the recently reported linear detectors in terms of lower complexity and faster convergence for the realistic massive MIMO systems.

Slepian Transform Based Detectors for HF Skywave Massive MIMO-OFDM Systems

In this paper, we investigate signal detection for high frequency (HF) skywave massive multiple-input multiple-output (MIMO) systems with orthogonal frequency division multiplexing (OFDM) modulation. We first introduce the beam based channel model for HF skywave massive MIMO-OFDM channels and show the relationship of sparse supports between the beam domain channel and the Fourier spectrum of the space domain channel. Based on the sparse beam domain channel, we propose a separate Slepian transform (SST) based detector, where a set of modulated Slepian sequences are designed independently for user terminals (UTs). Before the minimum mean-squared error (MMSE) detection, the Slepian transform is performed for each UT to reduce the dimension of the observation vector and the channel matrix, thus avoiding high dimensional matrices multiplications and inversions. Due to the sparsity of the beam domain channel, the Slepian transform of channel vectors can be efficiently implemented by low-dimensional matrix-vector multiplications. To further reduce the computational complexity, we propose a joint Slepian transform (JST) based detector, where a fixed set of modulated Slepian sequences are designed. As a result, Slepian transforms of the observation vector can be efficiently implemented using low-dimensional fast Fourier transform (FFT). Simulation results demonstrate the advantages of high performance and low complexity of proposed detectors.

Deep learning based MIMO systems using open-loop autoencoder

This article introduces two novel multiple input multiple output spatial division multiplexing (MIMO-SDM) systems based on deep learning techniques using bit-wise (BW) and symbol-wise (SW) open-loop autoencoders (AE), abbreviated as SWAE-MIMO and BWAE-MIMO. Based on the detection methods, we introduce three detectors at the receiver: Radio Transformation Network (RTN), Minimum Mean Square Error (MMSE) technique, and the combination of MMSE technique and neural network (MMSEnet), which can suppress co-channel interference (CCI) among received signal streams resulting in low bit error rates (BER). Furthermore, the considered systems are trained in a single phase to optimally synchronize the transmitter’s and receiver’s learning parameters, thus successfully exploiting spatial diversities to improve the error performance of conventional MIMO systems using the MMSE detector with different numbers of transmit-receive antennas. In a specific case, the BWAE-MIMO system using the RTN detector (BWAE-MIMO-RTN) achieves a BER comparable to that of the conventional MIMO system with a maximum likelihood detector (MIMO-ML) when both systems are equipped with two transmitting and receiving antennas.

On the Design of Optimal One-Shot Distributed Combining for Cooperative Multi-UAV Systems

Unmanned aerial vehicle (UAV) networks will become one of the key components of the future mobile communication systems, especially suitable for on-demand coverage extension and prompt capacity enhancement. However, UAV networks, detached from the ground infrastructure, are usually constrained for traffic-intensive network-wide signal processing. This paper tackles this issue by considering the multi-user signal detection at the UAV swarm, where the uplink signals of multiple ground users are cooperatively recovered. In particular, to reduce the signaling exchange and the coordination latency, a two-stage distributed minimum mean squared error (MMSE) detection is proposed for the UAV swarm, which merges the local MMSE detections at each UAV with one-shot weighted combining at a central station. The combining weights only depend on the long-term statistical channel state informations (CSIs) and therefore, are suitable for distributed network with limited signaling exchange. Numerical results show that the proposed distributed MMSE detection achieves similar performance to the centralized MMSE detection.

Multiuser-MIMO Systems Using Comparator Network-Aided Receivers With 1-Bit Quantization

Low-resolution analog-to-digital converters (ADCs) are promising for reducing energy consumption and costs of multiuser multiple-input multiple-output (MIMO) systems with many antennas. We propose low-resolution multiuser MIMO receivers where the signals are simultaneously processed by 1-bit ADCs and a comparator network, which can be interpreted as additional virtual channels with binary outputs. We distinguish the proposed comparator networks in fully and partially connected. For such receivers, we develop the low-resolution aware linear minimum mean-squared error (LRA-LMMSE) channel estimator and detector according to the Bussgang theorem. We also develop a robust detector which takes into account the channel state information (CSI) mismatch statistics. By exploiting knowledge of the channel coefficients we devise a mean-square error (MSE) greedy search and a sequential signal-to-interference-plus-noise ratio (SINR) search for optimization of partially connected networks. Numerical results show that a system with extra virtual channels can outperform a system with additional receive antennas, in terms of bit error rate (BER). Furthermore, by employing the proposed channel estimation with its error statistics, we construct a lower bound on the ergodic sum rate for a linear receiver. Simulation results confirm that the proposed approach outperforms the conventional 1-bit MIMO system in terms of BER, MSE and sum rate.

