Reverse link pilot-tones aided synchronization in DS-CDMA communication system

We generalize the multiuser (CDMA spread spectrum) communication systems to the fading environments. We first extend Verdu's (1986) conventional optimum receiver to Rayleigh-fading environments and then evaluate its performance. Having no knowledge of the received power at the receiving end, we therefore need an estimator to efficiently estimate the received signal strength of each user in fading environments. A linear minimum mean square error (LMMSE) unbiased estimator is proposed to attain this goal. By using the minimum mean square error (MMSE) Bayesian estimation, we further propose the LMMSE bit estimator for efficient demodulation. Its performance is close to the optimum multiuser receiver but with a much simpler polynomial complexity. To further reduce the complexity, we extend the LMMSE estimator to the sequential LMMSE estimator. In sequential estimation, we do not need to implement the matched filter banks and to perform the matrix inversion when estimating. In addition, it converges after approximately 2k iterations, where k is the number of users. With this fast convergence property and the simple structure, the sequential LMMSE estimator provides an attractive alternative to the implementation of a multiuser system.

With the increasing rate of wireless devices and high bandwidth operations, wireless networking and communications are becoming over crowded. To cope with such crowded and messy situation, massive MIMO is designed to work with hundreds of low-cost serving antennas at a time as well as improve the spectral efficiency at the same time. Time Division Duplexing (TDD) has been used for gaining beamforming which is a major part of massive MIMO, to gain its best improvement to transmit and receive pilot sequences. All the benefits are only possible if the channel state information or channel estimation is gained properly. Least Square (LS), Minimum Mean Square Error (MMSE) and Linear Minimum Mean Square Error (LMMSE) are the estimators commonly used for estimating channel matrices. We have optimized these methods using genetic algorithm to minimize the mean squared error and finding the best channel matrix from existing algorithms with less computational complexity. Our simulation result has shown that the use of Genetic Algorithm (GA) worked well on existing algorithms in a Rayleigh slow fading channel and existence of Additive White Gaussian Noise. We found that the GA optimized LS is better than existing algorithms. GA provides optimal result in some few iterations in terms of Mean Square Error (MSE) with respect to SNRand computational complexity.

The multistage Wiener filter (MWF) is an iterative Schur complement procedure for estimating a scalar or a vector of random variables in the linear minimum mean square error sense. When a complementary orthogonal projector is used as a blocking matrix, intermediate vectors in the development of the MWF have singular covariance matrices, and the rationale of the MWF is undermined. For this situation, we validate the structure of the MWF by showing that it can be developed as an iterative generalized Schur complement procedure which relies on the Moore-Penrose generalized inverse. The validated filter does not require any generalized inverse, and it can be implemented as usual by using scalar Wiener filters when estimating a scalar random variable. Next, we show, under a condition which is commonly met in practice, that the MWF is a least squares reduced rank estimate of the Wiener filter from the Krylov subspace associated with the Wiener-Hopf equation. The MWF is then compared with Brillinger's reduced rank minimum mean square error filter. The two filters differ in the subspaces from which signal estimation is performed and in the order in which projection onto the respective subspaces and Wiener estimation are performed. A forward recursion for the mean square estimation error in each stage of the MWF is provided, and the performance of the MWF is demonstrated by a numerical example.

Visible light communication (VLC) has been proposed as a promising way for next generation wireless communication networks to mitigate the scarcity of the radio frequency (RF) spectrum, and has consequently attracted much attention. This paper introduces a single-input single-output (SISO) VLC system under the joint effects of statistical random channel and signal-dependent shot noise (SDSN). Moreover, it estimates the channel of the considered system using maximum likelihood (ML), least square (LS), linear minimum mean square error (LMMSE), maximum posteriori probability (MAP) and minimum mean square error (MMSE) estimators. Furthermore, a Bayesian Cramér-Rao lower bound (BCRLB) is derived for the proposed system and it is compared to the mean square error (MSE) of the proposed estimators. The problem of unknown SDSN factor, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\zeta ^{2}$</tex-math></inline-formula> , at the receiver side is discussed and two solutions are investigated. The receiver of a VLC system under SDSN and random channel gain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$h$</tex-math></inline-formula> is designed and its BER is studied. Finally, Monte Carlo simulation results of the proposed estimators, which show the dramatic effect of the SDSN on the considered system, are provided. In particular, the presence of noise variance, as well as the SDSN factor, causes an increase in the MSE of the system, while increasing the power reinforces the system performance.

