Jack Salz

The impact of antenna diversity on the capacity of wireless communication systems

For a broad class of interference-dominated wireless systems including mobile, personal communications, and wireless PBX/LAN networks, the authors show that a significant increase in system capacity can be achieved by the use of spatial diversity (multiple antennas), and optimum combining. This is explained by the following observation: for independent flat-Rayleigh fading wireless systems with N mutually interfering users, they demonstrate that with K+N antennas, N-1 interferers can be nulled out and K+1 path diversity improvement can be achieved by each of the N users. Monte Carlo evaluations show that these results also hold with frequency-selective fading when optimum equalization is used at the receiver. Thus an N-fold increase in user capacity can be achieved, allowing for modular growth and improved performance by increasing the number of antennas. The interferers can also be users in other cells, users in other radio systems, or even other types of radiating devices, and thus interference cancellation also allows radio systems to operate in high interference environments. As an example of the potential system gain, the authors show that with 2 or 3 antennas the capacity of the mobile radio system IS-54 can be doubled, and with 5 antennas a 7-fold capacity increase (frequency reuse in every cell) can be achieved. >

Effect of fading correlation on adaptive arrays in digital mobile radio

In this paper, we investigate the effect of correlations among the fading signals at the antenna elements of an adaptive array in a digital wireless communication system. With an adaptive array, the signals received by multiple antennas are optimally weighted and combined to suppress interference and combat desired signal fading. Previous results for flat and frequency-selective fading assumed independent fading at each antenna. Here, we present a model of local scattering around a mobile where the received multipath signals arrive at the base station within a given beamwidth, and derive a closed-form expression for the correlation as a function of antenna spacing. Results show that the degradation in performance with correlation in an adaptive array that combats fading and suppresses interference is only slightly larger than that for combating fading alone, i.e., with maximal ratio combining. This degradation is small even with correlation as high as 0.5. >

Optimum diversity combining and equalization in digital data transmission with applications to cellular mobile radio. I. Theoretical considerations

A comprehensive theory for Nth-order space diversity reception combined with various equalization techniques in digital data transmission over frequency-selective fading channels is developed. The channels are characterized by N arbitrary impulse responses possessing random parameters as well as N additive Gaussian noise sources. Various combiner-equalizers that minimize the mean-squared error are determined. Formulas are presented for the attainable least-mean-squared errors and upper bounds on average probabilities of error. The theory is applied to optimize system parameters and to predict performance for QAM data transmission operating over a model for the mobile radio channel. For this model, estimates of average attainable error rates and outage probabilities are provided as functions of system parameters. In the channel models the uncoded data rates as well as Shannon capacity are regarded as random variables. >

Dual diversity combining and equalization in digital cellular mobile radio

The performance of digital data transmission over frequency-selective fading channels is investigated. For statistically independent diversity paths, estimates of average attainable error rates and outage probabilities as functions of system parameters are provided. The dependences among the important system parameters are exhibited graphically for several examples, including quaternary phase-shift keying (QPSK). In the optimized uncoded QPSK with 1.5 b/s/Hz, two orders of magnitude in outage probability can be gained by diversity reception. When one compares the uncoded average probability of error for the optimized mean squared error (MSE) systems one finds at most an order-of-magnitude difference among the different equalizers investigated except for the zero-forcing equalizer, whose performance is drastically inferior to the others. Again, dual diversity can provide two orders of magnitude improvement in the average error rate or in outage probability for the uncoded optimized systems. >

A Basic Dynamic Routing Problem and Diffusion

Diffusion theory has sometimes been successful in providing excellent approximate solutions to difficult queueing problems. Here we explore whether such methods can be used to analyze a basic dynamic routing strategy associated with a single idealized node in a data network. We analyze a dynamic routing policy where messages, or packets, that arrive at a certain node are routed to leave the node on the link having the shorter queue. In the model, message or packet arrivals are Poisson and the service time is exponentially distributed. We explore a heavy traffic diffusion method and we also discuss the limitations of an ad hoc approach to applying diffusion. For a node with K outgoing queues we find, under the assumption of heavy traffic, the optimum dynamic strategy, in the sense of minimizing the average delay. When this optimum dynamic strategy is compared to a static strategy where the outgoing traffic is split among the K queues, we find that the average delay for the dynamic system is better by a factor of K .

