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 Shannon‘s 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.

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

The general technique of parallel transmission on many carriers, called multicarrier modulation (MCM), is explained. The performance that can be achieved on an undistorted channel and algorithms for achieving that performance are discussed. Ways of dealing with channel impairments and of improving the performance through coding are described, and implementation methods are considered. Duplex operation of MCM and the possible use of this on the general switched telephone network are examined. >

Multicarrier modulation for data transmission: an idea whose time has come

The use of infrared radiation as a medium for high-speed short-range wireless digital communication is discussed. Available infrared links and local-area networks are described. Advantages and drawbacks of the infrared medium are compared to those of radio and microwave media. The physical characteristics of infrared channels using intensity modulation with direct detection (IM/DD) are presented including path losses and multipath responses. Natural and artificial ambient infrared noise sources are characterized. Strategies for designs of transmitter and receivers that maximize link signal-to-noise ratio (SNR) are described. Several modification formats are discussed in detail, including on-off keying (OOK) pulse-position modulation (PPM), and subcarrier modulation. The performance of these techniques in the presence of multipath distortion is quantified. Techniques for multiplexing the transmissions of different users are reviewed. The performance of an experimental 50-Mb/s on-off-keyed diffuse infrared link is described.

Wireless Infrared Communications

Conventional equalization and carrier recovery algorithms for minimizing mean-square error in digital communication systems generally require an initial training period during which a known data sequence is transmitted and properly synchronized at the receiver. This paper solves the general problem of adaptive channel equalization without resorting to a known training sequence or to conditions of limited distortion. The criterion for equalizer adaptation is the minimization of a new class of nonconvex cost functions which are shown to characterize intersymbol interference independently of carrier phase and of the data symbol constellation used in the transmission system. Equalizer convergence does not require carrier recovery, so that carrier phase tracking can be carried out at the equalizer output in a decision-directed mode. The convergence properties of the self-recovering algorithms are analyzed mathematically and confirmed by computer simulation.

Self-Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication Systems

This paper discusses the analysis and simulation of a technique for combating the effects of multipath propagation and cochannel interference on a narrow-band digital mobile channel. This system uses the discrete Fourier transform to orthogonally frequency multiplex many narrow subchannels, each signaling at a very low rate, into one high-rate channel. When this technique is used with pilot-based correction, the effects of flat Rayleigh fading can be reduced significantly. An improvement in signal-to-interference ratio of 6 dB can be obtained over the bursty Rayleigh channel. In addition, with each subchannel signaling at a low rate, this technique can provide added protection against delay spread. To enhance the behavior of the technique in a heavily frequency-selective environment, interpolated pilots are used. A frequency offset reference scheme is employed for the pilots to improve protection against cochannel interference.

Analysis and Simulation of a Digital Mobile Channel Using Orthogonal Frequency Division Multiplexing

Up to this point in the text, we have made two key assumptions in discussing the structures described in Chapter 7: we have assumed arbitrary receiver complexity and we have also assumed that the channel characteristics are known at the receiver. For the maximum likelihood sequence estimation receiver, implemented via the Viterbi algorithm, the number of states was allowed to grow without bound and the observables used to compute the transition metrics are outputs of a (presumed known) filter matched to the channel. In the optimum linear receiver, the matched filter appears again along with a tapped delay line equalizer of arbitrary length. In the optimum linear receiver which does not use a matched filter, the tap weights are dependent on the channel covariance matrix. In practice, the channel characteristics are generally not known. If a dialed telephone line is used, the channel is different on each call. Even for private or leased channels, the characteristics may be known only within certain limits. For many channels, such as fading radio systems, phase perturbations and other time-varying channel variations are present, requiring constant tracking to avoid deterioration of performance. The optimum receivers we have described in the preceding chapters would be of academic interest only if it were not possible to adapt the parameters appearing in their structures to accurately model the actual channel or a function of the channel, such as its inverse.

Automatic and Adaptive Equalization

Gemeinsame adaptive echounterdrueckungs- und entzerrervorrichtung fuer eine zweidraht-vollduplex-datenuebertragungsanordnung

Modulation is the process by which a baseband information signal is converted into a passband signal that can transit a passband channel constrained in bandwidth and possibly other ways. In order to conserve bandwidth, it is convenient to impress the information signal onto a sinusoidal carrier signal. Spread spectrum systems, on the other hand, effectively modulate information signals onto wideband carriers. We shall restrict attention here to digital modulation formats that are spectrally efficient, that is, the breadth of spectrum taken up by the modulated waveform is the same or not much more than that taken up by the baseband signal.

Passband Data Transmission

It is proved that the random-variable coefficients of the orthonormal vector components of a Gaussian noise process converge to uncorrelated and identically distributed random variables as the power density spectrum of the process approaches a constant almost everywhere. An example is then given to suggest the rate of convergence and the ratio of noise bandwidth to signal bandwidth required for good approximation of the noise process by the white noise process.

The White Noise Approximation

The degree of complexity of a digital signal processor is closely related to the precision with which samples of an incoming analog waveform are represented. There is considerable interest in determining how coarse this representation can be without seriously degrading performance from that of an ideal processor of unquantized samples. This question is examined for a receiver of noisy, linearly distorted pulse amplitude modulation (PAM) signals. An optimum [maximum likelihood (ML)] detector, analogous to the Viterbi detector for unquantized samples, is derived for the case of a quantized sample sequence. Performance is evaluated under the assumption of high signal-to-noise ratio (SNR), and the resultant error probability is a good approximation for coarse quantization, and an upper bound for any degree of quantization. For a specified error probability, the degree of quantization suggested by this approach is conservative. Since receiver complexity is closely associated with the length of the digital representation of an input sample, an upper bound on receiver complexity is also suggested. Numerical evaluation of the error probability is quite tedious for an arbitrary channel; however, system performance may be readily evaluated for partial-response (PR) signaling. For the PR channels

Stephen B. Weinstein

Papers

Automatic and Adaptive Equalization

Gemeinsame adaptive echounterdrueckungs- und entzerrervorrichtung fuer eine zweidraht-vollduplex-datenuebertragungsanordnung

Passband Data Transmission

The White Noise Approximation

Optimum Detection of Quantized PAM Data Signals