Search

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.

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.

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.

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.

Two unified expressions for computing the refined outage criterion (which considers the receiver noise) in cellular mobile radio systems are derived using the Laplace and Fourier inversion formulas. Since these expressions do not impose any restrictions on the signal statistics while being easy to program, they provide a powerful tool for outage analysis over generalized fading channels. We also assess compatibility and applicability of previously published approaches that treat noise as cochannel interference (noise-limited model) or consider a minimum detectable receiver signal threshold and receiver noise. The outage probability in an interference-limited case can be evaluated directly by setting the minimum power threshold to zero. The analysis of correlated interferers is presented. Results are also developed for a random number of interferers. Several new closed-form expressions for the outage probability are also derived. Some previous studies have suggested approximating Rician desired signal statistics by a Nakagami-m model (with positive integer fading severity index) to circumvent the difficulty in evaluating the outage in Rician fading. The suitability of this approximation is examined by comparing the outage performance under these two fading conditions. Surprisingly, some basic results for Nakagami-m channel have been overlooked, which has led to misleadingly optimistic results with the Nakagami-m approximation model. However, similar approximation for the interferer signals is valid. Index Terms--Cochannel interference, fading channels, land mobile cellular radio systems.

This paper derives new closed-form formulas for error probabilities of single and multichannel communications in Rayleigh and Nakagami-m fading. Closed-form solutions to three generic trigonometric integrals are presented as part of the main result, providing a unified method for the derivation of exact closed-form average symbol-error probability expressions for binary and M-ary signals with L independent channel diversity reception. Both selection-diversity and maximal-ratio combining (MRC) techniques are considered. The results are generally applicable liar arbitrary two-dimensional signal constellations that have polygonal decision regions operating in a slow Nakagami-m fading environments with positive integer fading severity index. MRC with generically correlated fading is also considered. The new expressions are applicable in many cases of practical interest. The closed-form expressions derived for a single channel reception case can be extended to provide an approximation for the error tales of binary and M-ary signals that employ an equal-gain combining diversity receiver. Index Terms--Digital communications, diversity methods, Nakagami fading, wireless communications.

Two unified expressions for computing the refined outage criterion (which considers the receiver noise) in cellular mobile radio systems are derived using the Laplace and Fourier inversion formulas. Since these expressions do not impose any restrictions on the signal statistics while being easy to program, they provide a powerful tool for outage analysis over generalized fading channels. We also assess compatibility and applicability of previously published approaches that treat noise as cochannel interference (noise-limited model) or consider a minimum detectable receiver signal threshold and receiver noise. The outage probability in an interference-limited case can be evaluated directly by setting the minimum power threshold to zero. The analysis of correlated interferers is presented. Results are also developed for a random number of interferers. Several new closed-form expressions for the outage probability are also derived. Some previous studies have suggested approximating Rician desired signal statistics by a Nakagami-m model (with positive integer fading severity index) to circumvent the difficulty in evaluating the outage in Rician fading. The suitability of this approximation is examined by comparing the outage performance under these two fading conditions. Surprisingly, some basic results for Nakagami-m channel have been overlooked, which has led to misleadingly optimistic results with the Nakagami-m approximation model. However, similar approximation for the interferer signals is valid.

A frequent problem in digital communications is the computation of the probability density function (pdf) and cumulative distribution function (cdf), given the characteristic function (chf) of a random variable (RV). This problem arises in signal detection, equalizer performance, equal-gain diversity combining, intersymbol interference, and elsewhere. Often, it is impossible to analytically invert the chf to get the pdf and cdf in closed form. Beaulieu has derived an infinite series for the cdf of a sum of RVs that has been widely used. In this letter, we rederive his series using the Gil-Pelaez inversion formula and the Poisson sum formula. This derivation has several advantages including both the bridging of the well-known sampling theorem with Beaulieu's series and yielding a simple expression for calculating the truncation error term. It is also shown that the pdf and cdf can be computed directly using a discrete Fourier transform. Index Terms--Characteristic functions, diversity, Fourier analysis, intersymbol interference and cochannel interference, outage.

Performance analysis of equal-gain combining (EGC) diversity systems is notoriously difficult only more so given that the closed-form probability density function (pdf) of the EGC output is only available for dual-diversity combining in Rayleigh fading. In this paper, a powerful frequency-domain approach is therefore developed in which the average error-rate integral is transformed into the frequency domain, using Parseval's theorem. Such a transformation eliminates the need for computing (or approximating) the EGC output pdf (which is unknown), but instead requires the knowledge of the corresponding characteristic function (which is readily available). The frequency-domain method also circumvents the need to perform multiple-fold convolution integral operations, usually encountered in the calculation of the pdf of the sum of the received signal amplitudes. We then derive integral expressions for the average symbol-error rate of an arbitrary two-dimensional signaling scheme, with EGC reception in Rayleigh, Rician, Nakagami-m, and Nakagami-q fading channels. For practically important cases of second - and third-order diversity systems in Nakagami fading, both coherent and noncoherent detection methods for binary signaling are analyzed using the Appell hypergeometric function. A number of closed-form solutions are derived in which the results put forward by Zhang are shown to be special cases. Index Terms--Diversity systems, equal-gain combining, frequency-domain analysis, generalized fading channels, mobile radio systems.

A new, infinite series representation for the error function is developed. It is especially suitable for computing erfc (x) for large x. For instance, for any x [is greater than or equal to] 4, the error function can be evaluated with a relative error less than [10.sup.-10] by using only eight terms. Similarly, the error function can be evaluated with a relative error less than 8 x [10.sup.-7] for any x [is greater than or equal to] 2 using just six terms. An analytical bound is derived to show that the total error due to series truncation and undersampling rapidly decreases as x increases. Comparisons with two other series are provided. Index Terms--Error function, Fourier analysis, numerical methods, sampling theorem.

Exact integral expressions are derived for calculating the symbol-error rate (SER) of multilevel quadrature amplitude modulation (MQAM) in conjunction with L-fold antenna diversity on arbitrary Nakagami fading channel. Both maximal-ratio combining (MRC) (in independent and correlated fading) and equal-gain combining (EGC) predetection (in independent fading) diversity techniques have been considered. Exact closed-form SER expressions for two restricted Nakagami fading cases (MRC reception) are also derived. An exact analysis of EGC for MQAM has not been reported previously, despite its practical interest. Remarkably, the exact SER integrals can also be replaced by a finite-series approximation formula. A useful procedure for computing the confluent hypergeometric series is also presented. Index Terms - Diversity methods, Gauss-Chebychev quadrature, Nakagami fading channels, quadrature amplitude modulation.

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. [ABSTRACT FROM AUTHOR]