MMSE Equalizer Research Articles

Joint MMSE Equalization and Power Control for MIMO System under Multi-User Interference

The joint MMSE equalization and power control (JMEPC) algorithm, which jointly and iteratively adjusts the equalization weights and the power level of each user, is proposed for the MIMO system under multi-user interference. Two types of MMSE equalization, namely, the parallel MMSE equalization and the optimum successive decoding (OSD), are considered. In the JMEPC algorithm, we let the mean capacity among cochannel the users be the capacity target and make the resulting capacity approach the maximum achievable capacity through the iterations that can be finished in a distributed manner. Simulation results show that the JMEPC algorithm increases the capacity of the MIMO system and the parallel MMSE equalization with JMEPC can have larger capacity than the OSD without JMEPC.

Iterative Receiver in Time-Frequency Domain for Underwater Acoustic Communications

In this paper, we combine soft MMSE equalization method, and the serially concatenated trellis coded modulation (SCTCM) decoding to develop an iterative receiver in time-frequency domain (TFD) for SC underwater acoustic point to point communications. This iterative procedure can reduce the calculation complexity of equalization and obtain better performance using less receiving elements. Finally, we use sound speed profile (SSP) measured in the lake and Bellhop model to simulate underwater channel to verify the performance of the proposed receive algorithms.

BER Performance Improvement in Coded-OFDM Systems Using Equalization Algorithms

Intersymbol interference is a major cause to limit high data rate transmission in wireless communication. To avoid ISI OFDM is the preferred modulation technique. For frequency selective channels pure OFDM may not be sufficient to eliminate ISI. The use of time coding (interleaver and convolution coder) improves the ISI affected reception but do not eliminate ISI completely. The paper investigates the presence of equalizers to improve BER performance in ISI affected reception. The performance improvement is observed for two novel equalizers namely zero forcing equalizers and MMSE equalizers. Simulation results are presented to demonstrate the superiority of the CODED OFDM method with equalizers

Lattice-reduction-aided MMSE equalization and the successive estimation of correlated data

Over the last years, novel low-complexity approaches to the equalization of MIMO channels have gained much attention. Thereby, methods based on lattice basis reduction are of special interest, as they achieve the optimum diversity order. In this paper, a tutorial overview on LRA equalization optimized according to the MMSE criterion is given. It is proven that applying the zero-forcing BLAST algorithm to a suitably augmented channel matrix – the inverse of the square root of the correlation matrix of the data symbols times the noise variance forms its lower part – results in the optimum solution. This fact is already widely used but lacks a formal proof. It turns out that it is more important to take the correlations of the data correctly into account than what type of lattice reduction actually is used.

Optimal Design of Spatial Source-and-Relay Matrices for a Non-Regenerative Two-Way MIMO Relay System

This paper considers a system where two users exchange information via a non-regenerative half-duplex two-way MIMO relay and each of the two users and the relay is equipped with multiple antennas. We study the design of the spatial source covariance matrices (or source matrices) at the two users and the spatial transformation matrix (or relay matrix) at the relay to maximize the achievable weighted sum rate of the system. The source matrices and the relay matrix are optimized alternately until convergence. If the relay matrix is given, we show that the optimal design of the source matrices (for uniformly weighted sum rate) follows a generalized water filling (GWF) algorithm. If the source matrices are given, we show two search algorithms to optimize the relay matrix. The first algorithm is a hybrid gradient method which adaptively switches between the (steepest) gradient descent and the Newton's search. The second is an iterative weighted minimum mean square error (WMMSE) method which alternately refines the MMSE equalizers at the users and the relay matrix. We compare the convergence behaviors of the two algorithms and demonstrate their advantage over prior algorithms. We also show an optimal structure of the relay matrix, which is useful to reduce the search complexity.

The Precoder Design for Intrablock MMSE Equalization and Block Delay Detection with a Modified Oblique Projection Framework

This letter presents a method to enable the precoder design for intrablock MMSE equalization with previously proposed oblique projection framework. The joint design of the linear transceiver with optimum block delay detection is built. Simulation results validate the proposed approach and show the superior BER performance of the optimized transceiver.

