Single-antenna User Equipments Research Articles

Cell-Free Massive MIMO With Mixed-Resolution ADCs and I/Q Imbalance Over Rician Spatially Correlated Channels

The practical deployment of cell-free massive multiple-input multiple-output (CF mMIMO), a promising technology empowering the sixth-generation with multitudinous access points (APs). This paper considers a CF mMIMO system over Rician spatially correlated fading channels with the single-antenna user equipments (UEs) and multi-antenna APs, where the phase-shift induced by the UEs' movement exists at the line-of-sight path. Though the low-resolution analog-to-digital converters (ADCs) can effectively address the expensive hardware cost and power-hungry problems, complicated data processing algorithms are of vital importance to be well designed to compensate for the performance gap compared with the real scenarios since the hardware impairments. However, the novel mixed-ADC architecture could solve the above challenges with better performance. So, we investigate the effect of mixed-resolution ADCs deploying at APs and the in-phase and quadrature-phase imbalance (IQI) on the CF mMIMO systems. Furthermore, the achievable uplink spectral efficiency (SE) is analyzed considering IQI and quantization loss based on a two-layer decoding scheme. Moreover, the novel closed-form SE expression with the maximum ratio (MR) combining is derived. And we find the relationship between the SE performance and different combining schemes, quantization bits, and IQI parameters. Finally, the numerical results reveal the mixed-resolution ADCs show a great advantage in boosting the SE performance, and increasing the number of APs is an effective means to promote the system performance.

Deep learning-based energy efficiency and power consumption modeling for optical massive MIMO systems

The fifth generation (5G) wireless communication system is considered a promising and recent research. Massive Multiple-Input Multiple-Output (MIMO) system has an influential role in improving game-changing enhancements in area throughput and energy efficiency (EE). EE refers to one of the easiest and most cost-effective ways to combat climate change, reduce energy costs for consumers, and improve the competitiveness of businesses. Deep Learning (DL) can significantly improve area throughput and EE. It plays a crucial role in the 5G wireless communication systems. Optical systems are not far from this system, which include the optical components which serve more accurately.To assess the overall power usage in up-link and down-link communications, a power dissipated model is introduced. The proposed model incorporates the overall power used by the base station (BS) power amplifier and circuit components as well as single antenna user equipment (UE). In this paper, EE and power consumption of massive MIMO systems are calculated based on Convolutional Neural Network hybrid with Long Short-Term Memory cell (CNNLSTM). This model is proposed to overcome the high complexity and over fitting by replacing the inner dense connections with convolution layers resulting in improved model performance. There are different linear processing schemes applied for detection and precoding, as Minimum Mean Squared Error (MMSE), Zero-Forcing (ZF), and Maximum Ratio Transmission/Maximum Ratio Combining (MRT/MRC). These schemes are applied to train our proposed CNNLSTM.It is observed the results are improved by 12.8% when using ZF (perfect CSI) and the system outperforms other schemes by 10%, 10.44% and 12.05% when using MRT, ZF (imperfect CSI), and MMSE, respectively, for the EE performance. The obtained results also reveal that an improvement of 7.5% is achieved when using MRT. It outperforms other schemes by 6.5%, 5% and 5%, respectively, when using ZF (perfect CSI), ZF (imperfect CSI), and MMSE for average power consumption per antenna using the CNNLSTM model. When using MRT, an improvement of 7.5% is achieved in the area throughput performance, and it outperformed the other schemes, ZF (perfect CSI), ZF (imperfect CSI) and MMSE, by 5.2%, 5% and 5.2%, respectively.

Low-complexity signal detection networks based on Gauss-Seidel iterative method for massive MIMO systems

In massive multiple-input multiple-output (MIMO) systems with single- antenna user equipment (SAUE) or multiple-antenna user equipment (MAUE), with the increase of the number of received antennas at base station, the complexity of traditional detectors is also increasing. In order to reduce the high complexity of parallel running of the traditional Gauss-Seidel iterative method, this paper proposes a model-driven deep learning detector network, namely Block Gauss-Seidel Network (BGS-Net), which is based on the Gauss-Seidel iterative method. We reduce complexity by converting a large matrix inversion to small matrix inversions. In order to improve the symbol error ratio (SER) of BGS-Net under MAUE system, we propose Improved BGS-Net. The simulation results show that, compared with the existing model-driven algorithms, BGS-Net has lower complexity and similar the detection performance; good robustness, and its performance is less affected by changes in the number of antennas; Improved BGS-Net can improve the detection performance of BGS-Net.

