Peter J. McLane

Estimating the distribution of a sum of independent lognormal random variables

Four methods that can be used to approximate the distribution function (DF) of a sum of independent lognormal random variables (RVs) are compared. The aim is to determine the best method to compute the DF considering both accuracy and computational effort. The investigation focuses on values of the dB spread, σ, valid for practical problems in wireless transmission, where σ is between 6 dB and 12 dB. Contrary to some previous reports, our results show that the simpler Wilkinsons approach gives a more accurate estimate, in some cases of interest, than Schwartz and Yehs 1982 approach.

Symbol-aided plus decision-directed reception for PSK/TCM modulation on shadowed mobile satellite fading channels

The symbol-aided (SA) synchronization concept developed by Moher and Lodge (1989) is applied to the MSAT channel modeled with a shadowed Rician process. Simulation data demonstrate that it can track the severe phase jitter encountered on the fading channel free of the false lock which plagues conventional techniques. The algorithm multiplexes known symbols into the data stream, establishing an absolute reference free of decision errors that is used to estimate the fading phase. An improvement to the SA algorithm which extracts phase information from the data-bearing symbols is proposed. It is found that the new technique is more effective for larger K. The improved algorithm is referred to as symbol-aided plus decision-directed (SADD) phase estimation. A system employing SADD phase estimation, trellis-coded modulation, interleaving, and amplitude weighting within the Viterbi decoder yielded the best BER performance on the shadowed MSAT channel considered. >

PSK and DPSK trellis codes for fast fading, shadowed mobile satellite communication channels

The performance of 8-PSK and 8-DPSK trellis codes is presented for a class of fast fading, land mobile satellite communication channels. The fading model is Rician but, in addition, the line-of-sight path is subjected to a fast lognormal attenuation that represents tree shadowing. The fading parameters used in this study represent the degree of shadowing and are based on measured data. The primary application considered is for digital speech transmission and thus, bit error probabilities in the order of 10/sup -3/ are emphasized. Sensitivity of the bit error probability to amplitude fading, amplitude and phase fading, and decoding delay is presented. Performance is determined via digital computer simulation. Optimal four- and eight-state codes are determined and optimality is found to be dependent on the presence of lognormal shadowing. >

Error bounds for trellis-coded MPSK on a fading mobile satellite channel

Analytical performance bounds are presented for trellis-coded MPSK, transmitted over a satellite-based land mobile channel. Upper bounds are evaluated using the well-known transfer function bounding technique, and lower bounds are achieved through knowledge of exact pairwise error probabilities. In order to analyze practical trellis-codes (four or more states), the uniform properties displayed by a certain class of trellis-codes are exploited, enabling the encoder transfer function to be obtained from a modified state transition diagram, having no more states than the encoder itself. Monte Carlo simulation results are presented in confirmation of all performance bounds and indicate a general weakness in the transfer function upper bounds. A new asymptotically tight upper bound is derived based on a simple modification to the standard transfer function bound, and results are presented for the four- and eight-state trellis-codes in Rician and Rayleigh fading. >

Interception of frequency-hopped spread-spectrum signals

A frequency-hopped spread-spectrum signal is modeled as a sinusoid that has one of N random frequencies. Coherent and noncoherent interception receiver structures based on Neyman-Pearson detection theory are determined. Under the assumption that there is a single hop per detection period, the optimum receiver structure is shown to consist of a bank of matched filters called the average likelihood (AL) receiver. A suboptimum structure called the maximum likelihood (ML) receiver is also analyzed. It is shown that AL and ML receivers have essentially the same performance. Simple formulas that relate the probability of detection, P/sub D/, to the probability of false alarm, P/sub F/, and the signal-to-noise ratio (SNR) for large N are derived. Receiver structures are also derived and analyzed for the case where the signal hops a number of times in one detection interval. This may correspond to the detection of a multihop signal in one symbol interval or to detection based on integration over a number of symbol intervals. The relationships of P/sub D/ to P/sub F/, for both coherent and noncoherent multiple-hop receivers, are examined. >

Calculating error probabilities for DS-CDMA systems: when not to use the Gaussian approximation

Error probabilities for various unbalanced DS-CDMA systems are calculated using the standard Gaussian approximation, improved Gaussian approximation and the Fourier series based schemes. A scarcely populated system, a system with a dominant interferer, a system in a fading channel and a multimedia system with a single high processing gain user are considered. It is seen that the standard Gaussian approximation in all of these cases gives inaccurate results, especially when the number of users active in the system is low. The improved Gaussian approximation on the other hand, gives more accurate results for a scarcely populated system and a system with a dominant interferer. For systems in fading channels and multimedia systems, neither of the Gaussian approximations are accurate. For all of these cases, the Fourier series based scheme gives very accurate results without computational complexity.