Kalman Combining Based Iterative Detection and Decoding for MIMO Systems With Hybrid ARQ

This study proposes Kalman combining-based iterative detection and decoding (KC-IDD) schemes for multiple-input multiple-output (MIMO) systems with hybrid automatic repeat request (HARQ). The conventional Kalman filtering (KF) operation for Kalman combining performs the linear minimum mean-square error (LMMSE) detection with symbol-level combining (SLC), but it is unable to utilize <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information of retransmitted symbols. Therefore, a new KF operation is derived, wherein an observation adjustment is employed to adjust the observation for a given state of the state-space model with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information instead of directly utilizing it into the KF operation. Based on the modified KF operation, two KC-IDD schemes are developed: i) KC-IDD with the single-state observation adjustment, i.e., the observation adjustment for the current HARQ round, and ii) KC-IDD with multi-state observation adjustment (KC-IDD-MS), i.e., the observation adjustments throughout the HARQ rounds of a packet. Therefore, the proposed schemes can perform SLC-based LMMSE-IDD, where the complexity for a given number of turbo iterations is similar or smaller to that of the conventional LMMSE-IDD scheme with bit-level combining (BLC). Furthermore, the simulation results show that regardless of the retransmission strategy, the proposed schemes, especially the KC-IDD-MS scheme, outperformed the conventional LMMSE-IDD scheme in terms of error performance and decoding convergence speed for retransmissions.

Low Complexity Signal Detection for Massive MIMO in B5G Uplink System

Massive Multiple Input Multiple Output (M-MIMO) is realized as a mandatory technique for Beyond Fifth Generation (B5G) wireless networks. In next-generation node B (gNB) uplink transmission, M-MIMO requires a low-complexity signal detection scheme with an increased number of antennas to attain high channel capacity and reliability. To attain close-optimal performance in these B5G systems, the Minimum Mean Square Error (MMSE) detection scheme is preferred at the gNB but it demands a complex matrix inversion concerning the number of users. Hence, this article proposes a Modified Weighted Two Stage (MWTS) iterative algorithm with an appropriate initial solution to realize MMSE detection at reduced complexity. MWTS detection algorithm is formulated by integrating the first half iteration phase of weighted two stage with the previous phase and ignoring the second half iteration. Further to improve the performance of the B5G system, a low-complexity soft decision Viterbi decoder is introduced at gNB. With K users, the proposed modifications display a reduction in computational complexity of 4K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> +16K as compared to the weighted two stage algorithm of 7K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> +8K. Simulation results confirm that the proposed MWTS algorithm yields lower complexity and near-optimal performance close to MMSE detection.

Low-complexity soft-output signal detector based on AI-SSOR preconditioned conjugate gradient method over massive MIMO correlated channel

Massive multiple-input multiple-output (MIMO) techniques with a large number of antenna elements at base station (BS) have been proved as an alternative to provide potential opportunity to increase the spectrum and energy efficiency. However, in the system, there generally exists a spatial correlation effect due to insufficient antenna elements spacing and/or the lack of rich scattering at BS. The minimum mean square error (MMSE) method performs signal detection at the expense of large-scale matrix inversion operation. Thus, the conjugate gradient (CG) method has received a lot of attentions to realize the MMSE detection efficiently. Unfortunately, this efficiency can be compromised due to the ill-conditioned equalization matrix of MMSE method over the correlated channel environments. Moreover, the hard output signal detection exhibits a sharply degradation in performance for higher-order quadrature amplitude modulation (QAM). Therefore, the modern communication systems use the soft-output information, i.e., log-likelihood ratio (LLR) along with the forward error-correcting code (FEC) to achieve satisfactory performance. The LLR computation along with a higher-order QAM remains challenging due to the exhaustive search of symbol in the modulation constellation. In this paper, a low-complexity soft-output signal detector based on approximate inverse symmetric successive over-relaxation preconditioned conjugate gradient (AI-SSOR-CG-SOD) method is proposed to realize MMSE method detection for uplink multiuser massive MIMO correlated channel. In the proposed method, a new preconditioner, an AI-SSOR, which is based on the Neumann series approximation of the inverse of the conventional SSOR preconditioner is firstly developed to handle ill-conditioned matrix, and then incorporated with CG method to improve the convergence rate and performance. According to the characteristic of the Gray-coding that adjacent symbols in the constellation set have only one different bit, the constellation set is divided multiple times based on the bits of the inphase and the quadrature components of the symbol, which reduces the complexity of the LLR computation of the transmitted bits by avoiding the exhaustive search process. Simulation results show that the AI-SSOR preconditioner is robust against spatial correlation effect, and the proposed detector converges at 3 iterations. Simulation results also show that the proposed detector achieves a better trade-off between the complexity and the performance compared to other existing detectors.

