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Recently, the advantages of the discrete cosine transform (DCT) based orthogonal frequency-division multiplexing (OFDM) have come to the light. We thus consider DCT-OFDM with non-circular transmission (our results cover circular transmission as well) and present two blind joint maximum-likelihood frequency offset and phase offset estimators. Both our theoretical analysis and numerical comparisons reveal new advantages of DCT-OFDM over the traditional discrete Fourier transform (DFT) based OFDM. These advantages, as well as those already uncovered in the early works on DCT-OFDM, support the belief that DCT-OFDM is a promising multi-carrier modulation scheme. Index Terms--Non-circular, carrier frequency offset, phase offset, DCT-OFDM, maximum likelihood.

The cumulative distribution function (cdf) of a sum of correlated or even independent lognormal random variables (RVs), which is of wide interest in wireless communications, remains unsolved despite long standing efforts. Several cdf approximations are thus widely used. This letter derives bounds for the cdf of a sum of 2 or 3 arbitrarily correlated lognormal RVs and of a sum of any number of equally-correlated lognormal RVs. The bounds are single-fold integrals of readily computable functions and extend previously known bounds for independent lognormal summands. An improved set of bounds are also derived which are expressed as 2-fold integrals. For correlated lognormal fading channels, new expressions are derived for the moments of the output SNR and amount of fading for maximal ratio combining (MRC), selection combining (SC) and equal gain combining (EGC) and outage probability expressions for SC. Index Terms--Amount of fading, cochannel interference, log-normal distribution, diversity combining.

Motivated by practical considerations in the design of low-complexity receiver structures for wideband cellular code division multiple access, millimeter wave, and ultrawideband communications, the study on the generalized selection combining (GSC) receiver that adaptively combines a subset of M 'strongest' paths out of L available paths has intensified over the past few years. This paper derives concise analytical expressions for the moment generating function (MGF) of the GSC(M, L) output signal-to-noise ratio when the fading statistics are independent and identically distributed. The novelty of this mathematical framework in computing the MGF relies on the fact that it allows all common multipath fading channel models (Rayleigh, Rician, Nakagami-m, and Nakagami-q) to be treated in a unified sense. It also leads to a much more computationally efficient formula than those available in the literature and is valid for any combinations of M and L values. Using these newly derived MGFs, a unified error probability analysis for many coherent and noncoherent digital-modulation/detection schemes in a myriad of fading environments was provided. Index Terms--Coherent receiver, digital communications, diversity methods, quadratic receiver, reduced complexity receiver structures.

The study on generalized selection combining (GSC(N,L)) diversity systems that adaptively combines a subset of N paths with the highest instantaneous signal-to-noise ratios (SNRs) out of L available diversity paths has both theoretical and practical importance in the design of low-complexity receiver structures for cellular wideband CDMA, indoor millimeter-wave and ultra-wideband communications. This paper presents a novel mathematical framework to tackle the problem at hand by deriving a single integral expression for the moment generating function (mgf) of the GSC(N, L) output SNR when the L resolvable multipaths are independent with nonidentical fading statistics. The mgf is then used to unify the performance evaluation of a broad range of digital modulation/detection schemes in practical wireless channels. Index Terms--Coherent receiver, diversity methods, non-coherent (quadratic) receiver, reduced-complexity receiver structures, ultra-wideband, wideband CDMA (WCDMA).

Signal fading is a ubiquitous problem in mobile and wireless communications. In digital systems, fading results in bit errors, and evaluating the average error rate under fairly general fading models and multichannel reception is often required. Predominantly to date, most researchers perform the averaging using the probability density function method or the moment generating function (MGF) method. This paper presents a third method, called the characteristic function (CHF) method, for calculating the average error rates and outage performance of a broad class of coherent, differentially coherent, and noncoherent communication systems, with or without diversity reception, in a myriad of fading environments. Unlike the MGF technique, the proposed CHF method (based on Parseval's theorem) enables us to unify the average error-rate analysis of different modulation formats and all commonly used predetection diversity techniques (i.e., maximal-ratio combining, equal-gain combining, selection diversity, and switched diversity) within a single common framework. The CHF method also lends itself to the averaging of the conditional error probability involving the complementary incomplete Gamma function and the confluent hypergeometric function over fading amplitudes, which heretofore resisted to a simple form. As an aside, we show some previous results as special cases of our unified framework. Index Terms--Characteristic function (CHF) method, digital communications, fading channels, frequency-domain analysis, wireless communications.

Using a circular contour integral representation for the generalized Marcum-Q function, [Q.sub.m] (a, b), we derive a new closed-form formula for the moment generating function (MGF) of the output signal power of a dual-diversity selection combiner (SC) in bivariate (correlated) Nakagami-m fading with positive integer fading severity index. This result involves only elementary functions and holds for any value of the ratio a/b in [Q.sub.m] (a, b). As an aside, we show that previous integral representations for [Q.sub.m] (a, b) can be obtained from a contour integral and also derive a new, single finite-range integral representation for [Q.sub.m] (a, b). A new infinite series expression for the MGF with arbitrary m is also derived. These MGFs can be readily used to unify the evaluation of average error performance of the dual-branch SC for coherent, differentially coherent, and noncoherent communications systems. Index Terms--Digital communications, diversity reception, fading channels, wireless communications.