IRS-Aided SWIPT: Joint Waveform, Active and Passive Beamforming Design Under Nonlinear Harvester Model

The performance of Simultaneous Wireless Information and Power Transfer (SWIPT) is mainly constrained by the received Radio-Frequency (RF) signal strength. To tackle this problem, we introduce an Intelligent Reflecting Surface (IRS) to compensate the propagation loss and boost the transmission efficiency. This paper proposes a novel IRS-aided SWIPT system where a multi-carrier multi-antenna Access Point (AP) transmits information and power simultaneously, with the assist of an IRS, to a single-antenna User Equipment (UE) employing practical receiving schemes. Considering harvester nonlinearity, we characterize the achievable Rate-Energy (R-E) region through a joint optimization of waveform, active and passive beamforming based on the Channel State Information at the Transmitter (CSIT). This problem is solved by the Block Coordinate Descent (BCD) method, where we obtain the active precoder in closed form, the passive beamforming by the Successive Convex Approximation (SCA) approach, and the waveform amplitude by the Geometric Programming (GP) technique. To facilitate practical implementation, we also propose a low-complexity design based on closed-form adaptive waveform schemes. Simulation results demonstrate the proposed algorithms bring considerable R-E gains with robustness to CSIT inaccuracy and finite IRS states, and emphasize the importance of modeling harvester nonlinearity in the IRS-aided SWIPT design.

Capacity Approaching Low Density Spreading in Uplink NOMA via Asymptotic Analysis

Low-density spreading non-orthogonal multiple-access (LDS-NOMA) is considered where K single-antenna user-equipments (UEs) communicate with a base-station (BS) over F fading sub-carriers. Each UE k spreads its data symbols over d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> <; <; F sub-carriers. The performance of LDS-NOMA system depends on the allocation of the non-zero elements in the LDS-codes. We aim to identify the LDS resource allocations, based solely on pathlosses, that maximize the ergodic mutual information (EMI). This problem can be solved only via an exhaustive search. Thus, relying on analysis in the regime where F, K, and d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ,∀k converge to +∞ at the same rate, we present EMI as a deterministic equivalent plus a residual term. The deterministic equivalent is a function of pathloss values and LDS-codes, and the small residual term scales as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (1 / min(d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> )). First, we formulate an optimization problem to identify the resource allocations that maximize the deterministic equivalent of EMI. The Karush-Kuhn-Tucker conditions give a simple resource allocation rule that facilitates the construction of desired LDS-codes via an efficient partitioning algorithm. The finite-regime analysis shows that such sparse solutions additionally harness the small incremental gain inherent in the residual term, and thus, provides a near-optimal performance. The spectral efficiency enhancement relative to regular and random spreading is validated numerically.

Joint Power Control and LSFD for Wireless-Powered Cell-Free Massive MIMO

This paper considers wireless uplink information and downlink power transfer in cell-free massive multiple-input multiple-output systems. The single-antenna user equipments (UEs) utilize the energy harvested in the downlink to transmit uplink pilot and information signals to the multiple-antenna access points (APs). We consider Rician fading and maximum ratio processing based on either linear minimum mean-squared error (LMMSE) or least-squares (LS) channel estimation. We derive the average harvested energy by using a practical non-linear energy harvesting circuit model for both coherent and non-coherent transmission schemes. Furthermore, the uplink spectral efficiency (SE) is derived for all the considered methods and the max-min fairness problem is cast where the optimization variables are the AP and UE power control coefficients together with the large-scale fading decoding vectors. The objective is to maximize the minimum SE of the UEs’ under APs’ and UEs’ transmission power constraints. A novel alternating optimization algorithm with guaranteed convergence and improvement at each step is proposed to solve the highly-coupled non-convex problem.

