Minimum Mean Square Error Receiver Research Articles

Optimal and suboptimal receivers for code‐multiplexed transmitted‐reference ultra‐wideband systems

ABSTRACTIn this study, optimal and suboptimal receivers are investigated for code‐multiplexed transmitted‐reference (CM‐TR) ultra‐wideband systems. First, a single‐user scenario is considered, and a CM‐TR system is modeled as a generalized noncoherent pulse‐position modulated system. Based on that model, the optimal receiver that minimizes the bit error probability is derived. Then, it is shown that the conventional CM‐TR receiver converges to the optimal receiver under certain conditions and achieves close‐to‐optimal performance in practical cases. Next, multi‐user systems are considered, and the conventional receiver, blinking receiver, and chip discriminator are investigated. Also, the linear minimum mean‐squared error (MMSE) receiver is derived for the downlink of a multi‐user CM‐TR system. In addition, the maximum likelihood receiver is obtained as a performance benchmark. The practicality and the computational complexity of the receivers are discussed, and their performance is evaluated via simulations. The linear MMSE receiver is observed to provide the best trade‐off between performance and complexity/practicality. Copyright © 2011 John Wiley & Sons, Ltd.

Novel Generic Bounds on the Sum Rate of MIMO ZF Receivers

This paper introduces some novel upper and lower bounds on the achievable sum rate of multiple-input multiple-output (MIMO) systems with zero-forcing (ZF) receivers. The presented bounds are not only tractable but also generic since they apply for different fading models of interest, such as uncorrelated/correlated Rayleigh fading and Ricean fading. We further formulate a new relationship between the sum rate and the first negative moment of the unordered eigenvalue of the instantaneous correlation matrix. The derived expressions are explicitly compared with some existing results on MIMO systems operating with optimal and minimum mean-squared error (MMSE) receivers. Based on our analytical results, we gain valuable insights into the implications of the model parameters, such as the number of antennas, spatial correlation and Ricean-K factor, on the sum rate of MIMO ZF receivers.

Transmit Precoding for Flat-Fading MIMO Multiuser Systems With Maximum Ratio Combining Receivers

We examine the application of transmit precoding in multiuser multi-input-multi-output (MIMO) communication systems with maximum ratio combining (MRC) receivers. In many multiuser applications, the maximum-likelihood or minimum mean-square error (MMSE) receivers can be prohibitive to implement due to their high implementation complexity. We examine the performance of the system with simple MRC receivers and carefully selected precoders, which are designed to compensate the lack of high-complexity receivers, at the transmitter side. We examine the sum MSE minimization and signal-to-interference-plus-noise ratio (SINR) balancing frameworks for the selection of precoders. The performance of two frameworks with MRC receivers are compared between themselves as well as with their counterparts implementing MMSE receivers. It has been observed that the SINR balancing framework with simple MRC receivers has little performance loss in comparison with the MMSE receivers with a proper selection of precoders.

Multisector Eigenbeamforming With MMSE Reception in Spatially Correlated Channels

Single-sector eigenbeamforming is effective for obtaining transmit array gain in spatially correlated fading channels while reducing the feedback signaling overhead. However, it may suffer from interference near the sector boundary when applied to the downlink with universal frequency reuse. This interference may not sufficiently be handled by a minimum mean square error (MMSE)-type receiver. To alleviate the interference problem, we consider the use of multisector eigenbeamforming (MEB) in an MMSE receiver, which requires cooperation between adjacent sectors in the same cell. We analyze the performance of the MEB with the use of long-term channel information in terms of the ergodic capacity. Finally, the effectiveness of the proposed MEB near the sector boundary is verified by computer simulation.

