MMSE equalization of downlink CDMA channel utilizing unused orthogonal spreading sequences

The time reversal (TR) technique combined with the ultra-wideband (UWB) system offers a new potential for decreasing the cost and complexity of the UWB receivers. In spite of TR–UWB's good performance in perfect channel state information (CSI), it is very sensitive to the channel estimation error. The effect of channel imperfection on the TR–UWB system is considered in this paper. At first, based on a minimum mean square error (MMSE) equalizer receiver, a prefilter is calculated in closed form to improve the performance of the TR–UWB system in an imperfect CSI scenario. Furthermore, for comparison purposes, a similar calculation for prefilter is carried out based on a simple matched filter (MF) receiver. Then, in order to improve the MF receiver performance, a two-stage iteration-based algorithm is developed. The initial value for this iteration-based improved algorithm is considered to be a prefilter which is calculated in the TR–UWB system with MMSE equalizer. This optimized algorithm causes the channel estimation error in the TR–UWB system to become zero in some steps. Finally, exhaustive simulations are done to demonstrate the performance advantage attained by the improved algorithm.

In code division multiple access (CDMA) systems transmitting over time-varying multipath channels, both intersymbol interference (ISI) and multiple access interference (MAI) arise. The conventional suboptimum receiver consisting of a bank of matched filters is often inefficient because interference is treated as noise. The optimum multi-user detector is too complex to be implemented at present. Four suboptimum detection techniques based on zero forcing (ZF) and minimum mean square error (MMSE) equalization with and without decision feedback (DF) are presented and compared. They combat both ISI and MAI. The computational complexity of all four equalizers is essentially the same and they are independent of the size of the data symbol alphabet. It is shown that all four equalizers considerably outperform the conventional receiver. The MMSE equalizers are superior to the corresponding ZF equalizers. Furthermore, the equalizers with DF perform better than the corresponding equalizers without DF. An algorithm termed channel sorting is introduced to reduce the impairing effect of error propagation on the equalizers with DF. >

A signal-to-interference-noise ratio (SINR) constrained power control for code division multiple access (CDMA) and minimum mean square error (MMSE) multiuser detection is investigated. Two scenarios of a CDMA wireless local area network (WLAN) with MMSE multiuser detection are considered, i.e., the centralized power control for the uplink of a cellular WLAN, and the decentralized power control for an ad- hoc WLAN. It is proved that in both scenarios the interference between terminals is standard, so that the convergence of the proposed iterative power control (IPC) algorithm is guaranteed. Assuming asymptotically large number of communicating terminals and asymptotically large processing gain, it is shown that the power control becomes independent of particular spreading sequences, and thus, the random spreading sequences can be assumed. Furthermore, the transmitting powers can be readily adapted while the terminals join or leave the network. Numerical examples confirm that the simple IPC algorithm presented in this paper is very effective for cellular as well as ad-hoc CDMA WLAN's with MMSE multiuser detection for small to medium traffic loads and various SINR's requirements.

In orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced and the system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Unfortunately, the direct ZF method requires the inversion of an NxN ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. As for the direct MMSE method, in addition to an NxN matrix inverse, it requires an extra NxN matrix multiplication, making the required computational complexity higher compared to the direct ZF method. In this dissertation, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and to apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O(N^3) to O(Nlog_2 N) . Also, the required number of the iteration is typically one or two. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-noise-ratio (SINR). For the MMSE method, we first reformulate the MMSE solution in a way that the extra matrix multiplication can be avoided. Similar to the ZF method, we then exploit the structure of the ICI matrix and apply Newton's iteration to reduce the complexity of the matrix inversion. For a multiple-input-multiple-output (MIMO) OFDM system, the required complexity of the ZF and MMSE methods becomes more intractable. We then manage to extend the proposed ZF and MMSE methods for SISO-OFDM systems to MIMO-OFDM systems. It turns out that the computational complexity can be reduced even more significantly. Simulation results show that the performance of the proposed methods is almost as good as that of the direct ZF and MMSE methods, while the required computational complexity is reduced dramatically. Finally, we explore the application of the proposed methods in mobility-induced ICI mitigation for OFDM multiple access (OFDMA) systems, and in carrier frequency offset (CFO) induced ICI mitigation for OFDMA uplink systems. As that in OFDM systems, the proposed methods can reduce the required computational complexity, effectively.