Energy Efficiency Augmentation in Massive MIMO Systems through Linear Precoding Schemes and Power Consumption Modeling

Massive multiple-input multiple-output or massive MIMO system has great potential for 5th generation (5G) wireless communication systems as it is capable of providing game-changing enhancements in area throughput and energy efficiency (EE). This work proposes a realistic and practically implementable EE model for massive MIMO systems while a general and canonical system model is used for single-cell scenario. Linear processing schemes are used for detection and precoding, i.e., minimum mean squared error (MMSE), zero-forcing (ZF), and maximum ratio transmission (MRT/MRC). Moreover, a power dissipation model is proposed that considers overall power consumption in uplink and downlink communications. The proposed model includes the total power consumed by power amplifier and circuit components at the base station (BS) and single antenna user equipment (UE). An optimal number of BS antennas to serve total UEs and the overall transmitted power are also computed. The simulation results confirm considerable improvements in the gain of area throughput and EE, and it also shows that the optimum area throughput and EE can be realized wherein a larger number of antenna arrays at BS are installed for serving a greater number of UEs.

RISMA: Reconfigurable Intelligent Surfaces Enabling Beamforming for IoT Massive Access

Massive access for Internet-of-Things (IoT) in beyond 5G networks represents a daunting challenge for conventional bandwidth-limited technologies. Millimeter-wave technologies (mmWave)-which provide large chunks of bandwidth at the cost of more complex wireless processors in harsher radio environments-is a promising alternative to accommodate massive IoT but its cost and power requirements are an obstacle for wide adoption in practice. In this context, meta-materials arise as a key innovation enabler to address this challenge by Re-configurable Intelligent Surfaces (RISs). In this article we take on the challenge and study a beyond 5G scenario consisting of a multi-antenna base station (BS) serving a large set of single-antenna user equipments (UEs) with the aid of RISs to cope with non-line-of-sight paths. Specifically, we build a mathematical framework to jointly optimize the precoding strategy of the BS and the RIS parameters in order to minimize the system sum mean squared error (SMSE). This novel approach reveals convenient properties used to design two algorithms, RISMA and Lo- RISMA, which are able to either find simple and efficient solutions to our problem (the former) or accommodate practical constraints with low-resolution RISs (the latter). Numerical results show that our algorithms outperform conventional benchmarks that do not employ RIS (even with low-resolution meta-surfaces) with gains that span from 20% to 120% in sum rate performance.

Average Vector-Symbol Error Rate Closed-Form Expression for ML Group Detection Receivers in Large MU-MIMO Channels With Transmit Correlation

In this paper, we derive a closed-form expression for the evaluation of the average vectorsymbol error rate (VER) of group detection followed by maximum-likelihood (GD-ML) receivers in large multi-user multiple-input multiple-output (MU-MIMO) systems with transmit side correlated Rayleigh channels. We assume M antennas at the base station (BS), N closely-located, single-antenna user equipment (UEs) with load factor λ = N/M , and N ≫ 1; consequently, we evaluate the performance of GD-ML receivers as the load factor grows to unity. The derived expression requires a negligible correlation at the receive side of the communication channel. Hence, from a practical point-of-view, when considering scenarios with a large number of UEs, the derived analytical expression is generally more applicable for systems with a distributed massive number of BS antennas. Numerical results are provided to validate our derived expression. We observe that the GD-ML with Nu group size achieves a diversity order proportional to M - N + Nu. Moreover, we show that for small group sizes, the analytical and simulation results remain close, and at moderate to high signal-to-noise ratio (SNR), the derived expression very closely matches the simulations, whereas this match becomes perfect as the users' side correlation increases. We also demonstrate that GD-ML outperforms the zero-forcing (ZF) and minimum mean-squared error (MMSE) receivers, in terms of VER; where for high λ, GD-ML exploits the maximum spatial multiplexing gain. Moreover, in terms of floating-point operations (FLOPs), we show that GD-ML receivers have almost the same complexity as ZF and MMSE where the ML detection stage adds a negligible complexity compared to the channel matrix inversion operation.

