Performance analysis of multi‐input multi‐output systems with maximum likelihood detection over shadowed fading channels

Multiple‐input multiple‐output (MIMO) transmission techniques constitute an important technology in modern wireless communication. Hence, performance analysis methods for such systems are of considerable interest. This paper considers first the average pairwise error probability for uncoded MIMO systems employing maximum likelihood detection over a composite Rayleigh‐Lognormal fading channel with spatial correlation. It provides general results, applicable also to a wider class of shadowing models, concerning asymptotical diversity gains and shows that they are not changed by such shadowing. Then, analytical evaluation techniques for bit‐error‐rate (BER) over composite Rayleigh‐Lognormal fading channels, based on the truncated union bound and the transfer function, are considered. Furthermore, these techniques are modified for applications over spatially correlated channels. This paper shows that such performance evaluation techniques provide good approximations to BER of spatially uncorrelated MIMO systems and also in the presence of moderate spatial correlation, over Rayleigh‐Lognormal fading channels. Copyright © 2013 John Wiley & Sons, Ltd.     

An Efficient Scheme to Achieve Differential Unitary Space‐Time Modulation on MIMO‐OFDM Systems

Differential unitary space‐time modulation (DUSTM) has emerged as a promising technique to obtain spatial diversity without intractable channel estimation. This paper presents a study of the application of DUSTM on multiple‐input multiple‐output orthogonal frequency division multiplexing (MIMO‐OFDM) systems with frequency‐selective fading channels. From the view of a correlation analysis between subcarriers of OFDM, we obtain the maximum achievable diversity of DUSTM on MIMO‐OFDM systems. Moreover, an efficient implementation strategy based on subcarrier reconstruction is proposed, which transmits all the signals of one signal matrix in one OFDM transmission and performs differential processing between two adjacent OFDM blocks. The proposed method is capable of obtaining both spatial and multipath diversity while reducing the effect of time variation of channels to a minimum. The performance improvement is confirmed by simulation results.     

Evolution from symbol‐level space–time coded MIMO to chip‐level space–time coded MIMO: a review

Space–time coded multiple‐input multiple‐output (MIMO) technology is an important technique that improves the performance of wireless communication systems significantly without consuming bandwidth resource. This paper first discusses the characteristics and limitations of traditional symbol‐level space–time coding schemes, which work largely on the basis of an assumption that signals are sent to a block‐fading channel. Therefore, the symbol‐level space–time coding schemes rely on symbol‐level signal processing. Taking advantage of orthogonal complementary codes, we propose a novel MIMO scheme, in this paper, based on chip‐level space–time coding that is different from the traditional symbol‐level space–time coding. With the help of space–time–frequency complementary coding and multicarrier modem, the proposed scheme is able to achieve multipath interference‐free and multiuser interference‐free communications with simple a correlator detector. The proposed chip‐level space–time coded MIMO works well even in a fast fading channel in addition to its flexibility to achieve diversity and multiplexing gains simultaneously in varying channel environments. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive antennas for MIMO OFDM‐CDMA communication systems

In this paper, we propose symbol‐based receivers for orthogonal frequency division multiplexing (OFDM) code‐division multiple‐access (CDMA) multiple‐input‐multiple‐output (MIMO) communications in multipath fading channels. For multiuser and multipath fading environments, both intersymbol interference and multiple‐access interference must be considered. We propose narrowband and wideband antennas and Wiener code filter for MIMO OFDM‐CDMA systems. The proposed receivers are updated symbol‐by‐symbol to achieve low computational complexity. Simulation results show that the proposed Wiener code filter can improve the system performance for the proposed adaptive antennas. The wideband antenna can achieve better error‐rate performance than that of the narrowband antenna when multipath effect exists. The convergence rate of the recursive least squares antennas is faster than that of the least mean square antennas. Copyright © 2013 John Wiley & Sons, Ltd.     

Uplink bit combining for multiple base‐stations MIMO with applications to CoMP systems

This work considers a simple bit level combining technique, aided by robust bit reliability information, for uplink collaborating multiple‐input multiple‐output (MIMO) base‐stations (also known as macrodiversity MIMO), operating over composite Rayleigh‐lognormal fading channels. Bit reliability weights based on a robust modification of the logarithmic likelihood ratio, combined with instantaneous symbol signal‐to‐noise ratio information, are derived for different local MIMO detection schemes. This bit reliability information is used at the fusion center, together with locally detected data, for combining and producing final information bits delivered to the destination. Computer simulation results confirm that such bit level combining techniques, when used with minimum mean squared error ordered successive interference cancelation and also with sphere decoding maximum likelihood local detectors, provide significant performance improvements over non‐collaborative base‐stations systems. Performance gains are maintained even when these schemes suffer from channel estimation errors and also in the presence of space correlation. Low backhaul overhead and performance advantages make these bit level combining techniques attractive for applications in next generation cellular systems employing coordinated multi‐point (CoMP) technology, as well as for other collaborative MIMO communication schemes.Copyright © 2014 John Wiley & Sons, Ltd.     

