Stuart C. Schwartz

Stability properties of slotted Aloha with multipacket reception capability

The stability of the Aloha random-access algorithm in an infinite-user slotted channel with multipacket-reception capability is considered. This channel is a generalization of the usual collision channel, in that it allows the correct reception of one or more packets involved in a collision. The number of successfully received packets in each slot is modeled as a random variable which depends exclusively on the number of simultaneously attempted transmissions. This general model includes as special cases channels with capture, noise, and code-division multiplexing. It is shown by drift analysis that the channel backlog Markov chain is ergodic if the packet-arrival rate is less than the expected number of packets successfully received in a collision of n as n goes to infinity. The properties of the backlog in the nonergodicity region are examined. >

Optimal decentralized control in the random access multipacket channel

A decentralized control algorithm is sought that maximizes the stability region of the infinite-user slotted multipacket channel and is easily implementable. To this end, the perfect state information case in which the stations can use the instantaneous value of the backlog to compute the retransmission probability is studied first. The vest throughput possible for a decentralized control protocol is obtained, as well as an algorithm that achieves it. These results are then applied to derive a control scheme when the backlog is unknown, which is the case of practical relevance. This scheme, based on a binary feedback, is shown to be optimal, given some restrictions on the channel multipacket reception capability. >

Outage Probability in Mobile Telephony Due to Multiple Log-Normal Interferers

The mobile radio channel is characterized by three important factors: path losses larger than free space, fading typically taken as Rayleigh, and shadowing generally characterized as lognormal. For cellular systems, in order to determine acceptable reuse distances between base stations and to compare modulation methods, the probability of unacceptable cochannel interference (outage probability) has to be determined in the realistic situation where both fading and shadowing occur. In this paper, the average outage probability is computed for centrally located base stations when multiple log-normal interferers are present. This is done for both the mobile-to-base and base-to-mobile communication links. An unexpected result of this study is that the outage probabilities for the two cases do not differ in a significant way. Cumulative probability curves of the short-term average-signal-toaverage-interference ratio (SIR) are presented for a variety of system parameters: channel set number, propagation law exponent (γ), and dB spread (σ) of the log-normal distribution for the signal and interferers. An important observation is the large sensitivity of the performance curves to the propagation parameters: for a system with seven channel sets with a 10 dB SIR threshold, the average outage probability varies from 10 percent for \gamma = 3.7, \sigma = 6 dB, to 70 percent for \gamma = 3, \sigma = 14 dB. Alternatively, for a fixed outage objective of 10 percent, the required SIR threshold value ranges from -17 dB to 11 dB, depending on the propagation parameters. These variations make it imperative that accurate measurements of these parameters be obtained for the different service areas. Outage probabilities are also easily related to specific modulation methods and diversity approaches; detailed results are given for several representative cases.

Integrated spatial-temporal detectors for asynchronous Gaussian multiple-access channels

The optimum (maximum likelihood) multi-element global sequence detector is derived for the multiuser communication channel. The resulting integrated array-detector is composed of retrodirective beamformers in the users directions followed by a bank of matched filters and a processor implementing a dynamic programming (Viterbi) algorithm. Suboptimal realizations of the multi-element detector are considered, offering reduced complexity as compared to the optimum solution. The performance of the multi-element detector is analyzed in terms of error probability, detection asymptotic efficiency and near-far resistance. In particular, the effects of array beamforming on the performance is discussed and shown to generalize existing results for the scalar (single channel) case. Processing which uses the additional dimension of space can result in significant improvements in performance over the scalar case. Following a general performance analysis, a comparison of several suboptimal multi-element detectors is given. In particular, it is shown that a new combined spatial-temporal processing is always uniformly superior to that of using beamformers which result in separation of signals, followed by single-user detectors. >

Robust detection of a known signal in nearly Gaussian noise

A detector that is not nonparametric, but that nevertheless performs well over a broad class of noise distributions is termed a robust detector. One possible way to obtain a certain degree of robustness or stability is to look for a min-max solution. For the problem of detecting a signal of known form in additive, nearly Gaussian noise, the solution to the min-max problem is obtained when the signal amplitude is known and the nearly Gaussian noise is specified by a mixture model. The solution takes the form of a correlator-limiter detector. For a constant signal, the correlator-limiter detector reduces to a limiter detector, which is shown to be robust in terms of power and false alarm. By adding a symmetry constraint to the nearly normal noise and formulating the problem as one of local detection, the limiter-correlator is obtained as the local min-max solution. The limiter-correlator is shown to be robust in terms of asymptotic relative efficiency (ARE). For a pulse train of unknown phase, a limiter-envelope sum detector is also shown to be robust in terms of ARE.