Edge and Central Cloud Computing: A Perfect Pairing for High Energy Efficiency and Low-Latency

In this paper, we study the coexistence and synergy between edge and central cloud computing in a heterogeneous cellular network (HetNet), which contains a multi-antenna macro base station (MBS), multiple multi-antenna small base stations (SBSs) and multiple single-antenna user equipment (UEs). The SBSs are empowered by edge clouds offering limited computing services for UEs, whereas the MBS provides high-performance central cloud computing services to UEs via a restricted multiple-input multiple-output (MIMO) backhaul to their associated SBSs. With processing latency constraints at the central and the edge networks, we aim to minimize the system energy consumption used for task offloading and computation. The problem is formulated by jointly optimizing the cloud selection, the UEs' transmit powers, the SBSs' receive beamformers, and the SBSs' transmit covariance matrices, which is a mixed-integer and non-convex optimization problem. Based on the methods such as decomposition approach and successive pseudoconvex approach, a tractable solution is proposed via an iterative algorithm. The simulation results show that our proposed solution can achieve great performance gain over conventional schemes using edge or central cloud alone. Also, with large-scale antennas at the MBS, the massive MIMO backhaul can significantly reduce the complexity of the proposed algorithm and obtain even better performance.

Energy Efficient Beamforming for User-Centric Virtual Cell Networks

This paper aims to design beamforming vectors and cluster formation scheme by formulating an energy efficiency (EE) maximization problem in the user-centric networks, where several multi-antenna access points (APs) form a virtual cell to serve each single-antenna user equipment (UE). Considering both rate requirements and power budgets, we study the feasibility of the original EE maximization problem. To verify the feasibility, we design a max-min rate problem. Then, instead of solving the original problem directly, we deal with two subproblems: 1) relaxed EE maximization subproblem and 2) total power minimization subproblem. Through applying the weighted minimum mean square error (WMMSE) approach, we first transform the nonlinear data rate expression into a quadratic form and then solve each subproblem via using the Lagrangian dual method, which fortunately has closed-form solutions. Moreover, a novel threshold forming scheme is proposed for AP cluster formation and a simple but effective method called K-dimension grid search is devised to obtain the near-optimal threshold. The extensive simulation results indicate that our proposed algorithm converges fast and is robust to the simulation environment. In addition, the proposed algorithm outperforms the benchmark algorithms greatly in terms of EE and data rate.

Theoretical Performance Limits of Massive MIMO With Uncorrelated Rician Fading Channels

This paper considers a Massive MIMO network with $ {L}$ cells, each comprising a base stations (BS) with $ {M}$ antennas and $K$ single-antenna user equipments. Within this setting, we are interested in deriving approximations of the achievable rates in the uplink and downlink under the assumption that single-cell linear processing is used at each BS and that each intracell link forms an uncorrelated MIMO Rician fading channel matrix; that is, with a deterministic line-of-sight (LoS) path and a stochastic non-LoS component describing a spatial uncorrelated multipath environment. The analysis is conducted assuming that $ {N}$ and $ {K}$ grow large with a given ratio ${\textbf {N/K}}$ under the assumption that the data transmission in each cell is affected by channel estimation errors, pilot contamination, an arbitrary large scale attenuation and LoS components. Numerical results are used to prove that the approximations are asymptotically tight, but accurate for systems with finite dimensions. The asymptotic results are also used to evaluate the impact of LoS components. In particular, we exemplify how the number of antennas for achieving a target rate can be substantially reduced with LoS links of only a few dBs of strength.

Asymptotic Analysis of RZF in Large-Scale MU-MIMO Systems Over Rician Channels

In this paper, we focus on the downlink ergodic sum rate of a single-cell large-scale multiuser MIMO system in which the base station employs N antennas to communicate with K single-antenna user equipments (TIEs). A regularized zero-forcing (RZF) scheme is used for precoding under the assumption that each TIE uses a specific power and each link forms a spatially correlated MIMO Rician fading channel. The analysis is conducted assuming that N and K grow large with a given ratio and perfect channel state information is available at the base station. New results from random matrix theory and large system analysis are used to compute an asymptotic expression of the signal-to-interference-plus-noise ratio as a function of system parameters, spatial correlation matrix, and Rician factor. Numerical results are used to validate the accuracy of asymptotic approximations in the finite system regime and to evaluate the performance under different operating conditions. It turns out that the asymptotic expressions provide accurate approximations even for relatively small values of N and K.

