468 research outputs found
Optimizing quantization for Lasso recovery
This letter is focused on quantized Compressed Sensing, assuming that Lasso is used for signal estimation. Leveraging recent work, we provide a framework to optimize the quantization function and show that the recovered signal converges to the actual signal at a quadratic rate as a function of the quantization level. We show that when the number of observations is high, this method of quantization gives a significantly better recovery rate than standard Lloyd-Max quantization. We support our theoretical analysis with numerical simulations
Optimal Quantization for Compressive Sensing under Message Passing Reconstruction
We consider the optimal quantization of compressive sensing measurements
following the work on generalization of relaxed belief propagation (BP) for
arbitrary measurement channels. Relaxed BP is an iterative reconstruction
scheme inspired by message passing algorithms on bipartite graphs. Its
asymptotic error performance can be accurately predicted and tracked through
the state evolution formalism. We utilize these results to design mean-square
optimal scalar quantizers for relaxed BP signal reconstruction and empirically
demonstrate the superior error performance of the resulting quantizers.Comment: 5 pages, 3 figures, submitted to IEEE International Symposium on
Information Theory (ISIT) 2011; minor corrections in v
Compressed Sensing Based Multi-User Millimeter Wave Systems: How Many Measurements Are Needed?
Millimeter wave (mmWave) systems will likely employ directional beamforming
with large antenna arrays at both the transmitters and receivers. Acquiring
channel knowledge to design these beamformers, however, is challenging due to
the large antenna arrays and small signal-to-noise ratio before beamforming. In
this paper, we propose and evaluate a downlink system operation for multi-user
mmWave systems based on compressed sensing channel estimation and conjugate
analog beamforming. Adopting the achievable sum-rate as a performance metric,
we show how many compressed sensing measurements are needed to approach the
perfect channel knowledge performance. The results illustrate that the proposed
algorithm requires an order of magnitude less training overhead compared with
traditional lower-frequency solutions, while employing mmWave-suitable
hardware. They also show that the number of measurements need to be optimized
to handle the trade-off between the channel estimate quality and the training
overhead.Comment: IEEE International Conference on Acoustics, Speech and Signal
Processing (ICASSP) 201
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