Signature Quantization in Fading CDMA with Limited Feedback

In this work, we analyze the performance of a signature quantization scheme for reverse-link Direct Sequence (DS)- Code Division Multiple Access (CDMA). Assuming perfect estimates of the channel and interference covariance, the receiver selects the signature that minimizes interference power or maximizes signal-to-interference plus noise ratio (SINR) for a desired user from a signature codebook. The codebook index corresponding to the optimal signature is then relayed to the user with a finite number of bits via a feedback channel. Here we are interested in the performance of a Random Vector Quantization (RVQ) codebook, which contains independent isotropically distributed vectors. Assuming arbitrary transmit power allocation, we consider additive white Gaussian noise (AWGN) channel first with no fading and subsequently, with multipath fading. We derive the corresponding SINR in a large system limit at the output of matched filter and linear minimum mean squared error (MMSE) receiver. Numerical examples show that the derived large system results give a good approximation to the performance of finite-size system and that the MMSE receiver achieves close to a single-user performance with only one feedback bit per signature element.

Bit Error Rate Performance of MIMO MMSE Receivers in Correlated Rayleigh Flat-Fading Channels

This paper analyzes the average bit error rate (BER) of multiple-input–multiple-output (MIMO) systems in transmit-correlated Rayleigh flat-fading channels. The receiver scheme is based on the minimum mean square error (MMSE) criterion, and the input may be precoded to optimize the communication. Accurate closed-form formulations for the average BER are derived.

Performance of Interference Rejection Combining Receiver to Suppress Inter-Cell Interference in LTE-Advanced Downlink

The interference rejection combining (IRC) receiver, which can suppress inter-cell interference, is effective in improving the cell-edge user throughput. The IRC receiver is typically based on the minimum mean square error (MMSE) criteria, which requires highly accurate channel estimation and covariance matrix estimation that includes the inter-cell interference. This paper investigates the gain from the IRC receiver in terms of the downlink user throughput performance in a multi-cell environment. In the evaluation, to assess the actual gain, the inter-cell interference signals including reference signals from the surrounding 56 cells are generated in the same way as the desired signals, and the channel propagation from all of the cells is explicitly taken into account considering pathloss, shadowing, and multipath fading. The results of simulations that assume the inter-site distance of 500m, the spatial correlation at the transmitter and the receiver of 0.5, and the numbers of transmitter and receiver antennas of 2 and 2, respectively, show that the IRC receiver improves the cell-edge user throughput (defined as the 5% value in the cumulative distribution function) by approximately 15% compared to the simplified MMSE receiver that approximates the inter-cell interference as AWGN, at the cost of a drop in the average user throughput due to less accurate channel and covariance matrices. Furthermore, we consider dynamic switching between the IRC receiver and the simplified MMSE receiver according to the number of streams and modulation and coding scheme levels. The results show that with dynamic switching, both the cell-edge throughput and average user throughput are improved to the same level as that for the IRC receiver and the simplified MMSE receiver, respectively. Therefore, the best performance can be achieved by employing the dynamic switching in all throughput regions.

New Factorization Algorithms for Channel-Factorization Aided MMSE Receiver in MIMO Systems

Channel-factorization aided detector (CFAD) is one of the important low-complexity detectors used in multiple input, multiple output (MIMO) receivers. Through channel factorization, this method transforms the original MIMO system into an equivalent system with a better-conditioned channel where detection is performed with a low-complexity detector; the estimate is then transferred back to the original system to obtain the final decision. Traditionally, the channel factorization is done with the lattice reduction algorithms such as the Lenstra-Lenstra-Lovasz (LLL) and Seysen's algorithms with no consideration of the low-complexity detector used. In this paper, we propose a different approach: the channel factorization is designed specifically for the minimum mean-square-error (MMSE) detector that is a popular low-complexity detector in CFADs. Two new types of factorization algorithms are proposed. Type-I is LLL based, where the well-known DLLL-extended algorithm, the LLL algorithm working on the dual matrix of the extended channel matrix, is a member of this type but with a higher complexity. DLLL-extended is the best-performed factorization algorithm found in the literature, Type-II is greedy-search based where its members are differentiated with different algorithm's parameters. Type-II algorithms can provide around 0.5-1.0dB gain over Type-I algorithms and have a fixed computational complexity which is advantageous in hardware implementation.