Analyzing Coverage Probability of Multitier Heterogeneous Networks Under Quantized Multiuser ZF Beamforming

In this paper, we analyze the coverage probability of a large-scale heterogenous cellular network (HetNet) where base stations (BSs) are equipped with multiantennas, serving a number of single-antenna user equipments (UEs) in the downlink—space division multiple access (SDMA). Adopting the tool of stochastic geometry, we analyze the coverage probability under the quantized zero-forcing beamforming (ZFBF). This analysis, however, intricate as a typical UE in a given cell experiences: i) a residual inter-user interference (IUI) rendered by the quantization error; ii) quantization-driven statistical correlation between its attending signal power and IUI; iii) Nakagami-type fading environment, induced by postprocessing ZFBF; and iv) intercell interference (ICI). Current related literature has not effectively accounted for issues (i), (ii), and (iv) and commonly resorted to simplifying scenarios of full SDMA (i.e., exponential fading), independency of IUI and attending signal power, approximating IUI via an exponential random variable, and the quantization cell approximation (QCA). Our analysis relaxes such limiting assumptions; it includes the more relevant random vector quantization (RVQ) method, and compared to the literature, does not resort to the evaluation of a higher order differentiation for the evaluation of the coverage probability by exploiting our previously developed method. We further introduce three novel approximations of the coverage probability: RVQ-M , RVG-G , and QCA , which the first two approximations are given in semi-closed-form formulas (requiring a simple integration step) and the last approximation is in a closed-form expression. All approximations are numerically affordable, and we confirm the RVG-G approximation is the most accurate one. Finally, we exploit our analysis to study several practically insightful issues to shed some lights on: 1) for given feedback capacity and number of UEs, when desification becomes beneficial; 2) how multitierness of HetNets can be exploited for substantially reducing feedback capacity; and 3) an adaptive share of feedback capacity for the purpose of CDI as well as channel quality information (CQI) feedbacks, when there is an uplink penalty subjected for the feedback procedure and the scheduled data rate at each BS is specified adaptively based on the quantized CQI.

Low-Complexity Coordinated Beamforming for Full Duplex MIMO Wireless Cellulars

In this paper, we consider a full duplex (FD) MIMO multi-cell system, where each FD base station (BS) with multiple antennas serves multiple single-antenna user equipments (UEs) with half-duplex radios. Advancement in interference management is in demand to handle an even more severe case compared to single-cell scenario, as FD in multi-cell incurs additional BS-BS and UE–UE interferences. To this end, we propose a coordinated beamfroming (BF) at the BSs that maximizes a weighted sum rate subject to per-BS power constraint and BS–BS interference power constraints, with UE–UE interference handled by a pre-scheduling process. By converting the original non-convex problem into an auxiliary convex optimization, we can obtain the optimal BF vectors in closed-form. By utilizing an important feature of the optimal solution that naturally leads to a distributed implementation, we develop a low-complexity distributed BF approach, which only requires local channel state information. Simulation results demonstrate the performance of the proposed coordinated BF scheme, and reveal that the overall FD gains can be achieved despite the additional interferences introduced in the FD enabled cellulars.

Channel estimation for massive MIMO with 2-D nested array deployment

The problem of channel estimation in 5G is regarded as the one of the bottleneck problems due to its complexity related with large number of antenna elements at the BS side and more narrower beams when choosing high frequency such as millimeter wave. In this paper, we study the channel estimation problem for massive MIMO with a new antenna array at the base station (BS) side. The randomly deployed single antenna user equipments (UEs) within a single cell in the cellular network comprise of a random array. Based on the geometric channel model, using multiple snapshots of beamforming and combining vectors at the BS and UEs side respectively, the problem is formulated as a sparsity-aware problem and the coordinate descent algorithm is employed to retrieve the significant channel gain. Simulation results show the effective of the algorithm under two different scenarios with high SNR and low SNR respectively and for both cases, we can find the significant paths with properly chosen penalization parameter λ.

Downlink and Uplink Decoupling in Two-Tier Heterogeneous Networks With Multi- Antenna Base Stations

In order to improve the uplink performance of future cellular networks, the idea to decouple the downlink (DL) and uplink (UL) association has recently been shown to provide significant gain in terms of both coverage and rate performance. However, all the works are limited to a single input single output (SISO) network. Therefore, to study the gain provided by the DL and UL decoupling in multi-antenna base stations (BSs) setup, we study a two tier heterogeneous network consisting of multi-antenna BSs, and single antenna user equipments (UEs). We use maximal ratio combining (MRC) as a linear receiver at the BSs and tools from stochastic geometry, and we derive tractable expressions for both signal-to-interference ratio (SIR) coverage probability and rate coverage probability. We observe that as the disparity in the beamforming gain of both tiers increases, the gain in terms of SIR coverage probability provided by the decoupled association over non-decoupled association decreases. We further observe that when there is asymmetry in the number of antennas of both tiers, then we need further biasing toward femto-tier on the top of decoupled association to balance the load and get optimal rate coverage probability.