Fast-Converging and Low-Complexity Linear Massive MIMO Detection With L-BFGS Method

In massive multiple-input multiple-output (MIMO) uplink, linear minimum mean square error (MMSE) detection achieves near-optimal performance but suffers from undesirable computational burden due to the high-dimensional matrix inversion involved. To address this issue, the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) quasi-Newton method is introduced in this paper to realize free-matrix-inversion MMSE detection in an iterative way with significant reduction in computational complexity from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(K^{3})$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(L K^{2})$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L$</tex-math></inline-formula> denote the number of user antennas and iterations, respectively. For the better performance and complexity trade-off, three low-complexity L-BFGS based linear MMSE detection algorithms (namely E-LBFGS, I-LBFGS and S-LBFGS) are proposed successively. Furthermore, an efficient initialization strategy for the L-BFGS method based MMSE detection is devised, which helps to accelerate convergence and improve performance with acceptable complexity overhead added compared to the conventional L-BFGS based detection algorithms. Simulation results finally validate that the proposed detection scheme based on the L-BFGS method can closely approach to the MMSE accuracy with a small number of iterations even in poor propagation environments and provide attractive trade-offs between performance and complexity.

An embedded pilot power based channel estimation and low-complexity feedback equalization scheme for OTFS system

Orthogonal Time Frequency Space modulation (OTFS) has evolved as an astounding modulation technique for high-speed communication in a doubly dispersive channel. In any wireless communication system, channel estimation and equalization are essential at the receiver to recover the transmitted data. To accomplish this for the emerging OTFS based systems, a modified embedded pilot-based channel estimation technique and low complexity feedback equalization algorithm for integer Doppler shifts in the delay-Doppler domain are proposed in this paper. Our channel estimation scheme exploits embedded-pilot arrangement, and the symbol equalization relies on the Interference calculation and its mitigation iteratively. To achieve this we contemplate a prudent arrangement of symbols in the OTFS frame in such a way that the Guard symbols prevent the interference between data symbols and the pilot symbol at the receiver. Two distinct lumps of received data of the same OTFS frame will be engaged in channel estimation and data detection. An analytical expression of the theoretical Cramer Rao Lower Bound (CRLB) is derived and plotted for the proposed channel estimation scheme. The attained simulation results for Bit-Error-Rate (BER) under the proposed scheme show a significant error rate improvement over the Minimum Mean Squared Error (MMSE) equalization algorithm. Further, a lower computational complexity is also achieved in comparison with modified MMSE detection and MP detection algorithms.

Joint steepest descent and non‐stationary Richardson method for low‐complexity detection in massive MIMO systems

AbstractSignal detection is a major challenge in massive multiple‐input multiple‐output (MIMO) wireless systems due to array of hundreds of antennas. Linear minimum mean square error (MMSE) enables near‐optimal detection performance in massive MIMO but suffers from unbearable computational complexity due to complicated matrix inversions. To address this problem, we propose a novel low‐complexity signal detector based on joint steepest descent (SD) and non‐stationary Richardson (NSR) iteration method. The SD is applied to get an efficient searching direction for the following NSR method to enhance the performance. The key idea of the proposed algorithm is to utilize a combination of the scaled‐diagonal initialization and the system‐ and iteration‐dependent acceleration mechanism, so that the convergence can be significantly speeded up. An antenna‐ and eigenvalue‐based scaling parameter is introduced for the proposed detector to further improve the error‐rate performance. We also provide convergence guarantees for the proposed technique. Numerical results demonstrate that the proposed joint detection approach attains superior performance compared to existing iterative approaches and provides a lower computational complexity than the conventional MMSE detector.

