Gerard J. Foschini

On Limits of Wireless Communications in a Fading Environment when UsingMultiple Antennas

This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array (MEA) technology, that is processing the spatial dimension (not just the time dimension) to improve wireless capacities in certain applications. Specifically, we present some basic information theory results that promise great advantages of using MEAs in wireless LANs and building to building wireless communication links. We explore the important case when the channel characteristic is not available at the transmitter but the receiver knows (tracks) the characteristic which is subject to Rayleigh fading. Fixing the overall transmitted power, we express the capacity offered by MEA technology and we see how the capacity scales with increasing SNR for a large but practical number, n, of antenna elements at both transmitter and receiver.We investigate the case of independent Rayleigh faded paths between antenna elements and find that with high probability extraordinary capacity is available. Compared to the baseline n = 1 case, which by Shannons classical formula scales as one more bit/cycle for every 3 dB of signal-to-noise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take the cases n = 2, 4 and 16 at an average received SNR of 21 dB. For over 99% of the channels the capacity is about 7, 19 and 88 bits/cycle respectively, while if n = 1 there is only about 1.2 bit/cycle at the 99% level. For say a symbol rate equal to the channel bandwith, since it is the bits/symbol/dimension that is relevant for signal constellations, these higher capacities are not unreasonable. The 19 bits/cycle for n = 4 amounts to 4.75 bits/symbol/dimension while 88 bits/cycle for n = 16 amounts to 5.5 bits/symbol/dimension. Standard approaches such as selection and optimum combining are seen to be deficient when compared to what will ultimately be possible. New codecs need to be invented to realize a hefty portion of the great capacity promised.

V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel

Information theory research has shown that the rich-scattering wireless channel is capable of enormous theoretical capacities if the multipath is properly exploited. In this paper, we describe a wireless communication architecture known as vertical BLAST (Bell Laboratories Layered Space-Time) or V-BLAST, which has been implemented in real-time in the laboratory. Using our laboratory prototype, we have demonstrated spectral efficiencies of 20-40 bps/Hz in an indoor propagation environment at realistic SNRs and error rates. To the best of our knowledge, wireless spectral efficiencies of this magnitude are unprecedented and are furthermore unattainable using traditional techniques.

Fading correlation and its effect on the capacity of multielement antenna systems

We investigate the effects of fading correlations in multielement antenna (MEA) communication systems. Pioneering studies showed that if the fades connecting pairs of transmit and receive antenna elements are independently, identically distributed, MEAs offer a large increase in capacity compared to single-antenna systems. An MEA system can be described in terms of spatial eigenmodes, which are single-input single-output subchannels. The channel capacity of an MEA is the sum of capacities of these subchannels. We show that the fading correlation affects the MEA capacity by modifying the distributions of the gains of these subchannels. The fading correlation depends on the physical parameters of MEA and the scatterer characteristics. In this paper, to characterize the fading correlation, we employ an abstract model, which is appropriate for modeling narrow-band Rayleigh fading in fixed wireless systems.

A simple distributed autonomous power control algorithm and its convergence

For wireless cellular communication systems, one seeks a simple effective means of power control of signals associated with randomly dispersed users that are reusing a single channel in different cells. By effecting the lowest interference environment, in meeting a required minimum signal-to-interference ratio of rho per user, channel reuse is maximized. Distributed procedures for doing this are of special interest, since the centrally administered alternative requires added infrastructure, latency, and network vulnerability. Successful distributed powering entails guiding the evolution of the transmitted power level of each of the signals, using only focal measurements, so that eventually all users meet the rho requirement. The local per channel power measurements include that of the intended signal as well as the undesired interference from other users (plus receiver noise). For a certain simple distributed type of algorithm, whenever power settings exist for which all users meet the rho requirement, the authors demonstrate exponentially fast convergence to these settings. >

Simplified processing for high spectral efficiency wireless communication employing multi-element arrays

We investigate robust wireless communication in high-scattering propagation environments using multi-element antenna arrays (MEAs) at both transmit and receive sites. A simplified, but highly spectrally efficient space-time communication processing method is presented. The users bit stream is mapped to a vector of independently modulated equal bit-rate signal components that are simultaneously transmitted in the same band. A detection algorithm similar to multiuser detection is employed to detect the signal components in white Gaussian noise (WGN). For a large number of antennas, a more efficient architecture can offer no more than about 40% more capacity than the simple architecture presented. A testbed that is now being completed operates at 1.9 GHz with up to 16 quadrature amplitude modulation (QAM) transmitters and 16 receive antennas. Under ideal operation at 18 dB signal-to-noise ratio (SNR), using 12 transmit antennas and 16 receive antennas (even with uncoded communication), the theoretical spectral efficiency is 36 bit/s/Hz, whereas the Shannon capacity is 71.1 bit/s/Hz. The 36 bits per vector symbol, which corresponds to over 200 billion constellation points, assumes a 5% block error rate (BLER) for 100 vector symbol bursts.