Comparison of methods of computing lognormal sum distributions and outages for digital wireless applications

Four methods that can be used to approximate the distribution function (DF) of a sum of independent lognormal random variables (RVs) are investigated and compared. The aim is to determine the best method to compute the DF considering both accuracy and computational effort. The investigation focuses on values of the dB spread, /spl sigma/, valid for practical problems in wireless transmission (6 dB/spl les//spl sigma//spl les/12 dB). Similarly, we emphasize values of the DF which represent practical values of outage for current and future wireless systems. Contrary to some previous reports, our results show that the simpler Wilkinsons approach gives a more accurate estimate, in some cases of interest, than Schwartz and Yehs (1982) approach. Overall, it is found that the Schlehers (1977) cumulants matching approach is a good method for small to medium dB spreads (/spl sigma/=6 dB), and Farleys approach is a good method for large dB spreads (/spl sigma/=12 dB).<<ETX>>

Uniform distance and error probability properties of TCM schemes

The class of uniform trellis-coded modulation (TCM) techniques is defined, and simple explicit conditions for uniformity are derived. Uniformity is shown to depend on the metric properties of the two subconstellations resulting from the first step in set partitioning, as well as on the assignment of binary labels to channel symbols. The uniform distance property and uniform error property, which are both derived from uniformity but are not equivalent, are discussed. The derived concepts are extended to encompass transmission over a (not necessarily Gaussian) memoryless channel in which the metric used for detection may not be maximum likelihood. An appropriate distance measure is defined that generalizes the Euclidean distance. It is proved that uniformity of a TCM scheme can also be defined under this new distance. The results obtained are shown to hold for channels with phase offset or independent, amplitude-only fading. Examples are included to illustrate the applicability of the results. >

Bit-error-probability for noncoherent orthogonal signals in fading with optimum combining for correlated branch diversity

Due to the interest in wireless personal communications, there has been a lot of research on the performance of receivers with diversity. Most analyses assume the diversity branches are independent. This paper presents an analysis of the bit-error probability for receivers in which the diversity branches are correlated. Noncoherent orthogonal digital modulation (NCODM) with Rician and Rayleigh slow, nonselective fading models are assumed. Through the use of the diagonalization of quadratic forms, most of the calculations of the bit-error probability can be reduced to a two-dimensional numerical integration. For some cases for dual diversity, a closed-form expression for the error probability is given. A number of diversity combining laws, including square law and maximum likelihood, are considered. We find that Rician fading can be worse than Rayleigh fading in correlated diversity environments, a situation quite different from the independent diversity case. Also, for the Rayleigh fading model with correlated branch diversity, we find that an equal-weight, square-law combiner usually has the same error performance as the more complex maximum-likelihood combiner. However, this is not the case for a Rician fading model with the same correlation environment. Simple diagonalization methods that compensate for the lossy effect of correlation are specified and found to be effective when the dominant noise and interference have almost the same correlation distribution as the fading signals.

Bi-directional soft-output M-algorithm for iterative decoding

A method to produce soft-outputs is proposed for the M-algorithm. The soft-output M-algorithm (SOMA) reduces the complexity of trellis decoding by retaining only M states per trellis depth. Its complexity increases with M rather than with the number of states in the trellis. We also propose an improved SOMA that is based on bi-directional decoding. The performance of the SOMA and the bi-directional SOMA (bi-SOMA) are assessed in decoding a turbo code and in turbo equalization. Simulation results show negligible performance loss when a 16-state turbo code is decoded by the SOMA with M = 12. For turbo equalization, near-optimal performance can be achieved by retaining only a small number of equalizer states as long as the. number of states retained by the decoder is sufficiently large. For a BPSK turbo equalization system with 16 states in both trellises, a SOMA-equalizer with M = 4 and a bi-SOMA decoder with M = 8 suffices. For a QPSK system with 256 equalizer states and 16 decoder states, a SOMA-equalizer with M = 16 and a SOMA-decoder with M = 12 suffices.