Low‐complexity linear massive MIMO detection based on the improved BFGS method

Linear minimum mean square error (MMSE) detection achieves a good trade-off between performance and complexity for massive multiple-input multiple-output (MIMO) systems. To avoid the high-dimensional matrix inversion involved, MMSE detection can be transformed into an unconstrained optimization problem and then solved by efficient numerical algorithms in an iterative way. Three low-complexity Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton methods are proposed to iteratively realize massive MIMO MMSE detection without matrix inversion. The complexity can be reduced from O ( K 3 ) $\mathcal {O}(K^{3})$ to O ( L K 2 ) $\mathcal {O}(LK^{2})$ , where K and L denote the number of users and iterations, respectively. Leveraging the special properties of massive MIMO, the authors first explore a simplified BFGS method (named S-BFGS) to alleviate the computational burden in the search direction. For lower complexity, BFGS method with the unit step size (named U-BFGS) is presented subsequently. When the base station (BS)-to-user-antenna ratio (BUAR) is large enough, the two proposed BFGS methods can be integrated (named U-S-BFGS) to further reduce complexity. In addition, an efficient initialization strategy is devised to accelerate convergence. Simulation results verify that the proposed detection scheme can achieve near-MMSE performance with a small number of iterations L as low as 2 or 3.

Low-complexity soft-output signal detector based on adaptive pre-conditioned gradient descent method for uplink multiuser massive MIMO systems

In multiuser massive Multiple Input Multiple Output (MIMO) systems, a large amount of antennas are deployed at the Base Station (BS). In this case, the Minimum Mean Square Error (MMSE) detector with soft-output can achieve the near-optimal performance at the cost of a large-scale matrix inversion operation. The optimization algorithms such as Gradient Descent (GD) method have received a lot of attention to realize the MMSE detection efficiently without a large scale matrix inversion operation. However, they converge slowly when the condition number of the MMSE filtering matrix (the coefficient matrix) increases, which can compromise the efficiency of their implementation. Moreover, their soft information computation also involves a large-scale matrix-matrix multiplication operation. In this paper, a low-complexity soft-output signal detector based on Adaptive Pre-conditioned Gradient Descent (APGD-SOD) method is proposed to realize the MMSE detection with soft-output for uplink multiuser massive MIMO systems. In the proposed detector, an Adaptive Pre-conditioner (AP) matrix obtained through the Quasi-Newton Symmetric Rank One (QN-SR1) update in each iteration is used to accelerate the convergence of the GD method. The QN-SR1 update supports the intuitive notion that for the quadractic problem one should strive to make the pre-conditioner matrix close to the inverse of the coefficient matrix, since then the condition number would be close to unity and the convergence would be rapid. By expanding the signal model of the massive MIMO system and exploiting the channel hardening property of massive MIMO systems, the computational complexity of the soft information is simplified. The proposed AP matrix is applied to the GD method as a showcase. However, it also can be used by Conjugate Gradient (CG) method due to its generality. It is demonstrated that the proposed detector is robust and its convergence rate is superlinear. Simulation results show that the proposed detector converges at most four iterations. Simulation results also show that the proposed approach achieves a better trade-off between the complexity and the performance than several existing detectors and achieves a near-optimal performance of the MMSE detector with soft-output at four iterations without a complicated large scale matrix inversion operation, which entails a big challenge for the efficient implementation.

An Efficient Linear Detection Scheme Based on L-BFGS Method for Massive MIMO Systems

For massive multiple-input multiple-output (MIMO) systems, minimum mean square error (MMSE) detection is near-optimal, but requires high-complexity matrix inversion. To avoid matrix inversion, we formulate MMSE detection as a strictly convex quadratic optimization problem, which can be solved iteratively by the recognized most efficient Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method. According to special properties of massive MIMO systems, we propose a novel limited-memory BFGS (L-BFGS) scheme for MMSE detection with one correction search, unit step length, and simplified initialization, which can greatly reduce the storage and computation cost compared to BFGS method. Simulation results finally verify the effectiveness of the proposed scheme.