The structure of an optimum linear precoder for a rotation-invariant performance measure is obtained subject to the constraint of limited input power for a block transmission scheme. It is shown that several known performance measures of a communication system are rotation invariant. The rotation invariant property provides a unified framework for obtaining the structure of an optimum linear precoder for several criteria such as: 1) maximization of minimum distance; 2) maximization of channel capacity; and 3) optimization of different performance measures, such as bit-error rate (BER), mean square error, signal-to-noise ratio of optimum equalizers (linear minimum mean square error, zero-forcing, maximum likelihood (ML), zero forcing-block decision feedback, minimum mean square error-block decision feedback, etc.). This framework provides a method for obtaining the structure of an optimum linear precoder for BER performance measure of the ML equalizer. The structure turns out to be a channel diagonalizing structure after a prerotation of the input constellation. Using this structure, the properties of the optimum precoder that minimize the BER of the ML equalizer for two binary phase-shift keying symbols transmission under input-power constraint are studied.

In a code-division multiple-access system, multiuser detection (MUD) can exploit the information of signals from other interfering users to increase system capacity. However, the optimum MUD can be characterized as an NP-hard combinatorial optimization problem such that the computational complexity increases exponentially with the number of users. In this paper, we apply a new evolutionary algorithm, called particle swarm optimization (PSO), to develop a suboptimal MUD strategy. The decorrelating detector (DD) or linear minimum mean square error (LMMSE) detector is used as the first stage to initialize the PSO-based MUD. Then, the PSO algorithm is applied to detect the received data bit by optimizing an objective function incorporating the linear system of the DD or LMMSE detector. Simulation results show that the performance of our proposed decorrelating PSO and LMMSE-PSO MUD are promising and outperform the decorrelating and LMMSE MUD with a slight increase in computation.

Optimal detection in multiple-input multiple-output (MIMO) frequency-selective systems is known to have exponential complexity in the number of transmitter antennas and channel length resulting from intersymbol interference. Several studies focus on suboptimal detectors, proposing trade-offs between computational complexity and bit error rate. In this paper, we model the detection problem using factor graphs and apply the sum-product algorithm to derive the optimal detector. Then we propose a novel suboptimal particle filter detector, based on sequential Monte Carlo, followed by a Markov chain Monte Carlo step to further enhance performance. The proposed algorithm exchanges the exponential complexity in channel length for a linear complexity in the number of particles and achieves better bit error rate than the linear minimum mean square error (LMMSE) detector.

OCDMA is a promising candidate for next generation passive optical networks (NG-PON). OCDMA-PON can potentially provide all customers with a Gb/s-class BW upstream with inherent flexibility. Unfortunately OCDMA suffers from multiple access interference (MAI) and various detection noises. To mitigate MAI, we propose a novel parallel interference cancellation technique for incoherent DS-OCDMA that better exploits the non-negativity of the solution. The proposed PIC scheme incorporates this additional information into its structure. The proposed PIC detector is shown to outperform the conventional correlator detector, the decorrelator detector, the linear parallel interference Cancellation (LPIC) detector and even the linear minimum mean square error (LMMSE) detector.

Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

A decision-directed (DD) channel estimation based on iterative linear minimum mean square error (LMMSE) is proposed for orthogonal frequency division multiplexing systems. Existing DD channel estimation is well known to have the problem of error propagation because of symbol-by-symbol detection. The proposed algorithm can estimate the correction term of current channel state information (CSI) according to the error vector of previous CSI by applying the orthogonality principle, and corrects the current CSI with this correction term. Analysis and simulation results have shown that this method has no error propagation problem. The performance of the proposed algorithm is much better than the conventional DD channel estimation, and close to the optimal LMMSE estimator, but with much less computational complexity compared with the optimal LMMSE estimator.