Low Complexity Equalization for Doubly Selective Channels Modeled by a Basis Expansion

We propose a novel equalization method for doubly selective wireless channels, whose taps are represented by an arbitrary Basis Expansion Model (BEM). We view such a channel in the time domain as a sum of product-convolution operators created from the basis functions and the BEM coefficients. Equivalently, a frequency-domain channel can be represented as a sum of convolution-products. The product-convolution representation provides a low-complexity, memory efficient way to apply the channel matrix to a vector. We compute a regularized solution of a linear system involving the channel matrix by means of the GMRES and the LSQR algorithms, which utilize the product-convolution structure without ever explicitly creating the channel matrix. Our method applies to all cyclic-prefix transmissions. In an OFDM transmission with K subcarriers, each iteration of GMRES or LSQR requires only <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (K K) flops and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> (K) memory. Additionally, we further accelerate convergence of both GMRES and LSQR by using the single-tap equalizer as a preconditioner. We validate our method with numerical simulations of a WiMAX-like system (IEEE 802.16e) in channels with significant delay and Doppler spreads. The proposed equalizer achieves BERs comparable to those of MMSE equalization, and noticeably outperforms low-complexity equalizers using an approximation by a banded matrix in the frequency domain. With preconditioning, the lowest BERs are obtained within 3-16 iterations. Our approach does not use any statistical information about the wireless channel.

A comparison Study of Time Domain Equalization Technique Using Ultrawide Band Receivers Performance for High Data Rate WPAN System

For high data rate ultra wideband communication system, performance comparison of Rake, MMSE and Rake-MMSE receivers is attempted in this paper. We have taken into account of impact of all the parameters such as the effect of the number of Rake fingers and equalizer taps on the error performance by combating ISI are the major focus of our research. The bit error rate performances are investigated using semi analytical approach and Monte-Carlo simulation on IEEE 802.15.3a UWB channel models. A detail study on UWB channel model (IEEE 802.15.3a) is carried out using four channel models CM1CM4. Simulation results show that the bit error rate probability of rake-mmse receiver is much better than Rake receiver and MMSE equalizer. Within the distance 0 to 4 meter Rake-MMSE performs better in CM1 (LOS) channel model than that of CM2 (NLOS) channel model. Further the simulation results on non-line of sight indoor channel models illustrate bit error rate performance of Rake-MMSE improves for CM3 model with smaller spread compared to CM4 channel model. We show that for a MMSE equalizer operating at low to medium SNR’s, the number of Rake fingers is the dominant factor to improve system performance, while at high SNR’s the number of equalizer taps plays a more significant role in reducing error rates.

Performance Analysis of Ultra Wideband Receivers for High Data Rate Wireless Personal Area Network System

For high data rate ultra wideband communication system, performance comparison of Rake, MMSE and Rake-MMSE receivers is attempted in this paper. Further a detail study on Rake-MMSE time domain equalizers is carried out taking into account all the important parameters such as the effect of the number of Rake fingers and equalizer taps on the error rate performance. This receiver combats inter-symbol interference by taking advantages of both the Rake and equalizer structure. The bit error rate performances are investigated using MATLAB simulation on IEEE 802.15.3a defined UWB channel models. Simulation results show that the bit error rate probability of Rake-MMSE receiver is much better than Rake receiver and MMSE equalizer. Study on non-line of sight indoor channel models illustrates that bit error rate performance of Rake-MMSE (both LE and DFE) improves for CM3 model with smaller spread compared to CM4 channel model. It is indicated that for a MMSE equalizer operating at low to medium SNR values, the number of Rake fingers is the dominant factor to improve system performance, while at high SNR values the number of equalizer taps plays a more significant role in reducing the error rate.

Sampling Point Selection Scheme for Fractional Sampling-OFDM Receivers on Fast Time-Varying Multipath Channels

Fractional sampling (FS) and Doppler diversity equalization in OFDM receivers can achieve two types of diversity (path diversity and frequency diversity) simultaneously on time-varying multipath channels. However FS with a higher sampling rate requires the large amount of complexity in demodulation. In this paper, a novel sampling point selection (SPS) scheme with MMSE equalization in FS-OFDM receivers is proposed. On fast time-varying multipath channels, the proposed scheme selects the appropriate samples from the fractionally sampled signals. Through the computer simulation, it is demonstrated that with the proposed scheme, both path diversity gain and Doppler diversity gain can increase as compared to a conventional non-SPS scheme.

Decision-Feedback Closest Lattice Point Search for UMTS HSPA System

This letter considers a low-complexity multiuser detection based on the closest lattice point search (CLPS) for high speed packet access (HSPA) system. Instead of attempting to solve the ML detection problem in the presence of intersymbol and inter-cell interference, we utilize interference cancelled chips obtained from a bidirectional decision feedback operation to detect symbols. As a result, the worst case complexity of the CLPS is bounded to a controllable level irrespective of multipath spans. From the simulation on single and multi cell downlink communications in HSPA systems, we show that the proposed method offers substantial performance gain over conventional RAKE and MMSE equalizer.