Regularized MIMO Decoders

In the Multi Input Multi Output (MIMO) antenna system, it is known that the Linear Minimum Mean Squared Error (MMSE) receiver is equivalent to Tikhonov regularization.Given that, we develop a family of generalized receivers based on regularization with different penalty functions that penalize the received symbols outside the convex hull of the modulating constellation. For illustration purposes we consider two types of penalty functions, the deadzone and infinity norm penalty functions. The proposed decoders have low complexity and can be implemented efficiently using convex optimization algorithms. Simulation results show that the proposed receivers outperform the MMSE receiver by as high as 5-dB at low Signal to Noise Ratio (SNR).

Diversity Analysis and Design of Space–Time Multiblock Codes for MIMO Systems Equipped With Linear MMSE Receivers

This paper addresses the problem of designing optimum full-symbol-rate linear space-time block codes (STBC) for a multi-input multi-output (MIMO) communication system with M transmitter and N ≥ M receiver antennas and a linear minimum mean square error (MMSE) receiver. By analyzing the detection error probability expression for the optimized STBC, it is shown that for QAM signaling, the maximum diversity gain for such a system is N - M + 1. The minimum probability of error STBC design is then extended to systems in which the transmission spans L independent realizations from a block fading channel model, and a (multiblock) linear MMSE receiver is employed. Necessary and sufficient conditions for the optimality of the code are obtained, and a systematic design method for generating codes that satisfy these conditions is presented. The detection error probability and diversity gain of this optimized linear multiblock transceiver are analyzed. It is proved that the error probability decreases with L, and it is shown numerically that the diversity gain increases with L. Thus, if the corresponding latency can be accommodated, for sufficiently large L an optimally designed multiblock system with a linear receiver can exploit the temporal diversity provided by the block-fading channel and achieve higher diversity gain than that of any single-block system of the same symbol rate with a maximum likelihood (ML) receiver. The optimized multiblock linear system achieves this diversity at a substantially lower computational cost. In fact, the structure of the optimal codes can be exploited to significantly reduce the cost of the multiblock linear receiver.

Efficient Dynamic Spectrum Sharing in Cognitive Radio Networks: Centralized Dynamic Spectrum Leasing (C-DSL)

In this paper, we propose the concept of centralized dynamic spectrum leasing (C-DSL), in which multiple primary users belonging to the same primary system participate in the spectrum leasing process with secondary users (potential bidder for spectrum) under centralized control. We develop a new game-theoretic user interaction model suitable for C-DSL in a cognitive radio network. Dynamic Spectrum Leasing (DSL), proposed in allows active participation of both primary and secondary users in the spectrum sharing process. Motivated by network spectrum utilization considerations, we propose generalizations to the primary system utility function defined in and a new utility function for the secondary users. We also generalize the proposed non-cooperative C-DSL game to allow for linear multiuser detectors at the secondary base stations. We formulate the conditions on the primary system and the secondary user utility functions so that the proposed C-DSL game has desired equilibrium properties. We prove that the proposed C-DSL game has unique Nash equilibria (NE) under both matched filter (MF) and linear minimum mean-squared error (LMMSE) receivers. Equilibrium performance of the system and robustness of the proposed game theoretic adaptive implementation are investigated through simulations.

