Capacity limits of spectrum‐sharing systems over hyper‐fading channels

Cognitive radio (CR) with spectrum‐sharing feature is a promising technique to address the spectrum under‐utilization problem in dynamically changing environments. In this paper, the achievable capacity gain of spectrum‐sharing systems over dynamic fading environments is studied. To perform a general analysis, a theoretical fading model called hyper‐fading model that is suitable to the dynamic nature of CR channel is proposed. Closed‐form expressions of probability density function (PDF) and cumulative density function (CDF) of the signal‐to‐noise ratio (SNR) for secondary users (SUs) in spectrum‐sharing systems are derived. In addition, the capacity gains achievable with spectrum‐sharing systems in high and low power regions are obtained. The effects of different fading figures, average fading powers, interference temperatures, peak powers of secondary transmitters, and numbers of SUs on the achievable capacity are investigated. The analytical and simulation results show that the fading figure of the channel between SUs and primary base‐station (PBS), which describes the diversity of the channel, does not contribute significantly to the system performance gain. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimization of multi-branch switched diversity systems

A performance optimization based on the optimal switching threshold(s) for a multi-branch switched diversity system is discussed in this paper. For the conventional multi-branch switched diversity system with a single switching threshold, the optimal switching threshold is a function of both the average channel SNR and the number of diversity branches, where computing the optimal switching threshold is not a simple task when the number of diversity branches is high. The newly proposed multi-branch switched diversity system is based on a sequence of switching thresholds, instead of a single switching threshold, where a different diversity branch uses a different switching threshold for signal comparison. Thanks to the fact that each switching threshold in the sequence can be optimized only based on the number of the remaining diversity branches, the proposed system makes it easy to find these switching thresholds. Furthermore, some selected numerical and simulation results show that the proposed switched diversity system with the sequence of optimal switching thresholds outperforms the conventional system with the single optimal switching threshold.     

Exact Method for the Error Probability Calculation of Three-Dimensional Signal Constellations

The contribution of this letter is the computation of exact symbol error probability (SEP) of three-dimensional (3-D) signal constellations over an additive white Gaussian noise (AWGN) channel. The originality of the proposed method is that it can be applied to any arbitrary 3-D constellation whose decision regions may not meet at right angles. We express the SEP in a triple integral form which is further simplified. The simplified form requires a single integral evaluation of standard "erf" function. Using the derived exact SEP formula, we plot SEP for a number of selected 3-D constellations. The SEP obtained using the proposed formula is validated by simulation results. It is also compared with the union bound approximation, an upper bound for SEP.     

Finger Replacement Schemes for RAKE Receivers in the Soft Handover Region With Multiple Base Stations

We propose and analyze new finger replacement techniques for RAKE reception in the soft handover (SHO) region with multiple base stations. The proposed schemes are basically based on the block comparison among groups of resolvable paths from different base stations and lead to the reduction of complexity while offering commensurate performance in comparison with previously proposed schemes. Relying on the newly derived analytical expressions, we investigate not only the complexity in terms of the average number of required path estimations/comparisons and the SHO overhead but the error performance of the proposed scheme over independent identically distributed (i.i.d.) fading channels as well. We also examine, via computer simulations, the effect of path unbalance/correlation as well as outdated/imperfect channel estimation and show the robustness of our proposed scheme to these practical limitations.     

Outage probability of diversity systems over generalized fading channels

Outage probability is an important performance measure of communication systems operating over fading channels. Relying on a simple and accurate algorithm for the numerical inversion of the Laplace transforms of cumulative distribution functions, we develop a moment generating function-based numerical technique for the outage probability evaluation of maximal-ratio combining (MRC) and postdetection equal-gain combining (EGC) in generalized fading channels for which the fading in each diversity path need not be independent, identically distributed, nor even distributed according to the same family of distributions. The method is then extended to coherent EGC but only for the case of Nakagami-m fading channels. The mathematical formalism is illustrated by applying the method to some selected numerical examples of interest showing the impact of the power delay profile and the fading correlation on the outage probability of MRC and EGC systems.     

Variable-rate variable-power non-coherent M-FSK scheme for power limited systems

In response to the ongoing demand for low power applications, the two first authors have recently proposed in F.F. Digham and M.-S. Alouini (2004) a discrete-modulation and fixed-power non-coherent M-ary frequency shift keying scheme. In this paper, we propose an extension of that work by studying a discrete-modulation and continuous-power (DMCP) scheme for further power saving over Nakagami fading channels. The modulation level and power assignment are selected in order to minimize the average transmitted power while meeting average spectral efficiency and bit error rate constraints. We further investigate the problem with an additional peak power constraint. In this case, the modulation switching thresholds are shifted to higher values yielding reduction in both the achievable average spectral efficiency and the average transmitted power. However, the power loading function can be re-shaped to maintain the same average power of transmission for the cases on no-peak and with-peak power constraints. This reshaping is designed so as to involve constant power portions which can be of interest from a practical stand point.     

Capacity of MIMO Rician channels

This paper presents exact results on the capacity of multiple-input-multiple-output (MIMO) Rician channels when perfect channel state information (CSI) is assumed at the receiver but the transmitter has neither instantaneous nor statistical CSI. It first derives the exact expression for the average mutual information (MI) rate of MIMO Rician fading channels when the fading coefficients are independent but not necessarily identically distributed. The results for the independent and identically distributed (i.i.d.) MIMO Rician and Rayleigh fading channels are also obtained as special cases. These results are derived using a different approach than the one used by Telatar for the i.i.d. Rayleigh case. The complementary cumulative distribution function (CCDF) of the MI is also obtained using a Gaussian approximation. The CDF of MI can serve as an upper bound to the outage probability of nonergodic MIMO Rician channels. Numerical results confirm that for a fixed channel gain, a strong tine-of-sight component decreases the channel capacity due to the lack of scattering.     

A simple single integral representation of the bivariate Rayleighdistribution

Using an alternate representation of the Marcum Q-function, an expression for the bivariate Rayleigh cumulative distribution function is found in the form of a single integral with finite limits and an integrand composed of elementary functions. This result has advantage over previous forms of the same CDF which involve the Marcum Q-function itself or are expressed as infinite series of products of integrals     

A unified approach to the performance analysis of digitalcommunication over generalized fading channels

Presented here is a unified approach to evaluating the error-rate performance of digital communication systems operating over a generalized fading channel. What enables the unification is the recognition of the desirable form for alternate representations of the Gaussian and Marcum Q-functions that are characteristic of error-probability expressions for coherent, differentially coherent, and noncoherent forms of detection. It is shown that in the largest majority of cases, these error-rate expressions can be put in the form of a single integral with finite limits and an integrand composed of elementary functions, thus readily enabling numerical evaluation     

Average bit-error probability performance for optimum diversity combining of noncoherent FSK over Rayleigh fading channels

We derive the performance of the optimum noncoherent frequency-shift keying diversity combining receiver and compare it with that which implements the more traditional noncoherent postdetection equal gain combining scheme to reveal the degree of suboptimality of the latter.