Analytical modelling of multiservice switching networks with multiservice sources and resource management mechanisms

In this paper, we presents an analytical link capacity and outage performance analysis of downlink multiuser diversity (MUD) in multiple-input multiple-output (MIMO) system employing maximal-ratio combining (MRC) with transmit antenna selection (TAS) in the presence of imperfect channel state information (CSI) due to feedback delay over Rayleigh fading channels. The unified achievable analysis is appropriate for MUD–MIMO with TAS/MRC systems in which effective output signal-to-noise ratio (SNR) is specified as highest order statistic of chi-square distribution. Based on this framework, the closed-form channel capacity and outage probability expressions are examined for the MUD–MIMO exploiting TAS/MRC with normalized SNR based scheduling in heterogeneous wireless networks. Further, we derive approximate upper bound capacity as well as capacity at high SNR and low SNR region under delayed feedback CSI. The upper and lower bound of outage probability under delayed feedback CSI is also evaluated. Thereafter the impact of feedback delay and antenna structures with significance on the consideration of MUD on the performance of the system has been analyzed.     

Performance Analysis of Multiuser Diversity on OSTBC MIMO Systems with Antenna Selection in the Presence of Feedback Delay CSI

In this paper, we studied a comprehensive analytical symbol error probability (SEP) performance analysis of downlink multiuser diversity (MUD) on orthogonal space–time block code (OSTBC) system with transmit antenna selection (TAS) in the presence of imperfect channel state information (CSI) due to feedback delay over Rayleigh fading channels. The novel analytical approach is suitable for MUD with TAS/OSTBC systems in which effective receiver signal-to-noise ratio (SNR) is described as highest order statistic of Chi square distribution. Based on this framework, the closed-form SEP expressions are evaluated for the MUD exploiting TAS/OSTBC with normalized SNR based scheduling in heterogeneous wireless networks. Further, we derive approximate SEP; upper bound and lower bound SEP at high SNR under delayed feedback CSI. Thereafter the impact of feedback delay and antenna structures with significance on the consideration of MUD on the performance of the system has been analyzed.

     

Performance analysis of HARQ protocols with link adaptation on fading channels

This work considers hybrid automatic repeat request (HARQ) protocols on a fading channel with Chase combining and deals with both Rayleigh and Nakagami-m fading. We derive the packet loss probability and the throughput for HARQ both for a slow-varying and a fast-varying channel. We then consider link adaptation with complete channel state information (CSI) for which the instantaneous signal-to-noise ratio (SNR) is known and with incomplete CSI for which only the average SNR is known. We derive analytical formulae of the long-term throughput. These formulae are simple enough to be used for higher level simulations. We show that the throughput is slightly higher on a slow-varying channel but at the expense of a higher loss probability.     

Outage Performance of Cognitive AF Relay Networks with Imperfect CSI Based on Geometrical Analysis

This paper studies the outage performance of a cognitive Amplify-and-forward (AF) relay network subject to Rayleigh fading.Under the condition of imperfect Channel state information (CSI) estimations of the links from the secondary system to the Primary user (PU),the closed-form upper and lower bounds of the outage probability are derived through a geometrical analysis method.An asymptotic analysis of the outage probability is also derived in the high Signal-to-noise ratio (SNR) regime to gain additional insights on the system.The simulation results corroborate our theoretical analysis,and the effectiveness of the geometrical analysis method is verified with the conventional approach as a benchmark.The asymptotic results are very tight with the analytical lower bound in the high SNR regime.It also can be observed from the simulation results that the impact of the number of relays as well as the imperfect CSI on the outage probability and the diversity order.     

Outage probability of multiple-input single-output (MISO) systems with delayed feedback

We investigate the effect of feedback delay on the outage probability of multiple-input single-output (MISO) fading channels. Channel state information at the transmitter (CSIT) is a delayed version of the channel state information available at the receiver (CSIR). We consider two cases of CSIR: (a) perfect CSIR and (b) CSI estimated at the receiver using training symbols. With perfect CSIR, under a short-term power constraint, we determine: (a) the outage probability for beamforming with imperfect CSIT (BF-IC) analytically, and (b) the optimal spatial power allocation (OSPA) scheme that minimizes outage numerically. Results show that, for delayed CSIT, BF-IC is close to optimal for low SNR and uniform spatial power allocation (USPA) is close to optimal at high SNR. Similarly, under a longterm power constraint, we show that BF-IC is better for low SNR and USPA is better at high SNR. With imperfect CSIR, we obtain an upper bound on the outage probability with USPA and BF-IC. Results show that the loss in performance due to imperfection in CSIR is not significant, if the training power is chosen appropriately.     