Network coordination for spectrally efficient communications in cellular systems

In this article we consider network coordination as a means to provide spectrally efficient communications in cellular downlink systems. When network coordination is employed, all base antennas act together as a single network antenna array, and each mobile may receive useful signals from nearby base stations. Furthermore, the antenna outputs are chosen in ways to minimize the out-of-cell interference, and hence to increase the downlink system capacity. When the out-of-cell interference is mitigated, the links can operate in the high signal-to-noise ratio regime. This enables the cellular network to enjoy the great spectral efficiency improvement associated with using multiple antennas

Statistical theory of polarization dispersion in single mode fibers

An analytical characterization of polarization dispersion measurements is presented. The authors report the solution of Pooles stochastic dynamical equation for the evolution of the polarization dispersion vector with fiber length. The authors extend this to a more complete description by considering small, second-order dispersion effects through the frequency derivative of the dispersion vector. The complete analytical solution is seen to accord with what were originally empirically derived features of the joint probability distribution of the polarization dispersion vector and its frequency derivatives. Among the analytically determined properties are the Gaussian probability densities of the three components of the dispersion vector, and the hyperbolic secant (soliton shaped) probability densities of the components of the derivative of the dispersion vector. >

Link-optimal space-time processing with multiple transmit and receive antennas

Previous information theory results have demonstrated the enormous capacity potential of wireless communication systems with multiple transmit and receive antennas. To exploit this potential, a number of space-time architectures have been proposed which transmit parallel data streams, simultaneously and on the same frequency, in a multiple-input multiple-output fashion. With sufficient multipath propagation, these different streams can be separated at the receiver. Mostly, these space-time schemes have been studied only in the presence of spatially white noise. We present an architecture that is optimal, in the sense of maximum link spectral efficiency, in the presence of spatially colored interference. We evaluate this new architecture and compare it, under various propagation conditions, to other adaptive-antenna techniques with equal number of antennas.

Optimization of Two-Dimensional Signal Constellations in the Presence of Gaussian Noise

A considerable amount of literature exists on the problem of selecting an efficient set of N digital signals with in-phase and quadrature components for use in a suppressed carrier data transmission system. However, the signal constellation which minimizes the probability of error in Gaussian noise, under an average power constraint, has not been determined when the number of signals is greater than two. In this paper an asymptotic (large signal-to-noise ratio) expression, of the minimum distance type, is derived for the error rate. Using this expression, a gradient-search procedure, which is initiated from several randomly chosen N -point arrays, converges in each case to a locally optimum constellation. The algorithm incorporates a radial contraction technique to meet the average signal power constraint. The best solutions are described for several values of N and compared with well-known signal formats. As an example, the best locally optimum 16-point constellation shows an advantage of about 0.5 dB in signal-signal-to-noise ratio over quadrature amplitude modulation. The locally optimum constellations are the vertices of a trellis of (almost) equilateral triangles. As N \rightarrow \infty , it is rigorously proved in the Appendix that the optimum constellations tend toward an equilateral structure, and become uniformly distributed in a circle.

MIMO capacities and outage probabilities in spatially multiplexed optical transport systems

With wavelength-division multiplexing (WDM) rapidly nearing its scalability limits, space-division multiplexing (SDM) seems the only option to further scale the capacity of optical transport networks. In order for SDM systems to continue the WDM trend of reducing energy and cost per bit with system capacity, integration will be key to SDM. Since integration is likely to introduce non-negligible crosstalk between multiple parallel transmission paths, multiple-input multiple output (MIMO) signal processing techniques will have to be used. In this paper, we discuss MIMO capacities in optical SDM systems, including related outage considerations which are an important part in the design of such systems. In order to achieve the low-outage standards required for optical transport networks, SDM transponders should be capable of individually addressing, and preferably MIMO processing all modes supported by the optical SDM waveguide. We then discuss the effect of distributed optical noise in MIMO SDM systems and focus on the impact of mode-dependent loss (MDL) on system capacity and system outage. Through extensive numerical simulations, we extract scaling rules for mode-average and mode-dependent loss and show that MIMO SDM systems composed of up to 128 segments and supporting up to 128 modes can tolerate up to 1 dB of per-segment MDL at 90% of the systems full capacity at an outage probability of 10(-4).