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

Vector Orthogonal Frequency Division Multiplexing (OFDM) for single transmit antenna systems is a general transmission scheme, where OFDM and Single-Carrier Frequency Domain Equalization (SC-FDE) can be treated as two special/extreme cases. Due to its flexibility, it has drawn more and more attention recently. So far, all the studies about Vector OFDM assume the Maximum Likelihood (ML) receiver. In this paper, we investigate the performance of Vector OFDM with linear receivers, i.e., the Zero-Forcing (ZF) and Minimum Mean Square Error (MMSE) receivers. We first show that the detection SNR gap between the MMSE and ZF receivers increases with both channel SNR and the vector blocks (VB) size defined in Vector OFDM. Then, it is proved that for both ZF and MMSE receivers, all the transmitted symbols have equal performance. This is different from the Vector OFDM with ML receiver, where different VBs may have different coding gain, and thus may have different performances. We analyze the diversity order for Vector OFDM with MMSE receiver, and show that, regardless of the Vector OFDM symbol length <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> , the diversity order can be represented as min{[ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-R</sup> ], <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> }+1, where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> is the VB size, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> is the spectrum efficiency in bits/symbol, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> is the maximum delay of the multipath channel. For Vector OFDM with ZF receiver, we show that the diversity order equals 1 and the performance is the same as the conventional OFDM at high SNR.

In this paper, we elaborate on the ergodic sum rate of multiple-input multiple-output (MIMO) Nakagami-m fading channels with linear minimum mean square error (MMSE) receivers. For dual transmit antenna configurations, we present new, closed-form upper bounds on the ergodic sum rate of MMSE receivers. Moreover, we derive exact expressions for the two key parameters dictating the sum rate behavior in the low signal to noise ratio (SNR) regime, i.e., minimum energy per information bit to reliably convey any positive rate and the wideband slope. Our analytical results demonstrate the sub-optimality of linear MMSE receivers and provide useful insights into the impact of model parameters (e.g. number of antennas, fading parameters).

In most of the existing space-time code designs, achieving full diversity is based on maximum-likelihood (ML) decoding at the receiver that is usually computationally expensive and may not have soft outputs. Recently, Zhang-Liu-Wong introduced Toeplitz codes and showed that Toeplitz codes achieve full diversity when a linear receiver, zero-forcing (ZF) or minimum mean square error (MMSE) receiver, is used. Motivated from Zhang-Liu-Wong's results on Toeplitz codes, in this paper, we propose a design criterion for space-time block codes (STBC), in which information symbols and their complex conjugates are linearly embedded, to achieve full diversity when ZF or MMSE receiver is used. Subsequently, we propose a novel family of STBC that satisfy the criterion and thus achieve full diversity with ZF or MMSE receiver. Our newly proposed STBC are constructed by overlapping the 2times2 Alamouti code and hence named overlapped Alamouti codes in this paper. The new codes are close to orthogonal while their symbol rates can approach 1 for any number of transmit antennas. Simulation results show that overlapped Alamouti codes significantly outperform Toeplitz codes for all numbers of transmit antennas and also outperform orthogonal STBC (OSTBC) when the number of transmit antennas is above 4.

In most of the existing space-time code designs, achieving full diversity is based on maximum-likelihood (ML) decoding at the receiver that is usually computationally expensive and may not have soft outputs. Recently, Zhang-Liu-Wong introduced Toeplitz codes and showed that Toeplitz codes achieve full diversity when a linear receiver, zero-forcing (ZF) or minimum mean square error (MMSE) receiver, is used. Motivated from Zhang-Liu-Wong's results on Toeplitz codes, in this paper, we propose a design criterion for space-time block codes (STBC), in which information symbols and their complex conjugates are linearly embedded, to achieve full diversity when ZF or MMSE receiver is used. The (complex) orthogonal STBC (OSTBC) satisfy the criterion as one may expect. We also show that the symbol rates of STBC under this criterion are upper bounded by 1. Subsequently, we propose a novel family of STBC that satisfy the criterion and thus achieve full diversity with ZF or MMSE receiver. Our newly proposed STBC are constructed by overlapping the 2times2 Alamouti code and hence named overlapped Alamouti codes in this paper. The new codes are close to orthogonal and their symbol rates can approach 1 for any number of transmit antennas. Simulation results show that overlapped Alamouti codes significantly outperform Toeplitz codes for all numbers of transmit antennas and also outperform OSTBC when the number of transmit antennas is above 4.

This paper presents a new design method for delay-tolerant linear dispersion codes (DT-LDCs) for asynchronous cooperative communication networks. We consider a system that is equipped with linear minimum mean square error (MMSE) receiver. Based on the DT-LDC framework, we propose a new design method to yield DT-LDCs that approach near-optimal capacity as well as minimum average MSE. The proposed design employs stochastic gradient algorithm to guarantee the local optimum. Moreover, it is improved by using simulated annealing type optimization to approach the global optimum. Simulation results confirm the performance of the newly-proposed delay-tolerant LDCs.

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.