Equalisation is one of the most important algorithms to improve the Bit-Error-Rate (BER) performance in communication systems. In general, equalisation can be classified into two categories: linear and non-linear equalisation. The linear equalisers include Zero Forcing (ZF), and Minimum Mean Square Error (MMSE) equalisers. The non-linear equalisers include ZF and MMSE equalisers that are based on Successive Interference Cancellation (SIC). The ZF equaliser suffers from noise enhancement. The MMSE equaliser can mitigate the noise enhancement using the estimated Signal-to-Noise Ratio (SNR). The ZF-SIC and MMSE-SIC equalisers suffer from error propagation, and high computational complexity, respectively. In this paper, the Orthogonal Frequency Division Multiplexing (OFDM) system is modulated and demodulated using Inverse Discrete Wavelet Transform (IDWT), and DWT instead of Inverse Discrete Fourier Transform (IDFT) and DFT, respectively. Also, we propose a Joint Low-complexity Regularised ZF-SIC (JLRZF-SIC) equaliser that jointly performs the equalisation, and Carrier Frequency Offset (CFO) compensation with lower complexity using banded matrix approximation. The proposed JLRZF-SIC equaliser can accomplish the equalisation, and CFO compensation processes with low-complexity compared to the corresponding MMSE-SIC equaliser. Simulation results show that the proposed JLRZF-SIC equaliser outperforms different linearand non-linear equalisers.

In minimum mean squared error (MMSE) based turbo equalization, the decoder's extrinsic information is used as the MMSE equalizer's prior information. In order to improve the performance, the combined prior information which consists of the whole decoder's extrinsic information and the partial decoder's full information in the last iteration, is used by the MMSE equalizer. Meanwhile, the MMSE equalizer is lead by matched filter as a preprocessor to reduce the complexity. The extrinsic information transfer (EXIT) chart analysis and simulation results show that the performance of the proposed scheme is much better than that of the conventional turbo equalizer.

We first develop a reduced-rank minimum mean square error (MMSE) detector for direct-sequence (DS) code division multiple access (CDMA) by forcing the linear MMSE detector to lie in a signal subspace of a reduced dimension. While a reduced-rank MMSE detector has lower complexity, it cannot outperform the full-rank MMSE detector. We then concentrate on the blind reduced-rank MMSE detector which is obtained from an estimated covariance matrix. Our analysis and simulation results show that when the desired user's signal is in a low-dimensional subspace, there exists an optimal subspace so that the blind reduced-rank MMSE detector lying in this subspace has the best performance. By properly choosing a subspace, we guarantee that the optimal blind reduced-rank MMSE detector is obtained. An adaptive blind reduced-rank MMSE detector, based on a subspace tracking algorithm, is developed. The adaptive blind reduced-rank MMSE detector exhibits superior steady-state performance and fast convergence speed.

We consider interference rejection for code-division multiple-access (CDMA) channels using decision-feedback detectors. Performance of zero-forcing and the minimum mean square error (MMSE) multiuser decision-feedback detectors is studied, and the full and partial feedback approaches are investigated. We also derive the maximum-likelihood detector based on the white noise CDMA channel model. Comparison among the decision-feedback detectors, the two-stage receivers, the conventional detector, and the linear decorrelating detector is undertaken for a four-user bandwidth-efficient asynchronous CDMA channel. We find that the decision-feedback detectors compare favorably to other suboptimal methods and maintain good performance under diverse channel conditions. This conclusion is further strengthened by performance analysis of the decision-feedback detector for a two-user synchronous CDMA flat Rayleigh fading channel. >

Affine frequency division multiplexing (AFDM) is an effective modulation technology using waveform with frequency variation, offering robust performance in high-speed mobile environments and having the ability to obtain diversity gain over frequency selective fading channels. While performance of AFDM under ideal conditions is well-established, the impact of incomplete channel information on AFDM systems employing minimum mean square error (MMSE) equalizer over frequency-selective channels remains less explored. We study the performance degradation of AFDM with MMSE equalizer caused by incomplete channel information in this letter. To mitigate this degradation and optimize system performance, it is necessary to redesign the AFDM parameters, specifically tailored for MMSE equalization operations under such incomplete channel information. Extensive computer simulations demonstrate the significant performance superiority of AFDM system over frequency selective channels. Crucially, our findings confirm that parameter adjustment is essential for AFDM to achieve optimal performance when only incomplete channel information is available.

In orthogonal frequency division multiplexing (OFDM), Fourier Transform (FT) is used as a modulation technique. To avoid inter-symbol interference (ISI) in OFDM by a time dispersive channel, a cyclic prefix (CP) is used which also reduces its spectral efficiency. wavelet packet transform (WPT) as a modulation scheme has been proposed for wireless communication. In this paper, WPT based OFDM is presented and proposed using minimum mean square error (MMSE) equalizer. Equalization is a major factor in wavelets. MMSE is proposed for wavelet based OFDM (WOFDM) based on WPT and compared with zero forcing equalizer (ZFE). The performance is measured for arbitrary magnitude finite impulse response (FIR) channels in the presence of additive white Gaussian noise (AWGN) and impulse noise. Simulation results show a clear improvement in bit error rate (BER) for MMSE over ZFE equalization technique in the presence of noise.