Performance bounds of multihop wireless communications with blind relays over generalized fading channels

In this letter, efficient performance bounds for multihop wireless communications systems with non-regenerative blind relays over non-identical Nakagami-n (Rice), Nakagami-m and Nakagami-q (Hoyt) generalized fading channels, are presented. More specifically, the end-to-end signal-to-noise ratio (SNR) is formulated and upper bounded by using the well-known inequality between harmonic and geometric mean of positive random variables. This bound is used to study important system's performance metrics: i) the moments of the end-to-end SNR which are obtained in closed-forms, and ii) the outage probability and the average error probability for coherent and non-coherent modulations, which are accurately approximated using the moments-based approach. Furthermore, new analytical formulae are derived for the gain of previously proposed semi-blind relays in generalized fading environments. These kind of relays are used in numerical examples and computer simulations to verify the accuracy and to show the tightness of the proposed bounds.     

Performance of M-PSK with GSC and EGC with Gaussian weighting errors

Using a moment-generating function (MGF)-based approach, we study the performance of M-ary phase-shift keying (M-PSK) with generalized selection combining (GSC) and equal gain combining (EGC) in fading channels (including Rayleigh, Rician, Nakagami-m, and Nakagami-q fading) with independent and identically distributed (i.i.d) branches. Analytical expressions for the error and outage probabilities, the signal-to-noise-ratio (SNR) statistics, and the channel capacity of M-PSK diversity receivers are derived, taking into account the effects of Gaussian weighting errors and all relevant system and channel parameters. Unlike the case of perfect channel-state information (CSI), the outage probability for the case of imperfect channel estimation (ICE) is not only a function of the normalized SNR with respect to the SNR threshold, but also a function of the operating SNR itself. The SNR loss of the M-PSK GSC and EGC receivers due to ICE and the relation between the receiver input and output SNRs for ICE are derived. Our results show that, even with ICE, GSC and EGC are effective in improving the output SNR and significantly reduce the error floor and the channel-capacity loss caused by ICE.     

Pairwise error probability evaluation of multiple symbol trellis-coded continuous phase frequency shift keying in a slow fading channel

This article evaluates the pairwise error probability (PEP) of multiple symbol trellis-coded modulation applied to continuous phase frequency shift keying (MTCM/CPFSK) in a slow fading environment with and without channel state information (CSI). The fading amplitude is assumed to be constant during an error event and distributed as Rician. For the case with CSI, the PEP is approximated using the Gauss-Chebysev formula and a tight upper bound is presented. For the case without CSI, a simplified upper bound is derived by using the improved Chernoff bound technique. Simulation results are also presented.     

Performance analysis of ZF receivers with imperfect CSI for uplink massive MIMO systems

We consider the uplink of massive multiple-input multiple-output systems in a multicell environment. Since the base station (BS) estimates the channel state information (CSI) using the pilot signals transmitted from the users, each BS will have imperfect CSI in practice. Assuming zero-forcing method to eliminate the multi-user interference, we derive the exact analytical expressions for the probability density function of the signal-to-interference-plus-noise ratio, the corresponding achievable rate, the outage probability, and the symbol error rate (SER) when the BS has imperfect CSI. An upper bound of the SER is also derived for an arbitrary number of antennas at the BS. Moreover, we derive the upper bound of the achievable rate for the case where the number of antennas at the BS goes to infinity, and the analysis is verified by presenting numerical results.     

On the Pairwise Error Probability of Linear Programming Decoding on Independent Rayleigh Flat-Fading Channels

In this paper, we consider the pairwise error probability (PEP) of a linear programming (LP) decoder for a general binary linear code as formulated by Feldman et al. (IEEE Trans. Inf. Theory, Mar. 2005) on an independent (or memoryless) Rayleigh flat-fading channel with coherent detection and perfect channel state information (CSI) at the receiver. Let H be a parity-check matrix of a binary linear code and consider LP decoding based on H. The output of the LP decoder is always a pseudocode-word. We will show that the PEP of decoding to a pseudocodeword w when the all-zero codeword is transmitted on the above-mentioned channel, behaves asymptotically as K(omega) ldr (E_s/N₀)^{-|chi(omega)|}, where chi(omega) is the support set of omega, i.e., the set of nonzero coordinates, E_s/N₀ is the average signal-to-noise ratio (SNR), and K(omega) is a constant independent of the SNR. Note that the support set chi(omega) of omega is a stopping set. Thus, the asymptotic decay rate of the error probability with the average SNR is determined by the size of the smallest nonempty stopping set in the Tanner graph of H. As an example, we analyze the well-known (155,64) Tanner code and present performance curves on the independent Rayleigh flat-fading channel.     