Massive multiple‐input multiple‐output (M‐MIMO) is one of the cutting edge technologies that provides significant improvement in throughput, coverage and spectral efficiency. The challenge with M‐MIMO systems is to extract individual signals from the composite signal, thus making optimal detectors prohibitively complex. Recently, approximate message passing (AMP) and its variant detectors have gained substantial importance due to their decreased complexity and improved performance. However, AMP algorithm does not always converge. Non‐linear detectors like vertical Bell‐Labs layered space‐iime improve the bit error rate (BER) but with high complexity, whereas, linear minimum mean square error (MMSE) detector offers low complexity while compromising on BER performance. Neumann series based MMSE detectors further reduce MMSE computational complexity, however, the BER performance remains the same. In this work, the authors propose a hybrid Neumann series based MMSE detector which decomposes the detected signal into its constituent components and apply a neighbourhood selection algorithm on the obtained components thus improving the overall performance. Another contribution of this work is derivation of an off‐set value for optimised neighbourhood set selection that enables more accurate detection while further reducing computational complexity. Simulation results confirm that the proposed scheme outperforms aforementioned algorithms in terms of BER performance and computational complexity in a continuously changing Rayleigh channel.

An asymptotically minimum bit error rate (BER) linear block precoder is determined for block-by-block communication systems employing linear minimum mean square error (MMSE) equalisation and disjoint detection. The problem is solved by a two-stage optimisation procedure in which a lower bound on the BER is first minimised, and then it is shown how this minimised lower bound can be achieved. Simulation results show that the BER performance of the proposed scheme is superior to the standard MMSE precoder and several other conventional systems such as orthogonal frequency division multiplexing. At reasonable BERs, the signal-to-noise ratio (SNR) gain can be of the order of several decibels.

This paper presents some experimental results on both the channel estimation based minimum mean square error Turbo equalizer (CE MMSE-TEQ) and the direct-adaptation turbo equalizer (DA-TEQ) in single-input single-output (SISO) underwater acoustic (UWA) channels. For CE MMSE-TEQ, we compare the soft-decision feedback Turbo equalizer (SDFE), the bidirectional soft-decision feedback Turbo equalizer (Bi-SDFE) and the classic linear Minimum Mean Square Error (MMSE) Turbo equalizer in terms of bit error rate (BER) performance. For DA-TEQ, the recently proposed soft-decision direct-adaptation TEQ (Soft DA-TEQ) is evaluated with the same set of experimental data. Both QPSK and multilevel modulations (8PSK and 16QAM) have been tested with the symbol rate of 9.77 ksymbols/s. Experimental results show that the CE-TEQs are more robust in SISO underwater acoustic transmission under harsh channel conditions. Especially, with low pilot overheads, the recently proposed Bi-SDFE achieved low BER performance in all cases.

In this paper, we propose a joint channel estimation and symbol detection (JCESD) algorithm relying on message-passing algorithms (MPA) for orthogonal frequency division multiple access (OFDMA) systems. The channel estimation and symbol detection leverage the framework of expectation propagation (EP) and belief propagation (BP) with the aid of Gaussian approximation, respectively. Furthermore, to reduce the computation complexity involved in channel estimation, the matrix inversion is transformed into a series of diagonal matrix inversions through the Sherman-Morrison formula. Simulation experiments show that the proposed algorithm can reduce the pilot overhead by about 50%, compared with the traditional linear minimum mean square error (LMMSE) algorithm, and can approach to the bit error rate (BER) performance bound of perfectly known channel state information within 0.1 dB.

In this paper, we propose a set of joint transmit diversity selection (TDS) and relay selection (RS) algorithms based on discrete iterative stochastic optimization for the uplink of cooperative multiple-input-multiple-output (MIMO) systems. Decode-and-forward (DF) and amplify-and-forward (AF) multirelay systems with linear minimum mean square error (MSE), successive interference cancelation, and adaptive reception are considered. The problems of TDS and RS are expressed as MSE and mutual information (MI) joint discrete optimization problems and solved using iterative discrete stochastic algorithms. Such an approach circumvents the need for exhaustive searching and results in a range of procedures with low complexity and increased speed of convergence that can track the optimal selection over an estimated channel. The proposed schemes are analyzed in terms of their complexity, convergence, and diversity benefits and are shown to be both stable and computationally efficient. Their performance is then evaluated via MSE, MI, and bit error rate comparisons and shown to outperform conventional cooperative transmission and, in the majority of scenarios, match that of the optimal exhaustive solution.

This paper proposes a Nonlinear Distortion Cancellation (NDC) scheme of the nonlinearity HPA (High Power Amplifier) in the V-BLAST MIMO MC-CDMA (Vertical Bell Laboratories Layered Space-Time Multiple-Input Multiple-Output Multi-Carrier Code Division Multiplexing Access) systems over Rayleigh fading channel. The compensation of the nonlinearities effects in the different transmitter branches is applied at the receiver level. Moreover, the proposed scheme requires an estimation of the HPA parameters. A numerical performance evaluation shows that the proposed method can be successfully applied and reduces significantly the BER (Bit Error rate) of the MIMO MC-CDMA systems accompanied with the MMSE (Minimum Mean Square Error) receiver.

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.

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.

For large-scale multiple-input multiple-output (MIMO) systems, linear minimum mean square error (MMSE) method is one of the most near-optimal ways for signal detection. However, MMSE involves matrix inversion which is of high complexity for computation. In this paper, a Lanczos-based method is proposed to solve the problem by transferring the matrix inversion computation into an iteration process of solving a linear equation. The simulation result proves that the BER of Lanczos-based method outperforms the recently proposed Neumann series approximation algorithm with the same SNR. At the same time, the Lanczos-based method could reduce the computational complexity from O(K3) to O(K2), where K is the number of users. Then the convergence speed is analysed by Kaniel-Paige-Saad theory. Finally, the result shows that the performance of Lanczos-based method achieves the classical MMSE exact matrix inversion methods with only a small number of iterations.