Optimal Precoders for Tracking the AoD and AoA of a mm-Wave Path

In millimeter-wave channels, most of the received energy is carried by a few paths. Traditional precoders sweep the angle-of-departure (AoD) and angle-of-arrival (AoA) space with directional precoders to identify directions with largest power. Such precoders are heuristic and lead to sub-optimal AoD/AoA estimation. We derive optimal precoders, minimizing the Cram\'{e}r-Rao bound (CRB) of the AoD/AoA, assuming a fully digital architecture at the transmitter and spatial filtering of a single path. The precoders are found by solving a suitable convex optimization problem. We demonstrate that the accuracy can be improved by at least a factor of two over traditional precoders, and show that there is an optimal number of distinct precoders beyond which the CRB does not improve.Comment: Resubmission to IEEE Trans. on Signal Processing. 12 pages and 9 figure

On Optimum End-to-End Distortion in MIMO Systems

This paper presents the joint impact of the numbers of antennas, source-to-channel bandwidth ratio and spatial correlation on the optimum expected end-to-end distortion in an outage-free MIMO system. In particular, based on an analytical expression valid for any SNR, a closed-form expression of the optimum asymptotic expected end-to-end distortion valid for high SNR is derived. It is comprised of the optimum distortion exponent and the multiplicative optimum distortion factor. Demonstrated by the simulation results, the analysis on the joint impact of the optimum distortion exponent and the optimum distortion factor explains the behavior of the optimum expected end-to-end distortion varying with the numbers of antennas, source-to-channel bandwidth ratio and spatial correlation. It is also proved that as the correlation tends to zero, the optimum asymptotic expected end-to-end distortion in the setting of correlated channel approaches that in the setting of uncorrelated channel. The results in this paper could be performance objectives for analog-source transmission systems. To some extend, they are instructive for system design.Comment: 35 pages, 10 figures, submitted to EURASIP Journal on Wireless Communications and Networkin

The Use of Short-Count Methods on Field Collected Diatom Communities to Determine Water Quality of Small Streams

This study was undertaken to determine if short-count methods for calculation of diatom species diversity could be used to determine the water quality of small streams. Two small streams, located in North Central Iowa, were selected for study; one was chosen because it appeared to be in a relatively healthy condition and the other because it appeared to be highly polluted. Diatom samples were collected by direct field collection of the predominant diatom growths in each stream. Short-counts of 50, 100, 200, 500, and 1000 diatom valves were made and species diversity computed by 2 methods, the Shannon Index of General Diversity and the Sequential Comparison Index. A one-way analysis of variance using mean species diversity values was run on all diatom counts both within and between the samples of each stream. The results showed that short-counts could be used to determine differences in water quality of the 2 small streams studied and further suggest that such analyses might be suitable for other small streams

Large System Analysis of Linear Precoding in Correlated MISO Broadcast Channels under Limited Feedback

In this paper, we study the sum rate performance of zero-forcing (ZF) and regularized ZF (RZF) precoding in large MISO broadcast systems under the assumptions of imperfect channel state information at the transmitter and per-user channel transmit correlation. Our analysis assumes that the number of transmit antennas $M$ and the number of single-antenna users $K$ are large while their ratio remains bounded. We derive deterministic approximations of the empirical signal-to-interference plus noise ratio (SINR) at the receivers, which are tight as $M,K\to\infty$. In the course of this derivation, the per-user channel correlation model requires the development of a novel deterministic equivalent of the empirical Stieltjes transform of large dimensional random matrices with generalized variance profile. The deterministic SINR approximations enable us to solve various practical optimization problems. Under sum rate maximization, we derive (i) for RZF the optimal regularization parameter, (ii) for ZF the optimal number of users, (iii) for ZF and RZF the optimal power allocation scheme and (iv) the optimal amount of feedback in large FDD/TDD multi-user systems. Numerical simulations suggest that the deterministic approximations are accurate even for small $M,K$.Comment: submitted to IEEE Transactions on Information Theor