Diversity‐multiplexing tradeoff over correlated Rayleigh fading channels: a non‐asymptotic analysis

In this paper, we present a finite‐signal‐to‐noise ratio (finite‐SNR) framework to establish tight bounds on the diversity‐multiplexing tradeoff of a multiple input multiple output (MIMO) system. We focus on a more realistic propagation environment where MIMO channel fading coefficients are correlated and where SNR values are finite. The impact of spatial correlation on the fundamental diversity‐multiplexing tradeoff is investigated. We present tight lower bounds on the outage probability of both spatially uncorrelated and correlated MIMO channels. Using these lower bounds, accurate finite‐SNR estimates of the diversity‐multiplexing tradeoff are derived. These estimates allow to gain insight on the impact of spatial correlation on the diversity‐multiplexing tradeoff at finite‐SNR. As expected, the diversity‐multiplexing tradeoff is severely degraded as the spatial correlation increases. For example, a MIMO system operating at a spectral efficiency of R bps/Hz and at an SNR of 5 dB in a moderately correlated channel, achieves a better diversity gain than a system operating at the same spectral efficiency and at an SNR of 10 dB in a highly correlated channel, when the multiplexing gain r is greater than 0.8. Another interesting point is that provided that the spatial correlation channel matrix is of full rank, the maximum diversity gain is not affected by the spatial correlation. Copyright © 2009 John Wiley & Sons, Ltd.     

Second‐order statistics of system with N‐branch microdiversity and L‐branch macrodiversity operating over gamma shadowed Nakagami‐m fading channels

The problem concerning short‐term fading and long‐term fading (shadowing) and their deleterious effects on wireless systems performance has been in focus for a long time. In this paper, motivated by the results of propagation measurements in land‐mobile and indoor‐mobile systems, and by the fact that gamma distribution can describe shadowing reliably, Nakagami‐m distribution is used to model the signal envelope and gamma distribution is used to model the average signal power. Receive diversity with maximal‐ratio combining and selection combining is implemented at the microlevel and macrolevel, respectively. The general case is explored, which assumes that microdiversity and macrodiversity are provided through arbitrary number of channels. Because shadowing has larger correlation distance than short‐term fading, correlated macrodiversity channels are studied. This paper investigates the dynamics of the received signal. A novel rapidly converging infinite‐series expression for average level crossing rate and average fade duration are obtained. Numerical results are graphically presented to examine the impact of fading severity, shadowing severity, number of diversity branches at the microlevel, number of base stations and correlation between base stations to the system's performance. Computer simulations are also performed to verify the validity and the accuracy of proposed theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

Closed‐Form Expressions for Selection Combining System Statistics over Correlated Generalized‐K Fading Channels in the Presence of Interference

This paper considers the effects of simultaneous correlated multipath fading and shadowing on the performances of a signal‐to‐interference ratio (SIR)‐based dual‐branch selection combining (SC) diversity receiver. This analysis includes the presence of cochannel interference. A generalized fading/shadowing channel model in an interference‐limited correlated fading environment is modeled by generalized‐K distribution. Closed‐form expressions are obtained for probability density function and cumulative distribution function of the SC output SIR, as well as for the outage probability. Based on this, the influence of various fading and shadowing parameter values and the correlation level on the outage probability is examined.     

Performance analysis of uplink spatial multiplexing MIMO MT‐CDMA over multipath fading channels

In this paper, we consider multiple‐input multiple‐output (MIMO) multi‐tone code division multiple access (MT‐CDMA) uplink transmission over multipath fading channels. The zero‐forcing vertical Bell Laboratories layered space‐time architecture (ZF V‐BLAST) algorithm and maximum ratio combining scheme are applied at the receiver. The average bit error rate (BER) expression is derived provided that the number of receive antennas is not less than that of transmit antennas. The BER expression is verified by simulations. Numerical results show that the numbers of transmit and receive antennas have significant effects on the BER performance of the considered system. Spatial and path diversity show different capabilities to improve the BER performance. The MIMO MT‐CDMA system based on the ZF V‐BLAST algorithm is capable of achieving a better BER performance and a higher capacity than the conventional MT‐CDMA system. Copyright © 2011 John Wiley & Sons, Ltd.     

