Performance of multilevel‐turbo codes with blind/non‐blind equalization over WSSUS multipath channels

In this paper, in order to improve error performance, we introduce a new type of turbo codes, called ‘multilevel‐turbo codes (ML‐TC)’ and we evaluate their performance over wide‐sense stationary uncorrelated scattering (WSSUS) multipath channels. The basic idea of ML‐TC scheme is to partition a signal set into several levels and to encode each level separately by a proper component of the turbo encoder. In the considered structure, the parallel input data sequences are encoded by our multilevel scheme and mapped to any modulation type such as MPSK, MQAM, etc. Since WSSUS channels are very severe fading environments, it is needed to pass the received noisy signals through non‐blind or blind equalizers before turbo decoders. In ML‐TC schemes, noisy WSSUS corrupted signal sequence is first processed in equalizer block, then fed into the first level of turbo decoder and the first sequence is estimated from this first Turbo decoder. Subsequently, the other following input sequences of the frame are computed by using the estimated input bit streams of previous levels. Here, as a ML‐TC example, 4PSK 2 level‐turbo codes (2L‐TC) is chosen and its error performance is evaluated in WSSUS channel modelled by COST 207 (Cooperation in the field of Science & Technology, Project #207). It is shown that 2L‐TC signals with equalizer blocks exhibit considerable performance gains even at lower SNR values compared to 8PSK‐turbo trellis coded modulation (TTCM). The simulation results of the proposed scheme have up to 5.5 dB coding gain compared to 8PSK‐TTCM for all cases. It is interesting that after a constant SNR value, 2L‐TC with blind equalizer has better error performance than non‐blind filtered schemes. We conclude that our proposed scheme has promising results compared to classical schemes for all SNR values in WSSUS channels. Copyright © 2005 John Wiley & Sons, Ltd.     

Blind equalization of multilevel turbo coded‐continuous phase frequency shift keying over MIMO channels

In this paper, multilevel turbo coded‐continuous phase frequency shift keying (MLTC‐CPFSK) is introduced and its bit error performance in multiple input multiple output (MIMO) fading channels are investigated considering a blind maximum likelihood channel estimation. Multilevel turbo coded signals with continuous phase modulation (CPM) provides low spectral occupancy and is suitable for power and bandwidth‐limited channels. Besides, antenna diversity is one of the best method to combat with multipath fading effects. The performance of 2LTC for 4‐ary CPFSK over AWGN, Rician (for Rician channel parameter K=10 dB) and Rayleigh channels are given for 1Tx–1Rx, 2Tx–1Rx and 2Tx–2Rx antenna configurations. Channel capacities of 2LTC‐4CPFSK signals are obtained as ?5.26, ?7.65 and ?7.14 dB for 1Tx–1Rx, 2Tx–1Rx and 2Tx–2Rx antenna configurations, respectively. Baum–Welch (BW) algorithm is used to estimate the channel parameters. Bit error probabilities of 2 level turbo coded 4 CPFSK (2LTC‐4CPFSK) are drawn in the cases of no channel state information (CSI), BW estimation, and perfect CSI. Approximately 0.1 and 0.75 dB gains in E_s/N₀ are obtained using BW channel estimator for Rician and Rayleigh channels, respectively. Therefore, MLTC‐CPFSK with BW channel estimator has excellent performance in MIMO fading channels. Copyright © 2006 John Wiley & Sons, Ltd.     

Adaptive Channel‐Matched Extended Alamouti Space‐Time Code Exploiting Partial Feedback

Since the publication of Alamouti's famous space‐time block code, various quasi‐orthogonal space‐time block codes (QSTBC) for multi‐input multi‐output (MIMO) fading channels for more than two transmit antennas have been proposed. It has been shown that these codes cannot achieve full diversity at full rate. In this paper, we present a simple feedback scheme for rich scattering (flat Rayleigh fading) MIMO channels that improves the coding gain and diversity of a QSTBC for 2ⁿ (n = 3, 4,…) transmit antennas. The relevant channel state information is sent back from the receiver to the transmitter quantized to one or two bits per code block. In this way, signal transmission with an improved coding gain and diversity near to the maximum diversity order is achieved. Such high diversity can be exploited with either a maximum‐likelihood receiver or low‐complexity zero‐forcing receiver.     