Optimum diversity combining and equalization in digital data transmission with applications to cellular mobile radio II. Numerical results

For Pt.I, see ibid., vol.40, no.5, p.885-94 (1992). The probability distributions of the data rates that can be supported by optimum receiver structures as well as the distribution of the Shannon capacity are studied. The dependences among the important system parameters are exhibited graphically for several illustrative examples including QPSK. At outage probabilities >

The capacity of wireless communication systems can be substantially increased by the use of antenna diversity

For a broad class of interference-dominated wireless systems including mobile, personal communications, and wireless PBX/LAN networks, the authors show that a significant increase in system capacity can be achieved by the use of spatial diversity (multiple antennas), and optimum combining. This is explained by the following observation: for independent flat-Rayleigh fading wireless systems with N mutually interfering users, it is demonstrated that with K+N antennas, N-1 interferers can be nulled out and K+1 path diversity improvement can be achieved by each of the N users. Monte Carlo evaluations show that these results also hold with frequency selective fading when optimum equalization is used at the receiver. Thus an N-fold increase in user capacity can be achieved, allowing for modular growth and improved performance by increasing the number of antennas.<<ETX>>

Upper bounds on the bit-error rate of optimum combining in wireless systems

This paper presents upper bounds on the bit-error rate (BER) of optimum combining in wireless systems with multiple cochannel interferers in a Rayleigh fading environment. We present closed-form expressions for the upper bound on the bit-error rate with optimum combining, for any number of antennas and interferers, with coherent detection of BPSK and QAM signals, and differential detection of DPSK. We also present bounds on the performance gain of optimum combining over maximal ratio combining. These bounds are asymptotically tight with decreasing BER, and results show that the asymptotic gain is within 2 dB of the gain as determined by computer simulation for a variety of cases at a 10/sup -3/ BER. The closed-form expressions for the bound permit rapid calculation of the improvement with optimum combining for any number of interferers and antennas, as compared with the CPU hours previously required by Monte Carlo simulation. Thus these bounds allow calculation of the performance of optimum combining under a variety of conditions where it was not possible previously, including analysis of the outage probability with shadow fading and the combined effect of adaptive arrays and dynamic channel assignment in mobile radio systems.

Optimal reception of digital data over the Gaussian channel with unknown delay and phase jitter

Asymptotically optimum (in the sense of minimum per-symbol error rate) receiver structures for data communication over the white Gaussian channel with unknown time delay and carrier phase jitter are developed. The receiver structures apply to the following suppressed-carrier modulation systems: double sideband (DSB), quadrature amplitude modulation (QAM) with an arbitrary constellation, vestigial sideband (VSB) and single sideband. The resulting minimum error probability receivers are asymptotically equivalent to maximum-likelihood digital {\em sequence}-estimating receivers. The optimum structures implicitly derive joint maximum-likelihood estimates of the unknown parameters and of the sequence of data symbols. It is shown that the parameter estimates can be obtained from two data-directed stochastic approximation algorithms. Unlike traditional theoretical treatments of this communication situation, which have separated the highly important carrier phase and timing recovery problem from the detection problem, a unified theory is presented from which the complete ideal receiver structure can be deduced.

Transmitter design for data transmission in the presence of a data-like interferer

In many digital communications systems, crosstalk, rather than additive noise, is the primary channel impairment. For such systems, it is known that the spectral support of the optimum transmitter is not, in general, restricted to a Nyquist set, in contrast to the case for the additive-noise channel. Nevertheless, the problem of determining the optimum transmitter shaping function for the crosstalk channel without the Nyquist restriction is a difficult one, and has so far remained unsolved. Motivated by current interest in the high-speed digital subscriber line (HDSL) and related crosstalk-dominated applications, we explore a subcase of this problem in which only a single interferer is present. When applied to HDSL-like systems with a single (or dominant) interferer, our analysis and numerical results confirm that wider-than-Nyquist transmitters provide a large performance advantage over Nyquist-limited transmitters. Several interesting and counter-intuitive results also arise. For example, PAM and QAM systems operating at the same spectral efficiency do not, in general, perform identically over the crosstalk channel, despite their essential equivalence in additive noise. We explain why this is so, and show that for channels qualitatively similar to the HDSL wire-pair, QAM has a significant advantage over PAM at high data rates. Finally, we show how the characteristics of HDSL-like channels can be exploited by optimizing the symbol rate. >