A novel wideband space‐time channel simulator based on the geometrical one‐ring model with applications in MIMO‐OFDM systems

In this paper, we extend the geometrical one‐ring multiple‐input multiple‐output (MIMO) channel model with respect to frequency selectivity. Our approach enables the design of efficient and accurate simulation models for wideband space‐time MIMO channels under isotropic scattering conditions. Two methods will be provided to compute the parameters of the simulation model. Especially, the temporal, frequency and spatial correlation properties of the proposed wideband space‐time MIMO channel simulator are studied analytically. It is shown that any given specified or measured discrete power delay profile (PDP) can be incorporated into the simulation model. The high accuracy of the simulation model is demonstrated by comparing its statistical properties with those of the underlying reference model with specified correlation properties in the time, frequency and spatial domain. As an application example of the new MIMO frequency‐selective fading channel model, we study the influence of various channel model parameters on the system performance of a space‐time coded orthogonal frequency division multiplexing (OFDM) system. For example, we investigate the influence of the antenna element spacings of the base station (BS) antenna as well as the mobile station (MS) antenna. It turns out that an increasing of the antenna element spacing at the BS side results in a higher diversity gain than an increasing of the antenna element spacing at the MS side. Furthermore, the diversity gain brought in by space‐time block coding schemes is investigated by simulation. Our results show that transmitter diversity can significantly reduce the symbol error rate (SER) of multiple antenna systems. Finally, the influence of the Doppler effect and the impact of imperfect channel state information (CSI) on the system performance is also investigated. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

MVDR‐combining‐aided diversity and spatial multiplexing for MIMO multi‐cellular networks with cochannel interference

Two multiple‐input multiple‐output (MIMO) schemes (a diversity scheme and a spatial multiplexing scheme) that employ the minimum variance distortionless response (MVDR) combining are proposed for multi‐cellular networks with cochannel interference. With the receive diversity provided by the MVDR combining, the proposed diversity scheme can be benefited by both the transmit diversity and the receive diversity, also, the proposed spatial multiplexing scheme can be benefited by both the receive diversity and the spatial multiplexing. The proposed MIMO schemes do not require the space‐time coding or the successive interference cancellation, thus they can result in less computational complexity than space‐time block code (STBC) and vertical‐Bell Labs layered space‐time (V‐BLAST). We show that the capacity of the proposed diversity scheme is close to or larger than that of STBC for the noise‐corrupted case and is much larger than that of STBC for the interference‐corrupted case. We also show that the capacity of the proposed spatial multiplexing scheme can be much larger than that of V‐BLAST for the interference‐corrupted case and the noise‐corrupted case, and the proposed spatial multiplexing scheme can achieve good compromise between diversity and spatial multiplexing. Copyright © 2011 John Wiley & Sons, Ltd.     

Improved Design Criterion for Space‐Frequency Trellis Codes over MIMO‐OFDM Systems

In this paper, we discuss the design problem and the robustness of space‐frequency trellis codes (SFTCs) for multiple input multiple output, orthogonal frequency division multiplexing (MIMO‐OFDM) systems. We find that the channel constructed by the consecutive subcarriers of an OFDM block is a correlated fading channel with the regular correlation function of the number and time delay of the multipaths. By introducing the first‐order auto‐regressive model, we decompose the correlated fading channel into two independent components: a slow fading channel and a fast fading channel. Therefore, the design problem of SFTCs is converted into the joint design in both slow fading and fast fading channels. We present an improved design criterion for SFTCs. We also show that the SFTCs designed according to our criterion are robust against the multipath time delays. Simulation results are provided to confirm our theoretic analysis.     

ZCZ‐CDMA and OFDMA using M‐QAM for broadband wireless communications

This paper considers direct‐sequence code‐division multiple‐access with zero‐correlation zone sequences (ZCZ‐CDMA) and orthogonal frequency‐division multiple‐access (OFDMA) schemes using M‐ary QAM signaling for broadband wireless communications. Their system structures, complexities and performances in both AWGN and multipath frequency‐selective fading channels are evaluated and compared. For ZCZ‐CDMA, joint suppression of the multipath fading interference and multiple‐access interference can be achieved with a reduced family‐size of the spreading sequences. For OFDMA, analytical and simulation results indicate that it has the same performance as ZCZ‐CDMA in fast time‐varying multipath fading channels. In time‐invariant or slowly time‐varying channels, where the channel information can be made available to transmitters, OFDMA outperforms ZCZ‐CDMA, offers a higher capacity and is more flexible for system reconfiguration with a comparable computational complexity. Copyright © 2004 John Wiley & Sons, Ltd.     

Maximal Ratio Combining (MRC) in Shadowed Fading Channels in Presence of Shadowed Fading Cochannel Interference (CCI)

Simultaneous existence of multipath fading and shadowing leads to worsening conditions in wireless channels. This is further compounded by the interference from other base stations operating at the same frequency. The effect of this cochannel interference (CCI) and shadowed fading in error rates is studied when maximal ratio combining is used to mitigate short term fading. The CCI channels were also treated as undergoing shadowed fading. The generalized K distribution was used to model the signal-to-noise ratio of composite shadowed fading channel. The probability density functions of the signal-to-noise ratio taking into account the presence of multipath fading, shadowing and CCI were derived and used for the estimation of error rates. Results demonstrated the existence of degradation in the channel manifested as increased error rates and higher error floors. The improvements in the channel obtained through diversity were also demonstrated. The approach presented here can be easily adapted to the analysis of other diversity schemes in shadowed fading channels.     

