Estimation of Sparse MIMO Channels with Common Support

We consider the problem of estimating sparse communication channels in the MIMO context. In small to medium bandwidth communications, as in the current standards for OFDM and CDMA communication systems (with bandwidth up to 20 MHz), such channels are individually sparse and at the same time share a common support set. Since the underlying physical channels are inherently continuous-time, we propose a parametric sparse estimation technique based on finite rate of innovation (FRI) principles. Parametric estimation is especially relevant to MIMO communications as it allows for a robust estimation and concise description of the channels. The core of the algorithm is a generalization of conventional spectral estimation methods to multiple input signals with common support. We show the application of our technique for channel estimation in OFDM (uniformly/contiguous DFT pilots) and CDMA downlink (Walsh-Hadamard coded schemes). In the presence of additive white Gaussian noise, theoretical lower bounds on the estimation of SCS channel parameters in Rayleigh fading conditions are derived. Finally, an analytical spatial channel model is derived, and simulations on this model in the OFDM setting show the symbol error rate (SER) is reduced by a factor 2 (0 dB of SNR) to 5 (high SNR) compared to standard non-parametric methods - e.g. lowpass interpolation.Comment: 12 pages / 7 figures. Submitted to IEEE Transactions on Communicatio

EQUALIZATION BY THE PULSE SHAPE INVERSE OF THE INPUT TO THE FRI PROCESSING IN PULSE BASED COMMUNICATIONS

Certain aspects of the present disclosure relate to a method for equalizing a pulse signal corrupted by a noise and by various channel effects for obtaining a signal based on the periodic-sinc pulse, which is suitable for Finite Rate of Innovation (FRI) processing applied at a receiver of a pulse-based communication system (e.g., an Ultra-Wideband receiver)

Finite Rate of Innovation sampling techniques for embedded UWB devices.

This report studies the applicability of Finite Rate of Innovation (FRI) algorithms to UltraWide Band (UWB) communications, more precisely in the scope of Low Power Body Area Networks (LP-BAN ). Three main issues are studied and given proposed solutions. First, the classical FRI algorithm is modified to accomodate different symmetrical pulse shapes. Such a modification – necessary to get acceptable performances – is done by a simple equalization. Second, LP-BAN devices limitations such as drift, jitter and aggressive quantization are blended in the algorithm. It is done by adjusting the equalization template and development of a suited quantization algorithm. Third and last, the cost of FRI denoising procedure (Cadzow denoising) is greatly reduced to fit the requirements of a low power embedded device. It is centered on performing most of the computations in a low-dimension Krylov subspace of the matrix to be denoised. The particular structure of the projected matrix enables selective computation of the eigenpairs. The result is an algorithm able to resolve close paths within a reasonnable computational budget. Some issues remain on quantization

FASTER CADZOW DENOISING BASED ON PARTIAL EIGENVALUE DECOMPOSITION

Certain aspects of the present disclosure relate to a method for speeding up the Cadzow iterative denoising algorithm as a part of the Finite Rate of Innovation (FRI) processing and for decreasing its computational complexity

FINITE RATE OF INNOVATION (FRI) TECHNIQUES FOR LOW POWER BODY AREA NETWORK

Certain aspects of the present disclosure relate to a method for quantizing an analog received signal in a low-power body area network (LP-BAN) by using a limited number of quantization bits, while information of the received signal is preserved for accurate signal reconstruction. The quantized signal can be equalized in such a way to generate an output equalized signal based on the periodic-sine function, which is suitable for a subsequent Finite Rate of Innovation (FRI) processing. The noisy equalized signal can be further processed by applying improved (i.e., faster) Cadzow denoising algorithm as a part of the FRI processing

EMULATION OF N-BITS UNIFORM QUANTIZER FROM MULTIPLE INCOHERENT AND NOISY ONE-BIT MEASUREMENTS

Certain aspects of the present disclosure relate to a method for emulating N-bits uniform quantization of a received pulse signal by using one-bit signal measurements

Methods and apparatus for estimating a sparse channel

Embodiments include a method for sending a selected number of pilots (20) to a sparse channel having a channel impulse response limited in time comprising sending the selected number of the pilots (20). The pilots (20) are equally spaced in the frequency domain the number is selected based on the finite rate of innovation of the channel impulse response. Once received the pilots (20), such a channel is estimated by: low-pass filtering (100) the received pilots, sampling (200) the filtered pilots with a rate below the Nyquist rate of the pilots, applying a FFT (300) on the sampled pilots, verifying (500) the level of noise of the transformed pilots, if the level of noise is below to a determined threshold, applying an annihilating filter method (600) to the transformed pilots, and dividing the temporal parameters by the distance (D) between two consecutive pilots

Fast and robust estimation of jointly sparse channels

A device and method for estimating multipath jointly sparse channels. The method comprises receiving a number K of signal components by a number P of receiving antennas, where P≧2. The method further comprises estimating the sparsity condition of the multipath jointly sparse channels. The method further comprises, if the sparsity condition is not satisfied, estimating the channels by using a non-sparse technique. The method further comprises, if the sparsity condition is satisfied, estimating the channels by using a sparse technique

Sequences with Minimal Time-Frequency Uncertainty

A central problem in signal processing and communications is to design signals that are compact both in time and frequency. Heisenberg's uncertainty principle states that a given function cannot be arbitrarily compact both in time and frequency, defining an “uncertainty” lower bound. Taking the variance as a measure of localization in time and frequency, Gaussian functions reach this bound for continuous-time signals. For sequences, however, this is not true; it is known that Heisenberg's bound is generally unachievable. For a chosen frequency variance, we formulate the search for “maximally compact sequences” as an exactly and efficiently solved convex optimization problem, thus providing a sharp uncertainty principle for sequences. Interestingly, the optimization formulation also reveals that maximally compact sequences are derived from Mathieu's harmonic cosine function of order zero. We further provide rational asymptotic expansions of this sharp uncertainty bound. We use the derived bounds as a benchmark to compare the compactness of well-known window functions with that of the optimal Mathieu's functions