Capacity of Differential Versus Nondifferential Unitary Space–Time Modulation for MIMO Channels

Differential unitary space-time modulation (DUSTM) and its earlier nondifferential counterpart, USTM, permit high-throughput multiple-input multiple-output (MIMO) communication entirely without the possession of channel state information by either the transmitter or the receiver. For an isotropically random unitary input we obtain the exact closed-form expression for the probability density of the DUSTM received signal, permitting the straightforward Monte Carlo evaluation of its mutual information. We compare the performance of DUSTM and USTM through both numerical computations of mutual information and through the analysis of low- and high-signal-to-noise ratio (SNR) asymptotic expressions. In our comparisons the symbol durations of the equivalent unitary space-time signals are equal to T. For DUSTM the number of transmit antennas is constrained by the scheme to be M=T/2, while USTM has no such constraint. If DUSTM and USTM utilize the same number of transmit antennas at high SNRs the normalized mutual information of the two schemes expressed in bits/s/Hz are asymptotically equal, with the differential scheme performing somewhat better. At low SNRs the normalized mutual information of DUSTM is asymptotically twice the normalized mutual information of USTM. If, instead, USTM utilizes the optimum number of transmit antennas then USTM can outperform DUSTM at sufficiently low SNRs     

Estimating a covariance matrix from incomplete realizations of arandom vector

It is desired to estimate the mean and the covariance matrix of a Gaussian random vector from a set of independent realizations, with the complication that not every component of each realization of the random vector is observed. Subject to some restrictions, the authors obtained an exact, noniterative solution for the maximum likelihood (ML) estimates of the mean and the covariance matrix. The ML estimate of the covariance matrix that is obtained from the set of incomplete realizations is guaranteed to be positive definite, in contrast to ad hoc approaches based on averaging products of components from the same realization. The key to obtaining the ML estimates is a tractable expression for the likelihood function in terms of the Cholesky factors of the inverse covariance matrix. With this formulation, the ML estimates are found by fitting regression operators to appropriate subsets of the data. The Cholesky formulation also leads to a simple calculation by Cramer-Rao bounds     

Structured unitary space-time autocoding constellations

We previously showed that arbitrarily reliable communication is possible within a single coherence interval in Rayleigh flat fading as the symbol duration of the coherence interval and the number of transmit antennas grow simultaneously. This effect, where the space-time signals act as their own channel codes, is called autocoding. For relatively short (e.g., 16-symbol) coherence intervals, a codebook of independent isotropically random unitary space-time signals theoretically supports transmission rates that are a significant fraction of autocapacity with an extremely low probability of error. The exploitation of space-time autocoding requires the creation and decoding of extraordinarily large constellations-typically L = 2⁸⁰. We make progress on the first part of the problem through a random, but highly structured, constellation that is completely specified by log₂ L independent isotropically distributed unitary matrices. The distinguishing property of this construction is that any two signals in the constellation are pairwise statistically independent and isotropically distributed. Thus, the pairwise probability of error, and hence the union bound on the block probability of error, of the structured constellation is identical to that of a fully random constellation of independent signals. We establish the limitations of an earlier construction through a subsidiary result that is interesting in its own right: the square (or for that matter, any integer power greater than one) of an isotropically random unitary matrix is not isotropically random, with the sole exception of the one-by-one unitary matrix     

A Thermesthesiometer?An Instrument for Burn Hazard Measurement

Surface temperature measurement alone is insufficient to establish the hazard to the human of contact with a hot or cold object. A metal surface is more likely to cause thermal injury than a plastic surface at the same temperature. An instrument equipped with a measuring probe has been developed for indicating the temperature that would be experienced if human contact were made with the hot surface in question. The correct value of interface contact temperature can be read for a selected contact time without knowing the composition or temperature of the heated material under test.     

Capacity of a mobile multiple-antenna wireless link with isotropically random Rician fading

We analyze the capacity of a multiple-antenna wireless link with M antennas at the transmitter and N antennas at the receiver in a Rician fading channel when the channel is unknown at both the transmitter and the receiver. The Rician model is a nonstandard model with a Rayleigh component and an isotropically random rank-one specular component. The Rayleigh and specular components remain constant for T symbol periods, after which they change to completely independent realizations, and so on. To maximize mutual information over the joint density of T/spl middot/M complex transmitted signals it is sufficient to maximize over a joint density of min{T,M} real transmitted signal magnitudes. The capacity-achieving signal matrix is equal to the product of two independent matrices, a T/spl times/T isotropically random unitary matrix and a T/spl times/M real nonnegative diagonal matrix. If M>T, optimum signaling uses only T out of the M transmit antennas. We derive a novel lower bound on capacity which enables us to compute achievable rate regions for many cases. This lower bound is also valid for the case of purely Rayleigh-fading channels, where it has not been feasible, in general, to compute capacity, or mutual information. Our numerical results also indicate that the Rayleigh model is surprisingly robust: under our Rician model, up to half of the received energy can arrive via the specular component without significant reduction in capacity compared with the purely Rayleigh case.     