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.     

Performance analysis of orthogonal space-time block codes in spatially correlated MIMO Nakagami fading channels

Orthogonal space-time block coding (STBC) is an open-loop transmit diversity scheme that decouples the multiple-input multiple-output (MIMO) channel, thereby reducing the space-time decoding into a scalar detection process. This characteristic of STBC makes it a powerful tool, achieving full diversity over MIMO fading channels, and requiring little computational cost for both the encoding and decoding processes. In this paper, we exploit the single-input single-output equivalency of STBC in order to analyze its performance over nonselective Nakagami fading channels in the presence of spatial fading correlation. More specifically, we derive exact closed-form expressions for the outage probability and ergodic capacity of STBC, when the latter is employed over spatially correlated MIMO Nakagami fading channels. Moreover, we derive the exact symbol error probability of coherent M-PSK and M-QAM, when these modulation schemes are used along with STBC over such fading channels. The derived formulae are then used to assess the robustness of STBC to spatial correlation by considering general MIMO correlation models and analyzing their effects on the outage probability, ergodic capacity, and symbol error probability achieved by STBC.     

Performance analysis of secure communications over correlated slow‐fading additive white Gaussian noise channels

The broadcast nature of communications in wireless communication networks makes it vulnerable to some attacks, particularly eavesdrop attack. Hence, information security can have a key role to protect privacy and avoid identity theft in these networks, especially in distributed networks. In the wireless systems, the signal propagation is affected by path loss, slow fading (shadowing), and fast fading (multi‐path fading). As we know, there is a correlation between communication channels in the real radio environments. This correlation is defined by the correlation between their shadowing and/or multipath fading factors. So when there are several channels in the wireless systems, there is certainly a correlation between the channels. In this paper, we assume that the transmitter knows the full channel state information (CSI), it means the transmitter knows both the channel gains of the illegitimate (ie, eavesdropper) and the legitimate receivers and study the performance of secure communications of single‐input single‐output (SISO) systems consisting of single antenna devices, in the presence of a single antenna passive eavesdropper over correlated slow fading channels, where the main (transmitter to legitimate receiver) and eavesdropper (transmitter to illegitimate receiver) channels are correlated. Finally, we present numerical results and verify the accuracy of our analysis by Monte‐Carlo simulations.     

Constellation constrained multiuser multiple‐input multiple‐output for high capacity and error performance over correlated fading channels

Channels' correlation has direct impact to degrade the capacity and reliability of multiple‐input multiple‐output (MIMO) systems considerably. In this paper, new signal constellation designs are investigated to mitigate fading correlation and maximize the capacity and error performance of multiuser MIMO (MU‐MIMO) over correlated channels, which is a major research challenge. Two methods are studied in a novel constellation constrained MU‐MIMO approach, namely, unequal power allocation and rotated constellation. Based on principles of maximizing the minimum Euclidean distance (d_min) of composite received signals, users' data can be recovered using maximum likelihood joint detection irrespective of correlation values. Compared with the identical constellation scenario in conventional MU‐MIMO, it is shown that constellation rearrangement of transmitted signals has direct impact to resolve the detection ambiguity when the channel difference is not sufficient, particularly in moderate to high correlations. Extensive analysis and simulation results demonstrate the superiority of proposed technique to capture most of the promised gains of multiantenna systems and application for future wireless communications. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive modulation and decision feedback equalization for frequency‐selective MIMO channels

In this paper, an adaptive modulation scheme for the multiple‐input multiple‐output (MIMO) frequency‐selective channels is investigated. We consider a scenario with precoded block‐based transceivers over spatially correlated Rayleigh multipath MIMO channels. To eliminate the inter‐block interference, the zero‐padding is used. The receiver is equipped with a MIMO minimum‐mean‐squared‐error decision feedback equalizer. The precoder aims to force each subchannel to have an identical signal‐to‐interference‐plus‐noise ratio (SINR). To adjust the constellation size, the unbiased mean square error at the equalizer output is sent back to the transmitter. To simplify our analysis, the feedback channel is considered as instantaneous and error free. We first derive the probability density function of the overall SINR for flat fading and frequency‐selective channels. On the basis of the probability density function of the upper bound of the SINR, we evaluate the system performance. We present accurate closed‐form expressions of the average spectral efficiency, the average bit error rate and the outage probability. The derived expressions are compared with Monte Carlo simulation results. Furthermore, we analyze the effect of the channel spatial correlation. Copyright © 2013 John Wiley & Sons, Ltd.