Time-reversal (TR) precoding focuses the energy of the effective channel in time and improves receive performance of a single tap receiver or a minimum mean square error (MMSE) receiver with distributed antenna systems (DAS). Frequency-domain equal-gain-combining (FD-EGC) scheme is proposed as a new TR scheme, which works in linear block precoding (LBP) fashion and has better temporal focusing performance than the traditional TR. Extending the FD-EGC as LBP in DAS, the mean square error is analyzed for the MMSE equalizer at receiver. We show that the FD-EGC with a few antennas, which is a more realistic case than that with many antennas, has better performance than the traditional TR.

Multiple-input multiple-output (MIMO) systems can achieve high data-rate and high capacity transmission. In MIMO systems, the scheme that weight substreams based on minimum mean square error (MMSE) criterion at the transmitter using feedback channel state information (CSI) achieves good performance (denoted hereafter as MMSE precoder). However, if the optimum number of substreams is not selected based on CSI and methods for reducing the performance degradation due to feedback delay is not used, MMSE precoder cannot achieve the full performance possible. In this paper, we propose an MMSE precoder with mode selection for MIMO systems, which selects both the number of substreams and the modulation scheme for each substream to minimize the average BER at a fixed rate. We evaluate the BER of the proposed MMSE precoder with two methods for reducing performance degradation due to feedback delay, channel prediction and receive weight robust to feedback delay. We also evaluate the BER of the proposed MMSE precoder with the method that combines channel prediction with receive weight robust to feedback delay. Simulation results show that the BER of the proposed MMSE precoder is improved compared to that of the conventional MMSE precoder using the fixed number of substreams. We also show that the method that combines channel prediction with receive weight robust to feedback delay can achieve good BER even when the large feedback delay exists.

In this contribution, we consider the performance of multiple-input multiple-output (MIMO) code division multiple access (CDMA) system for digital image transmission over correlated Rayleigh fading channel. MIMO system employs multiple antennas both at the transmitter and receiver. In our work, we consider turbo coded system to investigate the performance of MIMO-CDMA system. We realize turbo code using parallel concatenated convolutional encoder and second convolutional encoder is preceded by random interleaver. Further the output of two convolutional encoder are punctured to get rate of ½. At the receiver, we employ iterative decoding algorithm to reduce the effect of multiple access interference (MAI) and Inter-Symbol-Interference (ISI) and median filters to reduce the effect of salt and pepper noise.. In particular, we evaluate the performance of coded MIMO-CDMA system using Zero forcing (ZF) - multi-user detection (MUD) and minimum mean square error (MMSE)-MUD detection technique to mitigate the effects of multi-stream interference (MSI). It is shown through the simulation study that our considered coded MIMO-CDMA system with MMSE algorithm achieves better picture quality with less signal-to-noise ratio (SNR) as compared to ZF MUD.

This paper addresses multiuser detection and diversity combining for frequency selective fading code-division multiple access (CDMA) channels. It is well known that the decorrelating detector is an effective technique for separating signals of different users in bandwidth-efficient CDMA. For a general asynchronous CDMA channel, the output of the decorrelator for each user can be characterized by an equivalent single-user system with multiuser (MAI)-induced intersymbol interference (ISI). We investigate diversity combining techniques for this equivalent single-user channel using differential phase shift keying (DPSK) detection. This method does not require tracking of rapidly changing fading parameters. To improve the performance of the DPSK combiner, it can be beneficial to weigh the signals associated with different paths. We consider several criteria for choosing these weights. For the synchronous (ISI-free) channel, we show that the bit error rate (BER) of the optimal combiner can be closely approximated by a combination of two decorrelating detectors (with either noise whitening or signal whitening filters). We also discuss this hybrid approach for asynchronous channels with MAI-induced ISI. Finally, a minimum mean square error (MMSE) combiner is analyzed and compared to other techniques.

The paper makes a brief introduction of Multiple Carrier-Code Division Multiple Access (MC-CDMA) scheme based on the principles of Orthogonal Frequency Division Multiplexing (OFDM) and CDMA, and a mathematical model of the uplink is established in MC-CDMA system.The simulation research on different multi-user detection methods in MC-CDMA system is implemented by using MATLAB software, and it also compares the impacts to system performance by several different multi-user detection methods, such as De-Correlation (DEC) multi-user detection, Minimum Mean Square Error (MMSE) multi-user detection and Parallel Interference Cancellation (PIC) multi-user detection, based on understanding and analyzing the experimental results.In addition, the paper also focuses on the research of multi level PIC multi-user detection performance in different primary detection methods and different series detections.