Shivratna Giri Srinivasan

A new method of analysis of standing foot pressure images for detection of the plantar ulcers in early-stage diabetic neuropathy.

In this paper, studies are performed on a large number of diabetic patients belonging to different levels of plantar sensation loss, by analyzing the standing foot pressure images in the frequency domain. A new parameter, the power ratio (PR, the ratio of high frequency power to the total power in an image), is used to distinguish between foot pressure image patterns of diabetic neuropathic subjects (at different levels of sensation loss) and those of normal feet. The foot areas of the diabetic subjects are scanned in 10 specified areas using Semmes Weinsteins nylon monofilaments to quantify the diabetic neuropathy. A statistical study of the mean values of this parameter in different plantar areas of the feet for different levels of diabetic neuropathy indicates distinguishing trends. The result could help in the early detection of low-level sensation loss by establishing the threshold of the PR in a particular area above which there could be the possibility of plantar ulcer formation. This information could be utilized by orthopedic surgeons to devise early corrective methods to protect the feet from further damage due to plantar ulcers.

Optimal Constellations for the Low-SNR Noncoherent MIMO Block Rayleigh-Fading Channel

Reliable communication over the discrete-input/continuous-output noncoherent multiple-input multiple-output (MIMO) Rayleigh block-fading channel is considered when the signal-to-noise ratio (SNR) per degree of freedom is low. Two key problems are posed and solved to obtain the optimum discrete input. In both problems, the average and peak power per space-time slot of the input constellation are constrained. In the first one, the peak power to average power ratio (PPAPR) of the input constellation is held fixed, while in the second problem, the peak power is fixed independently of the average power. In the first PPAPR-constrained problem, the mutual information, which grows as O(SNR2), is maximized up to second order in SNR. In the second peak-constrained problem, where the mutual information behaves as O(SNR), the structure of constellations that are optimal up to first order, or equivalently, that minimize energy per bit, are explicitly characterized. Furthermore, among constellations that are first-order optimal, those that maximize the mutual information up to second order, or equivalently, the wideband slope, are characterized. In both PPAPR-constrained and peak-constrained problems, the optimal constellations are obtained in closed form as solutions to nonconvex optimizations, and interestingly, they are found to be identical. Due to its special structure, the common solution is referred to as space-time orthogonal rank one modulation, or STORM. In both problems, it is seen that STORM provides a sharp characterization of the behavior of noncoherent MIMO capacity.

Optimal Spatial Correlations for the Noncoherent MIMO Rayleigh Fading Channel

The behavior in terms of information theoretic metrics of the discrete-input, continuous-output noncoherent MIMO Rayleigh fading channel is studied as a function of spatial correlations. In the low SNR regime, the mutual information metric is considered, while at higher SNR regimes the cutoff rate expression is employed. For any fixed input constellation and at sufficiently low SNR, a fully correlated channel matrix is shown to maximize the mutual information. In contrast, at high SNR, a fully uncorrelated channel matrix (with independent identically distributed elements) is shown to be optimal, under a condition on the constellation which ensures full diversity. In the special case of the separable correlation model, it is shown that as a function of the receive correlation eigenvalues, the cutoff rate expression is a Schur-convex function at low SNR and a Schur-concave function at high SNR, and as a function of transmit correlation eigenvalues, the cutoff rate expression is Schur-concave at high SNR for full diversity constellations. Moreover, at sufficiently low SNR, the fully correlated transmit correlation matrix is optimal. Finally, for the general model, it is shown that the optimal correlation matrices at a general SNR can be obtained using a difference of convex programming formulation.

Code design for the low SNR noncoherent MIMO block Rayleigh fading channel

Code design for the low SNR MIMO noncoherent correlated Rayleigh fading channel is considered. Design rules which exploit the correlations in the transmit antennas in the MIMO case, to provide gains over the corresponding SIMO case are presented. The Chernoff bound on the average pairwise error probability (APEP) is used to study the effect of the receive correlation matrix on system performance at different SNR regimes. Based on a lower bound on the APEP, which is related to the Bhattacharya coefficient, a technique is proposed to design codes for use with transmit beamforming, with codewords having unequal prior probabilities. The motivation for such codes with unequal priors arises from recent information theoretic results on the low SNR channel. Such constellations are shown to perform substantially better than constellations designed assuming equal priors, at low SNRs

Mutual Information Optimal Constellations for the Low SNR Noncoherent MIMO Rayleigh Fading Channel

Reliable communication over the discrete input and continuous output noncoherent multiple-input multiple-output (MIMO) Rayleigh fading channel is considered when the SNR per degree of freedom is low. The input constellations are required to satisfy peak and average power constraints. When the peak-to- average power ratio of the input constellation is limited (PAPR- limited) and in the low SNR regime, the mutual information up to second order in SNR is maximized jointly over input signal matrices and their respective probabilities, over all T + 1 point constellations (where T is the coherence length). Even though the problem considered is a finite dimensional non-convex optimization, it admits an elegant solution in closed form. The constellation obtained is referred to as Space Time Orthogonal Rank one Modulation (STORM), and it provides new insights into noncoherent MIMO comunications in the low SNR regime. By deriving an appropriate upper bound, it is shown that in most cases with even moderate values for PAPR and T, STORM is near-optimal with respect to the maximum mutual information achievable with unconstrained cardinality. For the case when the peak-power constraint is a fixed constant (peak-constrained), STORM achieves the capacity per unit energy, while having a wideband slope T times that of the conventional approach of MIMO ON-OFF signaling. This translates to increased bandwidth efficiency or PAPR reduction by a factor of T in the wideband regime.

Constellation Design for the Noncoherent MIMO Rayleigh Fading Channel at General SNR

Constellation design for the noncoherent multiple-input-multiple-output (MIMO) block Rayleigh-fading channel is considered. For general signal-to-noise ratios (SNRs), starting from a given base unitary constellation of finite cardinality, and using the cutoff rate expression as the design criterion, input probabilities and per-antenna amplitudes for the constellation points are obtained via a difference of convex programming formulation. Using the mutual information as a performance metric, it is shown that the optimized constellations significantly outperform the base unitary designs from which they are obtained in the low-medium SNR regime, and indeed they also similarly outperform the mutual information achieved by isotropically distributed unitary inputs for the continuous input channel [i.e., the so-called unitary space-time capacity (USTC)]. At sufficiently high SNRs, the resulting mutual information coincides with that of the base unitary designs. Thus the optimum constellation design technique works over the entire range of SNRs. The bit energy/spectral efficiency tradeoff of the optimized constellations are also obtained, and these provide valuable insights on modulation and coding, which are especially useful for wideband channels where the SNR per degree of freedom is low

Diversity order analysis of training codes for MIMO block fading channels

A general class of training-based space-time codes is considered for the noncoherent block correlated Rayleigh fading channel. Such codes can be efficiently decoded by first forming the MMSE estimate of the channel and then decoding the underlying coherent space-time code using the channel estimate as if it were perfect. The diversity order of this (in general, suboptimal) estimator-decoder is obtained, and it is shown that under certain conditions on the channel correlation matrix, training codes inherit the diversity order of the underlying coherent code.