Memoryless block transceivers with minimum redundancy based on Hartley transforms

This paper proposes real linear transceivers employing minimum redundancy, unlike the standard block transceivers that require, at least, L elements of redundancy, where L is the channel order. In all block-based systems, there is an inherent interblock interference (IBI) that can be eliminated by inserting redundancy. For transceivers based on the discrete Fourier transform (DFT), the redundancy induces a circulant channel matrix, allowing superfast implementations. Although it has been known for some time that the minimum redundancy for IBI-free designs of block transceivers is ⌈ L / 2 ⌉ , only recently practical DFT-based solutions using minimum redundancy were proposed. However, the extension of these solutions to real transforms, such as the discrete Hartley transform (DHT), is not straightforward. The only known solution imposes a symmetry on the channel model that is unlikely to be met in practice. This paper proposes transceivers with practical zero-forcing (ZF) and minimum mean-squared error (MMSE) receivers using DHT, diagonal, and antidiagonal matrices. The resulting systems are asymptotically as simple as orthogonal frequency-division multiplex (OFDM) and single-carrier with frequency-domain (SC-FD) equalization transceivers. In addition, they do not enforce constraints on the channel model. Several computer simulations indicate the higher throughput of the proposals as compared to the standard solutions.

Managing the interference structure of MIMO HSDPA: A multi-user interference aware MMSE receiver with moderate complexity

It is known that Wideband Code-Division Multiple Access (W-CDMA) networks are limited by interference more than by any other single effect. Due to the frequency selectivity of the wireless channel, intra-cell interference composed of selfand other-user interference occurs. The intra-cell interference as a result of Transmit Antenna Array (TxAA) HSDPA multi-user transmissions, however, shows a special structure that can be exploited to allow for an efficient interference suppression. The contributions of this article are the following: we (a) propose a suitable system model to derive an intra-cell interference aware Minimum Mean Squared Error (MMSE) equalizer with moderate complexity and investigate its capabilities to suppress the multi-user intra-cell interference, (b) propose solutions to estimate the pre-coding state of the cell both with and without available training, and (c) investigate the resulting throughput performance with physical layer as well as system-level simulations. Our proposed solution can be interpreted as a multi-user extension of the classical MMSE equalizer for HSDPA systems without decoding the undesired users, resulting in only slightly increased complexity.

Space–Time Block Coding for Doubly-Selective Channels

In this paper, we present a new space-time block code for time- and frequency-selective (doubly-selective) channels. It can be interpreted as the extension of the Alamouti code to doubly-selective channels, and relies on a joint time-frequency reversal of the transmitted sequences. Under certain channel conditions, the proposed space-time block code belongs to the class that achieves full spatial, delay, and Doppler diversity using a maximum-likelihood (ML) receiver, as well as a linear zero-forcing (LZF) or linear minimum mean-squared error (LMMSE) receiver. For realistic doubly-selective channels, a real-valued linear data model is presented, for which different receiver structures can be developed.

Achievable Sum Rate of MIMO MMSE Receivers: A General Analytic Framework

This paper investigates the achievable sum rate of multiple-input multiple-output (MIMO) wireless systems employing linear minimum mean-squared error (MMSE) receivers. We present a new analytic framework which exploits an interesting connection between the achievable sum rate with MMSE receivers and the ergodic mutual information achieved with optimal receivers. This simple but powerful result enables the vast prior literature on ergodic MIMO mutual information to be directly applied to the analysis of MMSE receivers. The framework is particularized to various Rayleigh and Rician channel scenarios to yield new exact closed-form expressions for the achievable sum rate, as well as simplified expressions in the asymptotic regimes of high and low signal-to-noise ratios (SNRs). These expressions lead to the discovery of key insights into the performance of MIMO MMSE receivers under practical channel conditions.

BER and Outage Probability Approximations for LMMSE Detectors on Correlated MIMO Channels

This paper is devoted to the study of the performance of the linear minimum mean-square error (LMMSE) receiver for (receive) correlated multiple-input multiple-output (MIMO) systems. By the random matrix theory, it is well known that the signal-to-noise ratio (SNR) at the output of this receiver behaves asymptotically like a Gaussian random variable as the number of receive and transmit antennas converge to +infin at the same rate. However, this approximation being inaccurate for the estimation of some performance metrics such as the bit error rate (BER) and the outage probability, especially for small system dimensions, Li proposed convincingly to assume that the SNR follows a generalized gamma distribution which parameters are tuned by computing the first three asymptotic moments of the SNR. In this paper, this technique is generalized to (receive) correlated channels, and closed-form expressions for the first three asymptotic moments of the SNR are provided. To obtain these results, a random matrix theory technique adapted to matrices with Gaussian elements is used. This technique is believed to be simple, efficient, and of broad interest in wireless communications. Simulations are provided, and show that the proposed technique yields in general a good accuracy, even for small system dimensions.