Efficient Soft-Output Gauss–Seidel Data Detector for Massive MIMO Systems

For massive multiple-input multiple-output (MIMO) systems, linear minimum mean-square error (MMSE) detection has been shown to achieve near-optimal performance but suffers from excessively high complexity due to the large-scale matrix inversion. Being matrix inversion free, detection algorithms based on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Gauss</i> – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Seidel</i> (GS) method have been proved more efficient than conventional <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Neumann</i> series expansion-based ones. In this paper, an efficient GS-based soft-output data detector for massive MIMO and a corresponding VLSI architecture are proposed. To accelerate the convergence of the GS method, a new initial solution is proposed. Several optimizations on the VLSI architecture level are proposed to further reduce the processing latency and area. Our reference implementation results on a Xilinx Virtex-7 XC7VX690T FPGA for a 128 base-station antenna and eight user massive MIMO system show that our GS-based data detector achieves a throughput of 732 Mb/s with close-to-MMSE error-rate performance. Our implementation results demonstrate that the proposed solution has advantages over the existing designs in terms of complexity and efficiency, especially under challenging propagation conditions.

Asymptotic Performance Analysis of MMSE Receivers in Multicell MU-MIMO Systems

For large-scale antenna array multiple-input multiple-output (MIMO) systems, a typical solution often put forward for uplink detection consists in applying low-complexity linear receivers such as zero-forcing (ZF) and minimum mean-square error (MMSE) combiners. In this paper, the performance of uplink MMSE detection has been analyzed in the context of a multi-cell multiuser MIMO system. An approximate expression for the signal-to-interference-plus-noise ratio (SINR) is proposed, which is in simple form and becomes exact in the low SNR regime. This approximate SINR applies to systems where the base station (BS) has the statistical information of the out-of-cell interfering signals, and systems where the BS ignores the presence of such interfering signals. This approximate SINR is tight for arbitrary user powers, arbitrary number of antennas at the base station, and arbitrary channel correlation matrix associated with any particular user. Approximate expressions for capacity and bit-error rate/symbol-error rate have also been derived. Particularly, it can be proven that, when the MMSE receiver ignores the presence of out-of-cell interfering signals, the performance gap between ZF and MMSE vanishes in the high SNR regime.

Bayesian Learning Aided Sparse Channel Estimation for Orthogonal Time Frequency Space Modulated Systems

A novel sparse channel state information (CSI) estimation scheme is proposed for orthogonal time frequency space (OTFS) modulated systems, in which the pilots are directly transmitted over the time-frequency (TF)-domain grid for estimating the delay-Doppler (DD)-domain CSI. The proposed CSI estimation model leads to a reduction in the pilot overhead as well as the training duration required. Furthermore, it does not require a DD-domain guard interval between the pilot and data symbols, hence increasing the bandwidth efficiency. A novel Bayesian learning (BL) framework is proposed for CSI acquisition, which exploits the DD-domain sparsity for improving the estimation accuracy in comparison to the conventional minimum mean squared error (MMSE)-based scheme. A low-complexity linear MMSE detector is used in the subsequent data detection phase. Our simulation results demonstrate the performance improvement of the proposed BL-based scheme over the conventional MMSE-based scheme as well as over other existing sparse estimation schemes.

Extreme learning machine detector for millimeter-wave massive MIMO systems

In this paper, we present an extreme learning machine (ELM) neural network designed to perform multiple-input multiple-output (MIMO) detection for millimeter-wave (mm-wave) communications operating in the 28 GHz frequency band. The ELM strategy can perform online MIMO combining processing. This method does not require offline training like with deep neural networks. The proposed technique was compared in terms of the achievable bit error rate (BER) and spectral efficiency (SE) to the maximum ratio (MR) and minimum mean squared error (MMSE) MIMO detectors, considering an orthogonal frequency-division multiplexing (OFDM) uplink scheme based on the fifth generation (5G) New Radio standard. Numerical results show that the ELM strategy outperforms the MR and MMSE detectors since this method reduces the inter-user interference effects, specifically for low equivalent isotropic radiated power at the receiver during the uplink communication. Furthermore, the ELM method requires only 16 % of the floating-point operations required by the MMSE detector.