Exact expression and tight bound on pairwise error probability for performance analysis of turbo codes over nakagami-m fading channels

This letter presents derivation for an exact and efficient expression on pairwise error probability over fully interleaved Nakagami-m fading channels under ideal channel state information at the decoder. As an outcome, this derivation also leads to a tight upper bound on pairwise error probability which is close to the exact expression. Pairwise error probability plots for different values of Nakagami parameter m along with an already existing numerically computable expression are provided. As an application of pairwise error probability, average union upper bounds for turbo codes having (1,7/5,7/5) and (1,5/7,5/7) generator polynomials employing transfer function approach are presented to illustrate the usefulness of the new efficient results     

Performance of two-way amplify-and-forward relaying with adaptive modulation over Nakagami-m fading channels

This paper investigates the performance of a two-way amplify-and-forward(AF)relay system with adaptive modulation over independent and non-identical Nakagami-m fading channels.The tight closed-form cumulative distribution function(CDF)expression of the instantaneous end-to-end signal-to-noise ratio(SNR)is provided.Further,approximate closed-form expression for the average spectral efficiency of the two-way AF system with adaptive modulation is obtained.Then,a tight lower bound of outage probability is deriv...     

Antenna selection for unitary space-time modulation

This correspondence studies receive antenna selection (AS) for multiple-antenna systems that employ unitary space-time (ST) signals, where the channel state information (CSI) is known neither at the transmitter nor at the receiver. Without CSI at the receiver, we perform AS only at the receiver and the selection is based on a maximum-norm criterion, i.e., a subset of receive antennas that have the largest received signal power is chosen. Using a Chernoff bound approach, we present theoretical performance analysis based on the pairwise error probability (PEP) and quantify the asymptotic performance at high signal-to-noise ratio (SNR) by giving the diversity and coding gain expressions. We prove that with no CSI at the receiver, the diversity gain with AS is preserved for unitary ST codes with full spatial diversity, the same as the case with known CSI. As a concrete example, for differential unitary ST modulation with M=2 transmit antennas and N=2 receive antennas, we have devised new excellent-performing parametric codes based on the derived PEP bound. The new codes, which are specifically designed for differential AS systems, outperform known differential codes when AS is employed. Corroborating simulations validate our analysis and code design.     

Infinite series representations of the trivariate and quadrivariate nakagami-m distributions

In this paper, using Miller's approach and Dougall's identity, we derive new infinite series representations for the quadrivariate Nakagami-m joint density function, cumulative distribution function (cdf) and characteristic functions (chf). The classical joint density function of exponentially correlated Nakagami-m variables can be identified as a special case of the joint density function obtained here. Our results are based on the most general arbitrary correlation matrix possible. Moreover, the trivariate density function, cdf and chf for an arbitrary correlation matrix are also derived from our main result. Bounds on the series truncation error are also presented. Finally, we develop several representative applications: the outage probability of triple branch selection combining (SC), the moments of the equal gain combining (EGC) output signal to noise ratio (SNR) and the moment generation function of the generalized SC(2,3) output SNR in an arbitrarily correlated Nakagami-m environment. Simulation results are also presented to verify the accuracy of our theoretical results.     

Joint Source–Channel Codes for MIMO Block-Fading Channels

We consider transmission of a continuous amplitude source over an L-block Rayleigh-fading M_t x M_r multiple-input multiple-output (MIMO) channel when the channel state information is only available at the receiver. Since the channel is not ergodic, Shannon's source-channel separation theorem becomes obsolete and the optimal performance requires a joint source-channel approach. Our goal is to minimize the expected end-to-end distortion, particularly in the high signal-to-noise ratio (SNR) regime. The figure of merit is the distortion exponent, defined as the exponential decay rate of the expected distortion with increasing SNR. We provide an upper bound and lower bounds for the distortion exponent with respect to the bandwidth ratio among the channel and source bandwidths. For the lower bounds, we analyze three different strategies based on layered source coding concatenated with progressive superposition or hybrid digital/analog transmission. In each case, by adjusting the system parameters we optimize the distortion exponent as a function of the bandwidth ratio. We prove that the distortion exponent upper bound can be achieved when the channel has only one degree of freedom, that is L = 1, and min{M_t ,M_r} =1. When we have more degrees of freedom, our achievable distortion exponents meet the upper bound for only certain ranges of the bandwidth ratio. We demonstrate that our results, which were derived for a complex Gaussian source, can be extended to more general source distributions as well.     