Mobile‐to‐mobile MIMO transmit–receive diversity systems: analysis and performance in three‐dimensional double‐correlated channels

Mobile‐to‐mobile (M‐to‐M) communications are expected to play a crucial role in future wireless systems and networks. In this paper, we consider M‐to‐M multiple‐input multiple‐output (MIMO) maximal ratio combining system and assess its performance in spatially correlated channels. The analysis assumes double‐correlated Rayleigh‐and‐Lognormal fading channels and is performed in terms of average symbol error probability, outage probability, and ergodic capacity. To obtain the receive and transmit spatial correlation functions needed for the performance analysis, we used a three‐dimensional (3D) M‐to‐M MIMO channel model, which takes into account the effects of fast fading and shadowing. The expressions for the considered metrics are derived as a function of the average signal‐to‐noise ratio per receive antenna in closed‐form and are further approximated using the recursive adaptive Simpson quadrature method. Numerical results are provided to show the effects of system parameters, such as distance between antenna elements, maximum elevation angle of scatterers, orientation angle of antenna array in the x–y plane, angle between the x–y plane and the antenna array orientation, and degree of scattering in the x–y plane, on the system performance. Copyright © 2011 John Wiley & Sons, Ltd.     

EM‐based iterative receiver for coded MIMO systems in unknown spatially correlated noise

We present iterative channel estimation and decoding schemes for multi‐input multi‐output (MIMO) Rayleigh block fading channels in spatially correlated noise. An expectation‐maximization (EM) algorithm is utilized to find the maximum likelihood (ML) estimates of the channel and spatial noise covariance matrices, and to compute soft information of coded symbols which is sent to an error‐control decoder. The extrinsic information produced by the decoder is then used to refine channel estimation. Several iterations are performed between the above channel estimation and decoding steps. We derive modified Cramer–Rao Bound (MCRB) for the unknown channel and noise parameters, and show that the proposed EM‐based channel estimation scheme achieves the MCRB at medium and high SNRs. For a bit error rate of 10⁻⁶ and long frame length, there is negligible performance difference between the proposed scheme and the ideal coherent detector that utilizes the true channel and noise covariance matrices. Copyright © 2006 John Wiley & Sons, Ltd.     

Concatenation of space‐time block codes and turbo trellis coded modulation (ST‐TTCM) over Rician fading channels with imperfect phase

In this paper, the performance of space time‐turbo trellis coded modulation (ST‐TTCM) is evaluated over Rician and Rayleigh fading channels with imperfect phase. We modify Baum–Welch (BW) algorithm to estimate the fading and phase jitter parameters for multi‐antenna configurations. Thus, we assume that the channel parameters change slower than carrier frequency. We know that, at high data rate transmissions over wireless fading channels, space–time block codes (STBC) provide the maximal possible diversity advantage. Here, the combined effects of the amplitude and the phase of the received signal are considered, each one modelled by Rician and Tikhonov distributions, respectively. We investigate space time‐turbo trellis coded modulation (ST‐TTCM) for 8‐PSK for several Rician factor K and phase distortion factor η. Thus, our results reflect the degradations both due to the effects of the fading on the amplitude and phase noise of the received signal while the channel parameters are estimated by BW algorithm. Copyright © 2004 John Wiley & Sons, Ltd.     

Achievable sum‐rate analysis of correlated two‐antenna MIMO uplink channels

This paper analyzes the achievable sum‐rate of correlated two‐antenna multiple‐input multiple‐output (MIMO) uplink channels. Most of previous works have considered the case when a single user has multiple transmit antennas (i.e. multi‐antenna single‐user scenario). This paper considers the case when two‐antenna MIMO uplink channels comprise two users with a single transmit antenna (i.e. single‐antenna two‐user scenario). The analytic and simulation results show that the achievable sum‐rate of correlated single‐antenna two‐user MIMO uplink channels highly depends on the angle difference between the receive correlation coefficients of two users. It is also shown that the achievable sum‐rate of correlated single‐antenna two‐user MIMO uplink channels is larger than that of correlated two‐antenna single‐user MIMO uplink channels and can even be larger than that of independent and identically distributed Rayleigh two‐antenna MIMO uplink channels. Copyright © 2009 John Wiley & Sons, Ltd.     

