Nakagami Channels Research Articles

Pairwise Error Probability of Space-Time Codes in Rician–Nakagami Channels

In this letter, we investigate the shadowing effect on the performance of space-time codes, using the Rician-Nakagami channel model which has been recently introduced. Specifically, we derive an exact expression for the pairwise error probability (PEP) of space-time trellis codes over the Rician-Nakagami channel, which is in the form of a simple single finite-range integral. We also present numerical results how the PEP expressions for the Rician-Nakagami channel can be related to those for the classical Rician-lognormal channel based on the parameter transformation between these two models.

A New and Exact Analysis of DS-CDMA Cellular Radio System Based on the Physical Interpretation of Nakagami Wideband Channel

Summary In this paper we present the performance of two uplink/downlink DS-CDMA receivers in a Nakagami wideband channel. Two detection methods were considered; namely, coherent and differential detection RAKE receivers based on maximal ratio combining technique. We consider a new physical interpretation of the Nakagami channel and the instantaneous power of the multiple access interferers. In comparison with the previous researches in the literature, which are based on Gaussian approximation, this approach results in a more accurate solution for the problem. We analyzed and derived closed form formulae for probability of bit error for DS-CDMA cellular radio system in the Nakagami wideband channel. We presented a set of numerical results for coherent downlink receivers.

A generic correlated nakagami fading model for wireless communications

A complete statistical characterization of correlated Nakagami channels is either their joint probability density function or their joint characteristic function (CHF), which is indispensable to many applications in wireless communications. The classical correlated multivariate Nakagami model in current use is subject to a restriction that the fading parameters must be identical. We derive a generic correlated Nakagami fading model, in the form of a multiple CHF, allowing for an arbitrary covariance matrix and distinct real fading parameters. The application of the new model to wireless communications is also presented.

Estimation of nakagami-m fading channel parameters with application to optimized transmitter diversity systems

An optimum power loading algorithm for transmitter diversity systems over correlated and unbalanced Nakagami (1960) paths and its performance evaluation under perfect channel estimate conditions are derived. In addition, various online estimators of the required Nakagami channel parameters for optimized power loading and the comparison of their mean square error via Monte Carlo simulations are presented. Some of these estimators are used to obtain the performance of optimized transmitter diversity systems under imperfect channel estimation (ICE). These numerical results show that the diversity gain of these optimized systems compared with equipower systems increases as the severity of fading decreases and as the degree of branch imbalance increases even under ICE. On the other hand, in weakly correlated and (or) unbalanced branches, optimized transmitter diversity systems offer negligible gain or even losses compared with unoptimized systems because of the ICE.

A general analytical approach to multi-branch selection combining over various spatially correlated fading channels

Driven by the potential application to wireless communications, intensive research efforts have been made on the study of various selective combining (SC) schemes in the past decade. Nevertheless, regardless of its practical importance, performance analysis of multi-branch SC over spatially correlated fading channels is not available in literature except for the simplest case of dual diversity. The major difficulty lies in the fact that SC has its root in the theory of order statistics, and yet systematic methodology has been developed mainly for order statistics obtained from an independent population. In this paper, we formulate the problem in a very general framework, whereby a general solution is derived. The application of the new solution to SC with different modulation schemes and operational environments is elaborated. The fading environments to be addressed include correlated Nakagami, Rayleigh, and Rician channels. Numerical examples are also presented to illustrate the use of the theory.

Error Probabilities for MRC Diversity Reception of MDPSK in Slow Nakagami Fading

New closed form error probability expressions for M-ary differential-phase-shift-keying (MDPSK) with maximal ratio combining (MRC) diversity reception in Nakagami fading, are derived. These expressions involve easily computable Legendre polynomials and Associated Legendre functions. By setting the fading severity parameter m to unity, the new general error probability formula reduces to the known results for MDPSK systems in slow Rayleigh fading. For binary DPSK, the bit error rate (BER) performance with MRC is compared with known results for selection diversity combining (SDC). It is shown that MRC is more effective than SDC in improving BER performance for the Nakagami channels, as expected. We also discuss the ranges of the fading severity parameter and diversity order, within which the error probability expressions can be computed efficiently.

Unified error probability analysis for generalized selection combining in Nakagami fading channels

We study generalized selection combining (GSC) schemes in independent Nakagami fading channels, where N diversity branches with the largest instantaneous signal-to-noise ratios (SNRs) are selected from the total of L (N/spl les/L) branches and then coherently or noncoherently combined. We propose two different techniques to derive the moment generating function (MGF) expressions for the GSC output SNR in generalized Nakagami fading channels, where there are distinct and noninteger fading severity parameters, as well as different average SNRs in different diversity branches. For arbitrary fading severity parameter m/sub k/, k=1, /spl middot//spl middot//spl middot/L, the MGF expression is given in a summation of N-dimensional definite integrals with the limits independent of SNR or channel parameters, and therefore can be evaluated very efficiently with numerical methods. Furthermore, for integer m/sub k/ closed-form MGF expressions are derived. Specializations of our results to Rayleigh channels and independent identically distributed (i.i.d.) Nakagami channels are presented, which are either new or equivalent to previously published results. Using the newly derived MGF expression, we provide a unified error probability analysis for many coherent and noncoherent modulation/detection schemes.