Iterative Channel Estimation and Successive ICI Cancellation for OFDM Systems over Doubly Selective Channels

In orthogonal frequency division multiplexing systems, significant inter-carrier interference (ICI) caused by doubly selective channels make challenge for reliable reception. In this paper, channel estimation and ICI cancellation are considered jointly. Relying on the basis expansion model (BEM) of time-varying channel, the linear system model of transceiver is established, and the corresponding joint optimization of the transmitted data and BEM coefficients is formulated. Due to the separability of the data and BEM coefficients, we use cyclic minimizing technique to perform channel estimation and equalization alternately. This yields a linear minimum mean square-error (LMMSE) channel estimator and a block MMSE equalizer respectively. The block MMSE equalizer has complexity O(N 3), where N is the number of data subcarriers. To reduce the complexity, instead of equalizing all the data simultaneously, we consider estimating each data symbol successively. This idea results in the per subcarrier interference canceller with lower complexity O(N 2). Finally, an iterative receiver consisting of the data-aided LMMSE channel estimator and the successive interference canceller is developed. Simulation results show the scheme is effective over the channel with relatively large Doppler spread.

Blind MMSE Equalization of FIR/IIR Channels Using Oversampling and Multichannel Linear Prediction

Blind MMSE Equalization of FIR/IIR Channels Using Oversampling and Multichannel Linear Prediction

Blind MMSE Equalization of FIR/IIR Channels Using Oversampling and Multichannel Linear Prediction

A linear-prediction-based blind equalization algorithm for single-input single-output (SISO) finite impulse response/infinite impulse response (FIR/IIR) channels is proposed. The new algorithm is based on second-order statistics, and it does not require channel order estimation. By oversampling the channel output, the SISO channel model is converted to a special single-input multiple-output (SIMO) model. Two forward linear predictors with consecutive prediction delays are applied to the subchannel outputs of the SIMO model. It is demonstrated that the partial parameters of the SIMO model can be estimated from the difference between the prediction errors when the length of the predictors is sufficiently large. The sufficient filter length for achieving the optimal prediction is also derived. Based on the estimated parameters, both batch and adaptive minimum-mean-square-error equalizers are developed. The performance of the proposed equalizers is evaluated by computer simulations and compared with existing algorithms.

Synchronization, Channel Estimation, and Equalization in MB-OFDM Systems

This paper addresses preamble-based low complexity synchronization, channel estimation and equalization for Zero-padded (ZP) MB-OFDM based UWB systems. The proposed synchronization method consists of sync detection, coarse timing estimation, fine timing estimation, and oscillator frequency offset estimation. The distinctive features of MB-OFDM systems and the interplay between the timing and carrier frequency hopping at the receiver are judiciously incorporated in the proposed synchronization method. In order to apply the low complexity one-tap frequency-domain equalizer, the required circular convolution property of the received signal is obtained by means of an overlap-add method after the frequency offset compensation. The proposed low complexity channel estimator for each band is developed by first averaging the over-lapadded received preamble symbols within the same band and then applying time-domain least-squares method followed by the discrete Fourier transform. We develop an MMSE equalizer and its approximate version with low complexity. We also derive the probability density functions of the UWB channel path delays, and using them we present several optimization criteria for our proposed synchronization, channel estimation, and equalization. The effectiveness of our proposed methods and optimization criteria are confirmed by computer simulation results.

Optimizations of a MIMO Relay Network

Relay networks have received considerable attention recently, especially when limited size and power resources impose constraints on the number of antennas within a wireless sensor network. In this context, signal processing techniques play a fundamental role, and optimality within a given relay architecture can be achieved under several design criteria. In this paper, we extend recent optimal minimum-mean-square-error (MMSE) and signal-to-noise ratio (SNR) designs of relay networks to the corresponding multiple-input-multiple-output (MIMO) scenarios, whereby the source, relays and destination comprise multiple antennas. We investigate maximum SNR solutions subject to power constraints and zero-forcing (ZF) criteria, as well as approximate MMSE equalizers with specified target SNR and power constraint at the receiver. We also maximize the transmission rate between the source and destination subject to power constraint at the receiver.