Windowing for multicarrier CDMA systems

The windows for achieving good multiple-access performance of multicarrier code-division multiple-access (MCCDMA) systems employing minimum mean-squared error receivers are studied. The mean-squared error (MSE) is used as the performance metric for the optimization. In a simplified two-user system, the rectangular window is found to be optimum while regarded as an inferior window in orthogonal frequency-division multiplexing systems because of its spectral inefficiency. Necessary conditions are given for improving the performances of spectrally efficient windows by exploiting the cyclic prefix and oversampling in the frequency domain.

Bit error performance of convolutional coded MIMO system with linear MMSE receiver

In this letter, we introduce an analytical expression to the coded bit error rate (BER) of a MIMO system with a linear minimum mean square error (MMSE) receiver. We derive the moment generating function (MGF) of the SINR for arbitrary antenna configurations from the cumulative density function of SINR.We show that the moment generating function of the SINR at the MMSE detector output can be used to estimate the BER performance of a coded MIMO system. The analysis is simple and gives an accurate BER estimation at a high SNR. Based on the analytical and simulated results, the diversity order is dependent on the antenna configuration and the free distance of the convolutional code. Finally, we compare the analytical expression with simulated results for validation.

Flexible Spectrum and Power Allocation for OFDM Unlicensed Wireless Systems

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Future generations of communication systems will benefit from cognitive radio technology, which significantly improves the efficient usage of the finite radio spectrum resource. In this paper we present a wireless unlicensed system that successfully coexists with the licensed systems in the same spectrum range. The proposed unlicensed system determines the level of signals and noise in each frequency band and properly adjusts the spectrum and power allocations subject to rate constraints. It employs orthogonal frequency-division multiplexing (OFDM) modulation and distributes each transmitted bit energy over all the bands using a novel concept of bit spectrum patterns. A distributed optimization problem is formulated as a dynamic selection of spectrum patterns and power allocations that are better suited to the available spectrum range without degrading the licensed system performance. Bit spectrum patterns are designed based on a normalized gradient approach and the transmission powers are minimized for a predefined quality of service (QoS). At the optimal equilibrium point, the receiver that employs a conventional correlation operation with the replica of the transmitted signal will have the same efficiency as the minimum mean-squared error (MMSE) receiver in the presence of noise and licensed systems. Additionally, the proposed approach maximizes the unlicensed system capacity for the optimal spectrum and power allocations. The performance of the proposed algorithm is verified through simulations. </para>

Low-complexity linear frequency domain equalization for continuous phase modulation

In this paper, we develop a new low-complexity linear frequency domain equalization (FDE) approach for continuous phase modulated (CPM) signals. As a CPM signal is highly correlated, calculating a linear minimum mean square error (MMSE) channel equalizer requires the inversion of a nondiagonal matrix, even in the frequency domain. In order to regain the FDE advantage of reduced computational complexity, we show that this matrix can be approximated by a block-diagonal matrix without performance loss. Moreover, our MMSE equalizer can be simplified to a low-complexity zero-forcing equalizer. The proposed techniques can be applied to any CPM scheme. To support this theory we present a new polyphase matrix model, valid for any block-based CPM system. Simulation results in a 60 GHz environment show that our reduced-complexity MMSE equalizer significantly outperforms the state of the art linear MMSE receiver for large modulation indices, while it performs only slightly worse for small ones.