A Game-Theoretic Approach to Energy-Efficient Modulation in CDMA Networks with Delay QoS Constraints

A game-theoretic framework is used to study the effect of constellation size on the energy efficiency of wireless networks for M-QAM modulation. A non-cooperative game is proposed in which each user seeks to choose its transmit power (and possibly transmit symbol rate) as well as the constellation size in order to maximize its own utility while satisfying its delay quality-of-service (QoS) constraint. The utility function used here measures the number of reliable bits transmitted per joule of energy consumed, and is particularly suitable for energy-constrained networks. The best-response strategies and Nash equilibrium solution for the proposed game are derived. It is shown that in order to maximize its utility (in bits per joule), a user must choose the lowest constellation size that can accommodate the users delay constraint. This strategy is different from one that would maximize spectral efficiency. Using this framework, the tradeoffs among energy efficiency, delay, throughput and constellation size are also studied and quantified. In addition, the effect of trellis-coded modulation on energy efficiency is discussed.

Joint frequency offset and channel estimation for OFDM

We investigate the problem of joint frequency offset and channel estimation for OFDM systems. The complexity of the joint maximum likelihood (ML) estimation procedure motivates us to propose an adaptive MLE algorithm which iterates between estimating the frequency offset and the channel parameters. Pilot tones are used to obtain the initial estimates and then a decision-directed technique provides an effective estimation technique. The joint modified (averaged) Cramer-Rao lower bounds (MCRB) of the channel coefficients and frequency offset estimates are derived and discussed. It is shown that, for the case of a large number of subcarriers in the OFDM system, there is approximately a 6 dB loss in the frequency offset estimate lower bound due to the lack of knowledge of the channel impulse response (CIR). The degradation of the CIR lower bound is less severe and depends on the channel delay spread. We show both analytically and by simulation, that the channel estimate accuracy is less sensitive to unknown frequency offset than the frequency offset estimation is affected by the unknown CIR. Comprehensive simulations have been carried out to validate the effectiveness of the adaptive joint estimation algorithm.

Comparison of adaptive and robust receivers for signal detection in ambient underwater noise

Three receivers are compared for the detection of a known signal in additive ambient underwater noise of seagoing merchant vessels. These receivers are: the matched filter, which is the classical linear receiver based on a Gaussian assumption; the correlation-limiter, which is the Neyman-Pearson minimax robust receiver when the noise uncertainty is modeled as a mixture process with a Gaussian nominal; and the Gaussian-Gaussian mixture likelihood ratio receiver. This last receiver is adaptive in the sense that it is based on a parametric model whose parameters are computed from the actual data. The principal results of this study are that, in terms of the receiving operating curves, the adaptive receiver performs better than the linear one which, in turn, performs slightly better than the robust correlator-limiter. This study illustrates, for one particular noise sample, the merit of the simple mixture model in adaptive processing for signal detection purposes. >

EM-based channel estimation algorithms for OFDM

Estimating a channel that is subject to frequency-selective Rayleigh fading is a challenging problem in an orthogonal frequency division multiplexing (OFDM) system. We propose three EM-based algorithms to efficiently estimate the channel impulse response (CIR) or channel frequency response of such a system operating on a channel with multipath fading and additive white Gaussian noise (AWGN). These algorithms are capable of improving the channel estimate by making use of a modest number of pilot tones or using the channel estimate of the previous frame to obtain the initial estimate for the iterative procedure. Simulation results show that the bit error rate (BER) as well as the mean square error (MSE) of the channel can be significantly reduced by these algorithms. We present simulation results to compare these algorithms on the basis of their performance and rate of convergence. We also derive Cramer-Rao-like lower bounds for the unbiased channel estimate, which can be achieved via these EM-based algorithms. It is shown that the convergence rate of two of the algorithms is independent of the length of the multipath spread. One of them also converges most rapidly and has the smallest overall computational burden.

A comparative analysis of linear multiuser detectors for fading multipath channels

In this paper, we compare two linear multiuser receivers for synchronous CDMA frequency-selective Rayleigh fading channels. The first receiver consists of a bank of matched filters followed by a linear transformation and an optimal combiner for each user. The second consists of a bank of RAKE receivers followed by a linear transformation. We consider receivers for both coherent and differentially coherent PSK demodulation. While the conventional single-user receivers performance is severely limited by near-far effects in the multiuser environment, both of these multiuser receivers mitigate the near-far problem and provide significant performance gains for moderate to high SNRs. It is shown that the second receiver has a uniformly lower error rate than the first and that its performance gains relative to the first increase as the number of users and received multipaths increases.