FPGA Implementation of an Iterative Receiver for MIMO-OFDM Systems

Today iterative receivers have proved their efficiency in cancelling interference within the field of wireless communications. However their complexity is often seen as a brake for their use in real systems. In this paper an efficient iterative receiver real-time implementation for a 4 times 4 MIMO system is presented. An architecture of MMSE iterative receiver for MIMO-OFDM systems is proposed to limit latency and complexity due to iterative process: MMSE equalization implementation is realized using CORDIC operators; the scheduling between MIMO detection and channel decoding is optimized and specific interleaving functions are introduced to reduce latency and accelerate the convergence process. The implemented receiver is integrated in a real-time FPGA testbench and compared in terms of complexity and performance with a non iterative solution.

Krylov Subspace Algorithms and Circulant-Embedding Method for Efficient Wideband Single-Carrier Equalization

Wider bandwidth allows higher data rate by transmitting narrower pulses. However, doing so would also increase the discrete channel memory length. For single-carrier communication systems this results in higher computational burden at the receiver. We are concerned with single-carrier nonblock transmission schemes with receiver oversampling, as they can provide higher spectral efficiency than block transmission schemes in the presence of large delay spreads. We first propose a simple finite-impulse-response (FIR) equalizer that is based on the circulant-embedding (CE) method and analyze its performance by investigating the relationship between solutions of various finite-dimensional models and the original infinite-dimensional problem. We show that under proper conditions the CE FIR equalizer converges exponentially fast to the IIR equalizer. We then focus on the conjugate gradient (CG) algorithm as an efficient means for equalization that is specifically well suited for dealing with large-delay-spread channels. We discuss the importance of stopping the iterations for the CG algorithm at the right time in the presence of noise and present several reliable low-cost stopping criteria. It turns out that the CG algorithm equipped with appropriate stopping criteria can outperform MMSE equalizers. Since both the CE and the CG methods can be efficiently implemented via fast Fourier transforms, equalization complexity is only in the order of N log(N) for N data symbols. Several numerical experiments demonstrate the performance of the proposed methods.

Power optimization of digital baseband WCDMA receiver components on algorithmic and architectural level

Abstract. High data rates combined with high mobility represent a challenge for the design of cellular devices. Advanced algorithms are required which result in higher complexity, more chip area and increased power consumption. However, this contrasts to the limited power supply of mobile devices. This presentation discusses the application of an HSDPA receiver which has been optimized regarding power consumption with the focus on the algorithmic and architectural level. On algorithmic level the Rake combiner, Prefilter-Rake equalizer and MMSE equalizer are compared regarding their BER performance. Both equalizer approaches provide a significant increase of performance for high data rates compared to the Rake combiner which is commonly used for lower data rates. For both equalizer approaches several adaptive algorithms are available which differ in complexity and convergence properties. To identify the algorithm which achieves the required performance with the lowest power consumption the algorithms have been investigated using SystemC models regarding their performance and arithmetic complexity. Additionally, for the Prefilter Rake equalizer the power estimations of a modified Griffith (LMS) and a Levinson (RLS) algorithm have been compared with the tool ORINOCO supplied by ChipVision. The accuracy of this tool has been verified with a scalable architecture of the UMTS channel estimation described both in SystemC and VHDL targeting a 130 nm CMOS standard cell library. An architecture combining all three approaches combined with an adaptive control unit is presented. The control unit monitors the current condition of the propagation channel and adjusts parameters for the receiver like filter size and oversampling ratio to minimize the power consumption while maintaining the required performance. The optimization strategies result in a reduction of the number of arithmetic operations up to 70% for single components which leads to an estimated power reduction of up to 40% while the BER performance is not affected. This work utilizes SystemC and ORINOCO for the first estimation of power consumption in an early step of the design flow. Thereby algorithms can be compared in different operating modes including the effects of control units. Here an algorithm having higher peak complexity and power consumption but providing more flexibility showed less consumption for normal operating modes compared to the algorithm which is optimized for peak performance.

Efficient Series Expansion for Matrix Inversion with Application to MMSE Equalization

In this paper, we describe an efficient approach to overcome the need for matrix inversion required in most wired applications encountered in practice. In particular, MMSE equalization based on series expansion to approximate the matrix inversion is addressed. By adjusting a scaling factor, the series expansion is directly optimized according to a fixed order with respect to a system performance criterion. In comparison with previous approaches, the resulting equalizer enables improved BER performance according to a fixed order, in addition to low complexity without the need for a complicated eigenvalue calculation procedure.