Carrier phase recovery for turbo‐coded systems with pre‐coded GMSK modulation

A carrier phase recovery scheme suited for turbo‐coded systems with pre‐coded Gaussian minimum shift keying (GMSK) modulation is proposed and evaluated in terms of bit‐error‐rate (BER) performance. This scheme involves utilizing the extrinsic information obtained from the turbo‐decoder to aid an iterative carrier phase estimation process, based on a maximum‐likelihood (ML) strategy. The phase estimator works jointly with the turbo‐decoder, using the updated extrinsic information from the turbo‐decoder in every iterative decoding. A pre‐coder is used to remove the inherent differential encoding of the GMSK modulation. Two bandwidths of GMSK signals are considered: BT=0.5 and 0.25, which are recommended by the European Cooperation for Space Standardization (ECSS). It is shown that the performance of this technique is quite close to the perfect synchronized system within a wide range of phase errors. This technique is further developed to recover nearly any phase error in [?π,+π] by increasing the number of phase estimators and joint decoding units. This, however, will increase the complexity of the system. Copyright © 2008 John Wiley & Sons, Ltd.     

Design of near‐optimal local likelihood search‐based detection algorithm for coded large‐scale MU‐MIMO system

Massive multiuser multiple input multiple output (MU‐MIMO) system is aimed to improve throughput and spectral efficiency through a large number of antennas incorporated at the transmitter and/or receiver. However, the MU‐MIMO system usually suffers from interantenna interference (IAI) and multiuser interference (MUI). The IAI imposes due to closely spaced antennas at each user equipment (UE), and MUI is enforced when one user comes under the vicinity of another user in the same cellular network. Most of the previous literatures considered any one of these interferences. However, the present work proposes singular value decomposition (SVD) precoding‐assisted user‐level local likelihood ascent search (LLAS) algorithm to mitigate both IAI and MUI. In the uplink MU‐MIMO, the IAI is cancelled by SVD, and the residual MUI is mitigated by LLAS detection. The LLAS detection balances the trade‐off between the classical suboptimal likelihood ascent search (LAS) and optimal maximum likelihood (ML) detection techniques. The proposed LLAS performs local search among all 2M_T‐dimensional neighborhood vectors at each UE, where M_T represents number of transmitting antennas of each UE. Thus, its performance is near optimal, and its complexity is much lower than ML detector.     

Analysis of minimum transmit sum power and scheduling power gain for multi‐user MIMO‐OFDM networks with rate constraints

Minimum transmit sum power (MTSP) is of high theoretical and practical value in multi‐user rate‐constrained systems; it is, however, quite difficult to be numerically characterized in complex channels for the prohibitively high computational power required. In this paper, we present a computationally efficient method to approximate the MTSP in multi‐user multiple‐input multiple‐output orthogonal frequency division multiplexing (MU‐MIMO‐OFDM) wireless networks. Specifically, we propose both lower and upper bounds of the MTSP, which are asymptotically accurate in the limit of large K, the number of users. Then, we develop two iterative water‐filling algorithms to numerically solve the proposed bounds. These algorithms are with low complexity, that is, linear in K, and therefore enable the analysis of MTSP in complex channels even if K is large. Numerical results demonstrate the effectiveness of the bounds in approximating the MTSP and the high computational efficiency of the proposed iterative water‐filling algorithms. With the proposed bounds, we further numerically study scheduling power gain (SPG), which is defined as MTSP reduction achieved by scheduling resources over multiple channel blocks in time domain. We simulate the SPG in different wireless environments defined in Third Generation Partnership Project spatial channel extended model and find insignificant SPG in some cases, indicating that the benefit from scheduling over multiple channel blocks is limited and simply allocating resources within the present channel is sufficient. Our analysis on the MTSP and SPG provides guidelines on the design of resource schedulers in MU‐MIMO‐OFDM networks. Copyright © 2014 John Wiley & Sons, Ltd.     

Low‐Complexity Massive MIMO Detectors Based on Richardson Method

In the uplink transmission of massive (or large‐scale) multi‐input multi‐output (MIMO) systems, large dimensional signal detection and its hardware design are challenging issues owing to the high computational complexity. In this paper, we propose low‐complexity hardware architectures of Richardson iterative method‐based massive MIMO detectors. We present two types of massive MIMO detectors, directly mapped (type1) and reformulated (type2) Richardson iterative methods. In the proposed Richardson method (type2), the matrix‐by‐matrix multiplications are reformulated to matrix‐vector multiplications, thus reducing the computational complexity from O(U²) to O(U). Both massive MIMO detectors are implemented using a 65 nm CMOS process and compared in terms of detection performance under different channel conditions (high‐mobility and flat fading channels). The hardware implementation results confirm that the proposed type1 Richardson method‐based detector demonstrates up to 50% power savings over the proposed type2 detector under a flat fading channel. The type2 detector indicates a 37% power savings compared to the type1 under a high‐mobility channel.     