The initial solution of a massive multiple-input multiple-output (M-MIMO) detector for uplink (UL) is greatly influence the balance between the bit error rate (BER) performance and the computational complexity. Although the maximum likelihood (ML) detector obtains the best BER performance, it has an extremely high computational complexity. Iterative linear minimum mean square error (MMSE) detector based on the Gauss–Seidel (GS), the successive over-relaxation (SOR), and the Jacobi (JA), obtains a good performance-complexity profile when the base station (BS)-to-user-antenna-ratio (BUAR) is large. However, when the BUAR is small, the system suffers from a considerable performance loss. In this paper, a hybrid detector based on the joint GS and SOR methods is proposed where the initial solution is determined by the first iteration of GS method. Numerical results show a considerable complexity reduction and performance enhancement using the proposed GS-SOR method over all methods when the BUAR is small.

SummaryThis paper introduces the concept of spatial and media‐based modulated (SMBM) orthogonal frequency division multiplexing (OFDM) as a potential candidate for highly mobile next generation beyond 5G (B5G) wireless communications. The proposed SMBM‐OFDM technique utilizes not only the transmit antenna and channel state indices but also OFDM subcarriers to improve the system performance under high mobility. In addition, this study sheds light on challenging fast time‐varying channel estimation problem of MBM‐based systems by using the linear minimum mean square error (LMMSE) approach due to its optimality to investigate the achievable system performance with the aid of basis expansion modeling. The minimum lower bound on the channel estimation error (Bayesian Cramer–Rao bound) is derived theoretically and shown to be attainable by the considered LMMSE estimator. Moreover, symbol detection performance is provided for different modulation types and higher mobile velocities. Simulation results demonstrate that SMBM‐OFDM system under high mobility is able to provide around 12‐dB performance gains in terms of both channel estimation and symbol detection error compared to conventional spatial modulation (SM)‐OFDM systems without MBM. The presented framework is important due to addressing the high mobility support of SMBM‐OFDM systems for B5G wireless communications in terms of achievable channel estimation and data detection performance.

Channel estimation (CE) is a challenging problem and one of the key technologies in Orthogonal Frequency Division Multiplexing (OFDM) systems. The Linear Minimum Mean Square Error (LMMSE) proposed for OFDM systems has excellent Mean Square Error (MSE) performance. However, the conventional method requires the statistical knowledge of the channel information in advance and the complicated inverse operation of large dimension matrices. In this case, an enhanced fast LMMSE channel estimation using Fast Fourier Transform (FFT) operation and the most significant taps (MST) algorithm for OFDM systems is proposed. This method has the advantage of low computational complexity and no requirement on the detailed channel information. In addition, simulation results demonstrate that the proposed algorithm outperforms other LMMSE methods in terms of bit error rate (BER) without the loss of MSE performance.

We derive the Linear Minimum Mean Square Error (LMMSE) receiver for Wyner's model of a linear cellular array. By exploiting the special structure of the channel model, we obtain explicit Mean Square Error (MSE) expressions and information capacity formulae for both finite-sized as well as infinite-sized linear cellular arrays. We show that the performance of an individual user becomes insensitive to the array size for large array sizes and that the proportion of users achieving almost the same performance converges to one, as the array size tends to infinity. The effects of intercell interference and noise on the performance of each user are also investigated.

In the present time, there is a rapid increase in demand for faster and reliable transmission of multimedia data through wireless channels. When multimedia data specially an image is to be transferred through the wireless channel, image is highly degraded due to wireless channel errors such as fading, interference and bursty errors. Multi-Carrier Code Division Multiple Access (MC-CDMA) technique is considered as the most promising technique for efficient wireless data transmission. This paper presents the performance comparison of image transmission over MC-CDMA system with two interleaving techniques; Helical interleaving and chaotic interleaving. At the receiver, Linear Minimum Mean Square Error (LMMSE) equalization is employed. System performance is measured through Peak Signal-to-Noise Ratio (PSNR) and Root Mean square Error (RMSE) values. From results, it has been evaluated that MC-CDMA system having chaotic interleaving and LMMSE performs better instead of having helical interleaving for image transmission over wireless channels.