Max–Min SINR in Large-Scale Single-Cell MU-MIMO: Asymptotic Analysis and Low-Complexity Transceivers

This work focuses on the downlink and uplink of large-scale single-cell MU-MIMO systems in which the base station (BS) endowed with $M$ antennas communicates with $K$ single-antenna user equipments (UEs). Particularly, we aim at reducing the complexity of the linear precoder and receiver that maximize the minimum signal-to-interference-plus-noise ratio subject to a given power constraint. To this end, we consider the asymptotic regime in which $M$ and $K$ grow large with a given ratio. Tools from random matrix theory (RMT) are then used to compute, in closed form, accurate approximations for the parameters of the optimal precoder and receiver, when imperfect channel state information (modeled by the generic Gauss-Markov formulation form) is available at the BS. The asymptotic analysis allows us to derive the asymptotically optimal linear precoder and receiver that are characterized by a lower complexity (due to the dependence on the large scale components of the channel) and, possibly, by a better resilience to imperfect channel state information. However, the implementation of both is still challenging as it requires fast inversions of large matrices in every coherence period. To overcome this issue, we apply the truncated polynomial expansion (TPE) technique to the precoding and receiving vector of each UE and make use of RMT to determine the optimal weighting coefficients on a per-UE basis that asymptotically solve the max-min SINR problem. Numerical results are used to validate the asymptotic analysis in the finite system regime and to show that the proposed TPE transceivers efficiently mimic the optimal ones, while requiring much lower computational complexity.

Large System Analysis of Base Station Cooperation for Power Minimization

This paper focuses on a large-scale multi-cell multi-user MIMO system in which $L$ base stations (BSs) of $N$ antennas each communicate with $K$ single-antenna user equipments. We consider the design of the linear precoder that minimizes the total power consumption while ensuring target user rates. Three configurations with different degrees of cooperation among BSs are considered: the coordinated beamforming scheme (only channel state information is shared among BSs), the coordinated multipoint MIMO processing technology or network MIMO (channel state and data cooperation), and a single-cell beamforming scheme (only local channel state information is used for beamforming, while channel state cooperation is needed for power allocation). The analysis is conducted assuming that $N$ and $K$ grow large with a non trivial ratio $K/N$ , and imperfect channel state information (modeled by the generic Gauss–Markov formulation form) is available at the BSs. Tools of random matrix theory are used to compute, in explicit form, deterministic approximations for: i) the parameters of the optimal precoder; ii) the powers needed to ensure target rates; and iii) the total transmit power. These results are instrumental to get further insight into the structure of the optimal precoders and also to reduce the implementation complexity in large-scale networks. Numerical results are used to validate the asymptotic analysis in the finite system regime and to make comparisons among the different configurations.

Low Complexity Polynomial Expansion Detector With Deterministic Equivalents of the Moments of Channel Gram Matrix for Massive MIMO Uplink

We consider a low complexity polynomial expansion (PE) detector in a massive multiple-input multiple-output (MIMO) uplink channel. In contrast to most massive MIMO systems in the literature, where single antenna user equipments (UEs) are assumed, multiple antenna UEs are employed in this paper. Moreover, the channel between a base station (BS) and a UE is a jointly correlated Rician fading channel. The PE detector reduces the computational complexity of the minimum mean square error (MMSE) detector by replacing the matrix inversion with an approximate matrix polynomial. The coefficients of the approximate matrix polynomial are computed from the deterministic equivalents of the moments of the channel Gram matrix. We use operator-valued free probability, which is a more general version of free probability, to derive the deterministic equivalents. In particular, we use the operator-valued moment-cumulant formula. The proposed low complexity PE detector is easy to compute. Simulation results show that the proposed detector can achieve performance close to the MMSE detector.