A decomposition technique for efficient generation of correlated Nakagami fading channels

Correlated Nakagami m-fading is commonly encountered in wireless communications. Its generation in a laboratory environment is therefore of theoretical and practical importance. However, no generic technique for this purpose is available in the literature. Correlated Rayleigh fading is easy to simulate since it has a simple relationship with a complex Gaussian process. Unfortunately, this is not the case for Nakagami fading. The difficulty lies in that the fading parameter can be a real number and there is no general theory linking a Nakagami vector to a finite set of correlated Gaussian vectors. In this paper, by introducing a direct-sum decomposition principle and determining the statistical mapping between the correlated Nakagami process and a set of Gaussian vectors for its generation, a simple general procedure is derived for the generation of correlated Nakagami channels with arbitrary parameters. A key parameter in the statistical mapping can be determined by using an iterative method. The validity of the new technique is examined through the generation of a correlated Nakagami sequence, as encountered in U.S. digital cellular, and a multibranch vector channel as encountered in diversity reception.

Some simple bounds on the symmetric capacity and outage probability for QAM wireless channels with Rice and Nakagami fadings

In this article, quickly computable upper and lower bounds are presented on the symmetric capacity of flat-faded Rice and Nakagami channels with side information (SI) for data-transmissions via finite-size quadrature amplitude modulation (QAM) constellations. The proposed bounds exhibit the appealing feature to be tight and asymptotically exact both for high and low signal-to-noise ratios (SNRs). Furthermore, exponentially tight Chernoff-like formulas are also presented for an analytical evaluation of the resulting system outage probabilities when interleaved packet transmissions are carried out.

Analysis of DQPSK under Frequency Non-Selective, Slowly Nakagami Fading Channel

In radio multipath channel Nakagami distribution is best fit for data signals received. As Differential QPSK is bandwidth efficient than BPSK and Differential QPSK is more useful in case of mobile radio communication. The close coherent detection performance can be obtained when adaptive differential detection is applied to differential QPSK. In this paper for differential QPSK under Nakagami channel BER analysis is done considering half Gausian Rayleigh channel as a special case of Nakagami channel.

Co-channel interference analysis for mobile radio suffering lognormal shadowed Nakagami fading

Determination of the outage performance of a cellular mobile system in lognormal shadowed Nakagami fading environments has been the focus of many researchers. However, general results are not available in the literature. The difficulty arises from the philosophy which attempts to determine first the outage probability for Nakagami fading and then average it over lognormal distributions. The consequence is outage expressions in the form of an intractable multi-fold integral. By formulating the problem in the framework of characteristic functions and naturally combining the two separated steps in a single one, the author obtains an expression for outage probability always in the form of a two-fold integral no matter how many co-channel users are in operation. The outage probability so obtained can be accurately and efficiently evaluated by using the Hermite and Gaussian quadrature. It thereby provides a general analysis tool for lognormal shadowed Nakagami channels with arbitrary parameters. Numerical results are also presented to illustrate the theory.

Generalized Cochannel Outage Analysis with DTX inPCS Channels

Spectrum limitations are often a deterrent for swift growth of cellular radio systems. Therefore, different technologies have been explored to enhance the Radio Frequency (RF) capacity as well as to improve the communication quality. Recent technologies suggest the use of Discontinuous Transmission (DTX) as a mean to achieve these goals. In this paper, we analyze and quantify the performance improvement which result from implementing DTX in microcellular systems. The performance criteria is chosen to be the outage probability of de signal to interference ratio. Closed form expressions are derived for outage probabilities for systems using discontinuous transmission. Results are obtained for generalized Nakagami(n)/Nakagami(m) channels as well as for Ricean/Nakagami(m) environments. Moreover, since DTX effectiveness depend on voice patterns, modified expressions are developed for average outage probabilities which take into consideration different voice activity factors.

Exact analysis of postdetection combining for DPSK and NFSK systems over arbitrarily correlated Nakagami channels

Postdetection combining is a popular means to improve the bit error performance of DPSK and noncoherent FSK (NFSK) systems over fading channels. Nevertheless, the error performance of such systems in an arbitrarily correlated Nakagami environment is not available in the literature. The difficulty arises from inherent nonlinearity in noncoherent detection and from attempts to determine explicitly the probability density function of the total signal-to-noise ratio at the combiner output. We directly determine the error probability from the characteristic function of decision variables, resulting in closed-form solutions involving matrix differentiation. The performance calculation is further simplified by developing a recursive technique. The theory is illustrated by analyzing two feasible antenna arrays used in base stations for diversity reception, ending up with some findings of interest to system design.

Concatenated Reed-Solomon/convolutional coding for data transmission in CDMA-based cellular systems

A robust error control scheme for data transmission in CDMA-based cellular systems is proposed which employs outer Reed-Solomon codes concatenated with inner convolutional codes. The performance of this scheme is analyzed assuming nonperiodic random spreading sequences and a Rake receiver with perfect knowledge of the channel. In particular, a simple model for the memoryless inner coding channel that encompasses the effects of multiple access interference, self-noise and thermal noise is first derived. Using new tight upper bounds on bit- and symbol-error probabilities of convolutional codes over Nakagami, Rayleigh, and Rician fading multipath channels, the performance of the concatenated coding scheme is then evaluated. The Reed-Solomon/convolutional coding scheme has been adopted by the European RACE Project Code Division Testbed (CODIT) and implemented in an experimental testbed. The code design methodology, which has been used to specify the 9.6-, 64-, and 128-kbit/s data traffic channels of the CODIT testbed, is presented and the single-cell CDMA capacity is computed.

Unknown Bounds on Performance in Nakagami Channels

Optimum performance of communication in Nakagami channels is reexamined. With novel functionals of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m/\gamma</tex> -distribution, analyses of signal interference and of coherent binary detection are greatly simplified. The general error-rate formula holds for coherent and noncoherent detection of PSK or FSK signals. A lower bound on error rates is established for some diversity systems.

Error probabilities for the Nakagami channel (Corresp.)

Error probabilities for the Nakagami channel (Corresp.)