Orthogonal frequency-division multiplexing (OFDM) is sensitive to the carrier frequency offset (CFO), which destroys orthogonality and causes intercarrier interference (ICI). Previously, two methods were available for the analysis of the resultant degradation in performance. Firstly, the statistical average of the ICI could be used as a performance measure. Secondly, the bit error rate (BER) caused by CFO could be approximated by assuming the ICI to be Gaussian. However, a more precise analysis of the performance (i.e., BER or SER) degradation is desirable. In this letter, we propose a precise numerical technique for calculating the effect of the CFO on the BER or symbol error in an OFDM system. The subcarriers can be modulated with binary phase shift keying (BPSK), quaternary phase shift keying (QPSK), or 16-ary quadrature amplitude modulation (16-QAM), used in many OFDM applications. The BPSK case is solved using a series due to Beaulieu. For the QPSK and 16-QAM cases, we use an infinite series expression for the error function in order to express the average probability of error in terms of the two-dimensional characteristic function of the ICI. Index Terms--Bit error rate, carrier frequency offset, inter-carrier interference, orthogonal frequency-division multiplexing, symbol error rate.

This letter provides a novel, efficient numerical solution to evaluate the moment generating function of a Suzuki probability density function using the sampling theorem. Applications include outage probability calculations for mobile radio networks in Rayleigh fading and shadowing. Index Terms - Approximation methods, cochannel interference, fading channels, land mobile radio, sampling methods.

This paper addresses the problem of selecting the optimum training sequence for channel estimation in communication systems over time-dispersive channels. By processing in the frequency domain, a new explicit form of search criterion is found, the gain loss factor (GLF), which minimizes the variance of the estimation error and is easy to compute. Theoretical upper and lower bounds on the GLF are derived. An efficient directed search strategy and optimal sequences up to length 42 are given. These sequences are optimal only for frequency domain estimation, not for time domain estimation.

This paper presents new upper bounds on the pairwise error probability (PEP) of trellis-coded modulation (TCM) schemes over nonindependent Rician fading channels. Cases considered are coherent and pilot-tone-aided detection and differential detection of trellis-coded multilevel phase-shift keying (TC-MPSK) systems. The average bit-error probability [P.sub.b] can be approximated by truncating the union bound. This method does not necessarily lead to an upper bound on [P.sub.b], and, hence, the approximation must be used with simulation results. In addition, for Rayleigh fading channels with an exponential autocovariance function, bounds resembling those for memoryless channels have been derived. The bounds are substantially more accurate than Chernoff bounds and hence allow for accurate estimation of system performance when the assumption of ideal interleaving is relaxed. Index Terms - Interleaving, Rician fading, trellis coding

An analytical technique well suited to numerical analysis is presented for computing the average bit-error rate (BER) and outage probability of M-ary phase-shift keying (PSK) in the land-mobile satellite channel (LMSC) with microdiversity reception. Closed-form expressions are found for L-branch microdiversity using both selection diversity combining (SDC) and maximal ratio combining (MRC). These expressions are extended to include both M-ary coherent PSK (M-PSK) and differential PSK [M-differential PSK (DPSK)]. Following previous empirical studies, the LMSC is modeled as a weighted sum of Rice and Suzuki distributions. Numerical results are provided illustrating the achievable performance of both M-PSK and M-DPSK with diversity reception. Using measured channel parameters, the performance in various mobile environments for various satellite elevation angles is also found. Index Terms - Diversity methods, fading channels, land-mobile radio, phase-shift keying.

An analytical technique is presented for computing the exact union bound on the average bit error probability of trellis coded modulation schemes over Rayleigh, Rician, or shadowed Rician-fading channels. To this end, an integral expression is derived for the pairwise error event probability (PEP). Existing bounds can be obtained as special cases of this expression. It turns out that a Gauss-Chebysev quadrature rule offers excellent accuracy for this integral. By extension, the exact union bound (i.e., the weighted sum of all exact PEP's of a code) can readily be evaluated. This method has the same complexity as the union-Chernoff bound, and a few examples are given to show its application.

The purpose of this comment is to provide a critical discussion of the new method of performance analysis of diversity systems proposed in the abovementioned paper. It is shown that this method provides incorrect results for equal-gain and selective combining.

Frequency-offset correction is considered for a HIPERLAN (High-PErformance Radio LAN) system over the indoor radio channel. Since the multipath channel response is not known a priori, a viable frequency-offset estimator should not depend on such knowledge. Such an estimator, using a single sample per symbol, is derived for HIPERLAN. The estimator is shown to approach the Cramer-Rao bound for frequency-offset estimation over a multipath channel. A HIPERLAN system simulation example shows that the performance with an offset of 150 kHz is within 0.5 dB of that of a system with zero frequency offset. Index Terms - Frequency-offset estimation, indoor radio communication, maximum-likelihood estimation, multipath channels.

A characteristic function method is used to calculate the probability that the signal-to-interference ratio (SIR) drops below some predefined threshold (probability of outage). The mobile unit receives a desired signal which has undergone Nakagami fading and multiple, cochannel, and independent Nakagami interferers. The development is based on a technique due to Bealieu. The advantages of the method are twofold. First, it places no integral restriction upon the Nakagami fading parameter. Second, it avoids the evaluation of higher order derivatives (residues). Index Terms - Cellular radio system, characteristic function, cochannel interference, Nakagami fading, outage.