We consider the use of block spreading in a multicarrier system to gain diversity advantage when employed over multipath fading channels. The main idea is to split the full set of subcarriers into smaller blocks and spread the data symbols across these blocks via unitary spreading matrices in order to gain multipath diversity across each block at the receiver. We pose the problem of designing the spreading matrix as a finite dimensional optimization problem in which the asymptotic error is minimized. This formulation allows us to find explicit solutions for the optimal spreading matrices. The performance is validated for the uncoded channel as well as for the coded channel employing turbo-iterative decoding. We further demonstrate that suboptimal linear complexity equalization strategies for spread orthogonal frequency division multiplexing (OFDM) do not gain any diversity advantage over traditional diagonal OFDM.

The problem of bandwidth constrained space-time signal design for the noncoherent Rayleigh block-fading channel is addressed. Existing design techniques for this channel subdivide the coherence interval into smaller time blocks and use repetitions of a basic waveform to signal in each subblock. When the coherence time of the channel is short this access technique becomes questionable, due to the inverse relationship between bandwidth and time support. In particular, there may not be sufficient time support to allow matched filtered reception with finite (or nearly finite) Shannon bandwidth waveforms. To address this problem, we consider other notions of bandwidth, such as the root-mean square (RMS) bandwidth and fractional out of band energy (FOBE), which are appropriate for signals with finite time support. We extend our previous work on unconstrained signal designs for the block fading channel to incorporate such bandwidth constraints. The resulting signal constellations can be used 1) as a comparison point for any signal design procedure and 2) to conclude that there is a performance advantage to be had when signals are properly matched to the finite time support of the channel.

We study the use of block spreading in a multicarrier system to gain diversity advantage over multipath fading channels. The main idea is to split the full set of subcarriers into smaller blocks and spread the data symbols across these blocks via unitary spreading matrices in order to gain multipath diversity across each block at the receiver. We extend the recent work of Bury et. al. (2003), by posing the problem as a finite dimensional optimization problem in which the asymptotic error is minimized over unitary spreading matrices. This formulation allows us to find explicit solutions for the optimal spreading matrices.

We consider M-ary communication with K users over a space diversity channel, consisting of a single transmit antenna for each user and multiple receive antennas. We examine two different flat fading models, namely, phase coherent wavefront fading and noncoherent element-to-element fading. In the case of wavefront fading, the fade is constant across the face of the receive antenna and we can associate an angle of arrival to the signal. We present a variation of the MUSIC algorithm for estimating this parameter and use it to form a spatial beam. In the case of noncoherent element-to-element fading, the fading path to each sensor is different (although possibly correlated) and no angle of arrival can be exploited for conventional beamforming. For each channel model, we develop several detection strategies which assume various amounts of prior information about the fading. We then consider blind extensions of these detectors based on subspace tracking, which do not require a prior model for the interfering users' signals.

We consider the problem of designing signal constellations for the multiple transmit-multiple receive antenna Rayleigh-fading communication channel, when neither the transmitter nor the receiver know the fading. In particular, by employing the asymptotic union bound (AUB) on the probability of error, we give a new formulation of the problem of signal design for the noncoherent fading channel. Since unitary signals are optimal for this channel (in the limit of large signal-to-noise ratios SNRs), the problem can be posed in terms of packings on the Grassmanian manifold. A key difference in our approach from that of other authors is that we use a notion of distance on this manifold that is suggested by the union bound. As a consequence of our use of this distance measure, we obtain signal designs that are guaranteed to achieve the full diversity order of the channel, a result that does not hold when the chordal distance is used. We introduce a new method of recursively designing signals, termed successive updates, to approximately optimize this performance measure. We then examine the use of our signals with several convolutional codes over the fading channel. An upper bound on the bit error probability of the maximum-likelihood decoder is presented together with an asymptotic analysis of that bound.

We develop the minimum mean-squared-error (MMSE) multiuser detector for nonorthogonal multipulse modulation over the noncoherent additive white Gaussian noise channel. We analyze the asymptotic performance of the detector and show that, unlike the case of linear modulation, the MMSE detector does not generally approach the generalized maximum-likelihood (GML) detection rule as the noise power vanishes. It does, however, approach a detector which nulls out the multiaccess interference. This detector is termed the multipulse decorrelating detector due to its similarity to the linear decorrelating detector. The probability of error for this detector is derived and used to find the asymptotic multiuser efficiencies of both the multipulse decorrelating detector and the MMSE detector. It is shown that for noncoherent binary signaling, in which the multipulse modulation is two-dimensional, the multipulse decorrelating detector is superior to the GML detector asymptotically. This result does not generalize to larger dimensionality signal sets.

We consider the detection of nonorthogonal multipulse signals on multiple-access fading channels. The generalized maximum-likelihood rule is employed to decode users whose complex fading gains are unknown. We develop geometrical interpretations for the resulting detectors and their corresponding asymptotic efficiencies. The generalized maximum-likelihood detection rule is then applied to find a matched subspace detector for the frequency-selective fading channel, under the assumption of a short coherence time (or long coherence time without the computational power to track the fading parameters). We propose blind implementations of these detectors for nonorthogonal multipulse signaling on both frequency-nonselective and frequency-selective multiple-access fading channels. These blind detectors extend the results of Wang and Poor (see ibid., vol.44, p.677-89, 1998) to multipulse modulation and fast frequency selective fading. For comparison, the minimum mean-squared error decision rules for these channels are derived and blind implementations of their corresponding detectors are developed.

A technique is presented for subband adaptive filtering with nonuniform filter banks. The bandwidth allocations of the subband analysis and synthesis filters are adapted to the spectral characteristics of the input data in such a manner as to minimize an objective function built from the subband error powers. The nonuniform filter bank structure allows for fast convergence times for high order systems with a reduced mean square error relative to the uniform subband scheme. Results are presented for the case of a nonstationary system with time-varying spectral characteristics.