Cross‐layer design for MIMO systems over spatially correlated and keyhole Nakagami‐m fading channels

Cross‐layer design is a generic designation for a set of efficient adaptive transmission schemes, across multiple layers of the protocol stack, that are aimed at enhancing the spectral efficiency and increasing the transmission reliability of wireless communication systems. In this paper, one such cross‐layer design scheme that combines physical layer adaptive modulation and coding (AMC) with link layer truncated automatic repeat request (T‐ARQ) is proposed for multiple‐input multiple‐output (MIMO) systems employing orthogonal space‐‐time block coding (OSTBC). The performance of the proposed cross‐layer design is evaluated in terms of achievable average spectral efficiency (ASE), average packet loss rate (PLR) and outage probability, for which analytical expressions are derived, considering transmission over two types of MIMO fading channels, namely, spatially correlated Nakagami‐m fading channels and keyhole Nakagami‐m fading channels. Furthermore, the effects of the maximum number of ARQ retransmissions, numbers of transmit and receive antennas, Nakagami fading parameter and spatial correlation parameters, are studied and discussed based on numerical results and comparisons. Copyright © 2009 John Wiley & Sons, Ltd.     

Signalling enhancement on multilevel turbo codes

The design of multilevel turbo codes using M‐PSK is optimized to achieve a low bit error rate (BER). Unequal error protection is employed via group set partitioning in multi‐stage decoding to minimize the error propagation and BER. Simulation results are performed under Gaussian and Rayleigh fading channels to depict the superiority of the new scheme. Copyright © 2008 John Wiley & Sons, Ltd.     

Efficient LDPC‐Based,Threaded Layered Space‐Time‐Frequency System with Iterative Receiver

We present a low‐density parity‐check (LDPC)‐based, threaded layered space‐time‐frequency system with emphasis on the iterative receiver design. First, the unbiased minimum mean‐squared‐error iterative‐tree‐search (U‐MMSE‐ITS) detector, which is known to be one of the most efficient multi‐input multi‐output (MIMO) detectors available, is improved by augmentation of the partial‐length paths and by the addition of one‐bit complement sequences. Compared with the U‐MMSE‐ITS detector, the improved detector provides better detection performance with lower complexity. Furthermore, the improved detector is robust to arbitrary MIMO channels and to any antenna configurations. Second, based on the structure of the iterative receiver, we present a low‐complexity belief‐propagation (BP) decoding algorithm for LDPC‐codes. This BP decoder not only has low computing complexity but also converges very fast (5 iterations is sufficient). With the efficient receiver employing the improved detector and the low‐complexity BP decoder, the proposed system is a promising solution to high‐data‐rate transmission over selective‐fading channels.     

Performance of a turbo‐coded CDMA system in a mobile satellite channel

The bit error rate (BER) performance of a turbo‐coded code‐division multiple‐access (CDMA) system operating in a satellite channel is analysed and simulated. The system performance is compared for various constituent decoders, including maximum a posteriori probability (MAP) and Max‐Log‐MAP algorithms, and the soft‐output Viterbi algorithm. The simulation results indicate that the Max‐Log‐MAP algorithm is the most promising among these three algorithms in overall terms of performance and complexity. It is also shown that, for fixed code rate, the BER performance is improved substantially by increasing the number of iterations in the turbo decoder, or by increasing the interleaver length in the turbo encoder. The results in this paper are of interest in CDMA‐based satellite communications applications. Copyright © 2005 John Wiley & Sons, Ltd.     

Multiuser MIMO receivers for space frequency block coded SC‐FDMA systems

Single carrier‐frequency division multiple access (SC‐FDMA) has been adopted as the uplink transmission standard in fourth generation cellular network to enable the power efficiency transmission in mobile station. Because multiuser MIMO (MU‐MIMO) is a promising technology to fully exploit the channel capacity in mobile radio network, this paper investigates the uplink transmission of SC‐FDMA systems with orthogonal space frequency block codes (SFBC). Two linear MU‐MIMO receivers, orthogonal SFBC (OSFBC) and minimum mean square error (MMSE), are derived for the scenarios with limited number of users or adequate receive antennas at base station. In order to effectively eliminate the multiple access interference (MAI) and fully exploit the capacity of MU‐MIMO channel, we propose a turbo MU‐MIMO receiver, which iteratively utilizes the soft information from maximum a posteriori decoder to cancel the MAI. By the simulation results in several typical MIMO channels, we find that the proposed MMSE MU‐MIMO receiver outperforms the OSFBC receiver over 1 dB at the cost of higher complexity. However, the proposed turbo MU‐MIMO receivers can effectively cancel the MAI under overloaded channel conditions and really achieve the capacity of MU‐MIMO channel. Copyright © 2014 John Wiley & Sons, Ltd.     