A surprising Radon transform result and its application to motiondetection

An elliptical region of the plane supports a positive-valued function whose Radon transform depends only on the slope of the integrating line. Any two parallel lines that intersect the ellipse generate equal line integrals of the function. We prove that this peculiar property is unique to the ellipse; no other convex, compact region of the plane supports a nonzero-valued function whose Radon transform depends only on slope. We motivate this problem by considering the detection of a constant-velocity moving object in a sequence of images. In the presence of additive, white, Gaussian noise. The intensity distribution of the object is known, but the velocity is only assumed to lie in some known set, for example, an ellipse or a rectangle. The object is to find a space-time linear filter, operating on the image sequence, whose minimum output signal-to-noise ratio (SNR) for any velocity in the set is maximized. For an ellipse (and its special cases, the disk and the line-segment) the special Radon transform property of the ellipse enables us to obtain a closed-form, analytical solution for the minimax filter, which significantly outperforms the conventional three-dimensional (3-D) matched filter. This analytical solution also suggests a constrained minimax filter for other velocity sets, obtainable in closed form, whose SNR can be very close to the minimax SNR.     

Cutoff rate and signal design for the quasi-static Rayleigh-fadingspace-time channel

We consider the computational cutoff rate and its implications on signal design for the complex quasi-static Rayleigh flat-fading spatio-temporal channel under a peak-power constraint where neither transmitter nor receiver know the channel matrix. The cutoff rate has an integral representation which is an increasing function of the distance between pairs of complex signal matrices. When the analysis is restricted to finite-dimensional sets of signals, interesting characterizations of the optimal rate-achieving signal constellation can be obtained. For an arbitrary finite dimension, the rate-optimal constellation must admit an equalizer distribution, i.e., a positive set of signal probabilities which equalizes the average distance between signal matrices in the constellation. When the number N of receive antennas is large, the distance-optimal constellation is nearly rate-optimal. When the number of matrices in the constellation is less than the ratio of the number of time samples to the number of transmit antennas, the rate-optimal cutoff rate attaining constellation is a set of equiprobable mutually orthogonal unitary matrices. When the signal-to-noise ratio (SNR) is below a specified threshold, the matrices in the constellation are rank one and the cutoff rate is achieved by applying all transmit power to a single antenna and using orthogonal signaling. Finally, we derive recursive necessary conditions and sufficient conditions for a constellation to lie in the feasible set     

Multiuser capacity in block fading with no channel stateinformation

Consider M independent users, each user having his own transmit antenna, that transmit simultaneously to a receiver equipped with N antennas through a Rayleigh block-fading channel having a coherence interval of T symbols, with no channel state information (CSI) available to either the transmitters or to the receiver. The total transmitted power is independent of the number of users. For a given coherence time T, we wish to identify the best multiaccess strategy that maximizes the total throughput. If perfect CSI were available to the receiver, it is known that the total capacity would increase monotonically with the number of users. If the CSI is available to both the receiver and to all transmitters, the throughput maximizing strategy implies for N=1 that only the single user who enjoys the best channel condition transmits. In the absence of CSI one is forced to a radically different conclusion. In particular, we show that if the propagation coefficients take on new independent values for every symbol (e.g., T=1) then the total capacity for any M > 1 users is equal to the capacity for M=1 user, in which case time division multiple access (TDMA) is an optimal scheme for handling multiple users. This result follows directly from a recent treatment of the single-user multiple antenna block-fading channel. Again, motivated by the single-user results, one is lead to the following conjecture for the multiple-user case: for any T > 1, the maximum total capacity can be achieved by no more than M = T users. The conjecture is supported by establishing the asymptotic result that, for a fixed N and a constant M/T for large T, the total capacity is maximized when M/T→0, which yields a total capacity per symbol of N log(1 + ρ), where ρ is the expected signal-to-noise ratio (SNR) at the receiver. We further support the conjecture by examining the asymptotic behavior with large to for fixed M, T, and N ⩽ T