Nakagami信道的中断容量分析

本文讨论了Nakagami-m衰落信道系统的中断容量性能,在发射端未知信道信息,接收端的信道估计存在误差时,给出了计算中断容量上界和下界的表达式,它们是接收端的估计误差和信道参数的函数,仿真结果表明随着估计误差的增大中断容量的上界和下界同时降低,但是中断容量的下界随着信道参数的增大而增大,上界随着信道参数的增大而减小。     

High SNR sum capacity analysis of BD MIMO BC systems with imperfect CSI

We investigate the sum capacity of Block Diagonalization precoding Multiple Input Multiple Output Broadcast Channels (BD MIMO BC) with imperfect Channel State Information (CSI) at the base station. Since it is difficult to obtain the exact expression, a lower and an upper bounds of the sum capacity under Gaussian channel estimation errors are drived instead. Analyses show that the gap between two bounds is considerably tight at all Signal to Noise Ratio (SNR) region. From the lower bound of the sum capacity, we can see that the multiplexing gain tends to be zero at high SNR region, which indicates that the BD MIMO BC system with channel estimation errors is interference-limited at high SNR.     

Performance Analysis of Cooperative Diversity Wireless Networks over Nakagami-m Fading Channel

This letter analyzes the performance of cooperative diversity wireless networks using amplify-and-forward relaying over independent, non-identical, Nakagami-m fading channels. The error rate and the outage probability are determined using the moment generating function (MGF) of the total signal-to-noise-ratio (SNR) at the destination. Since it is hard to find a closed form for the probability density function (PDF) of the total SNR, we use an approximate value instead. We first derive the PDF and the MGF of the approximate value of the total SNR. Then, the MGF is used to determine the error rate and the outage probability. We also use simulation to verify the analytical results. Results show that the derived error rate and outage probability are tight lower bounds particularly at medium and high SNR     

On the Distortion SNR Exponent of Hybrid Digital–Analog Space–Time Coding

We consider the transmission of a real independent and identically distributed (i.i.d.) "analog" source over a quasi-static M-input N-output multiple-input multiple-output (MIMO) block-fading channel. The relevant performance criterion is end-to-end average quadratic distortion D versus channel signal-to-noise ratio (SNR), for given spectral efficiency eta, defined as the ratio of the source bandwidth over the channel bandwidth. In the limit of high SNR, we define the distortion SNR exponent a*(eta) as the largest a such that D esdot snr^-a, over all possible source-channel coding schemes of spectral efficiency eta. We find a simple upper bound on a*(eta), an achievable lower bound a_sep(eta) achievable by separated (tandem) source-channel coding, and a tighter lower bound a_hybrid(eta) achievable by new hybrid digital analog space-time coding schemes. As a corollary, we have that a*(eta) is completely determined for the scalar case M = N = 1 and for the "bandwidth compression" case eta ges 2 min{M, N}. Expiicit and simple construction of hybrid space-time codes achieving a_hybrid(eta) are also given.     

Performance analysis for coded CDMA systems

This correspondence analyzes the bit-error rate (BER) performance of coded synchronous code-division multiple-access (CDMA) systems assuming perfect channel state information (CSI) and optimal joint multiuser detection/decoding (OJMUDD). Our analysis is conducted in the same framework as that of uncoded systems. First, we derive the precise probability of an error event, then we provide an upper bound on the BER based on the sum of pairwise error probabilities, and, finally, we tighten the upper bound by considering decomposable error events. Many new concepts unique to coded systems are introduced. We propose to use quasi parity checks for identifying permissible error events, introduce the concept of compatible probability of error matrices, extend the list of conditions for identifying decomposable error events, and introduce the concept of conjugate sets to explore the symmetry among indecomposable error events. Simulation results are given along with theoretical predictions.