Network‐coded MIMO‐NOMA systems with FEC codes in two‐way relay networks

This paper assumes two users and a two‐way relay network with the combination of 2×2 multi‐input multi‐output (MIMO) and nonorthogonal multiple access (NOMA). To achieve network reliability without sacrificing network throughput, network‐coded MIMO‐NOMA schemes with convolutional, Reed‐Solomon (RS), and turbo codes are applied. Messages from two users at the relay node are network‐coded and combined in NOMA scheme. Interleaved differential encoding with redundancy (R‐RIDE) scheme is proposed together with MIMO‐NOMA system. Quadrature phase‐shift keying (QPSK) modulation technique is used. Bit error rate (BER) versus signal‐to‐noise ratio (SNR) (dB) and average mutual information (AMI) (bps/Hz) versus SNR (dB) in NOMA and MIMO‐NOMA schemes are evaluated and presented. From the simulated results, the combination of MIMO‐NOMA system with the proposed R‐RIDE‐Turbo network‐coded scheme in two‐way relay networks has better BER and higher AMI performance than conventional coded NOMA system. Furthermore, R‐RIDE‐Turbo scheme in MIMO‐NOMA system outperforms the other coded schemes in both MIMO‐NOMA and NOMA systems.     

A comparative study on the performance of MIMO‐STBC subject to Weibull fading channels

In this paper, we investigate the analytical performance of the multiple‐input multiple‐output system (MIMO) with orthogonal space‐time block codes (STBCs) subject to Weibull fading channels (WFC). Space‐time block code technique provides an efficient pattern for wireless transmission over various fading channels using multiple transmit antennas. Two approximating methods of the sum of independent Weibull random variables are studied. For each approach, we derive accurate approximate expressions for several performance metrics of MIMO‐STBC system operating under independent and nonidentical WFC. The proposed approximations are expressed in terms of 2 generalized hypergeometric functions, namely, Fox's H and Meijer's G functions. All the derived approximate expressions prove high accuracy, while compared with the simulation results established via Monte Carlo method and Kolmogorov‐Smirnov test as well. Although the 2 approaches have approximately the same accuracy, the second method approximate expressions are much less complex than those of the first method.     

Power distribution methods for MIMO‐OFDM systems and field experimentations

In this paper, we propose several power allocation schemes for multi‐input multi‐output (MIMO) orthogonal frequency division multiplexing (OFDM) transmission based on the minimization of an approximated bit error rate (BER) expression, and we evaluate the different solutions via field trial experimentations. The methods illustrated in this paper, serve to allocate power among the different transmit antennas and the different subcarriers which compose the MIMO OFDM transmitted signal. Several solutions are available to perform power allocation. Frequency domain power allocation, spatial domain power allocation and combined spatial and frequency power allocation are evaluated. We first review and describe the analytical solution for each power allocation scheme and then evaluate the complexity in terms of both computational operations and BER performances. Simulation results show the performance in term of BER and link the advantage of each possibility of power distribution with the associated complexity. Copyright © 2009 John Wiley & Sons, Ltd.     

Low‐complexity turbo detection for single‐carrier low‐density parity‐check‐coded multiple‐input multiple‐output underwater acoustic communications

A low‐complexity turbo detection scheme is proposed for single‐carrier multiple‐input multiple‐output (MIMO) underwater acoustic (UWA) communications using low‐density parity‐check (LDPC) channel coding. The low complexity of the proposed detection algorithm is achieved in two aspects: first, the frequency‐domain equalization technique is adopted, and it maintains a low complexity irrespective of the highly dispersive UWA channels; second, the computation of the soft equalizer output, in the form of extrinsic log‐likelihood ratio, is performed with an approximating method, which further reduces the complexity. Moreover, attributed to the LDPC decoding, the turbo detection converges within only a few iterations. The proposed turbo detection scheme has been used for processing real‐world data collected in two different undersea trials: WHOI09 and ACOMM09. Experimental results show that it provides robust detection for MIMO UWA communications with different modulations and different symbol rates, at different transmission ranges. Copyright © 2011 John Wiley & Sons, Ltd.