15,896 research outputs found
Mismatched Estimation in Large Linear Systems
We study the excess mean square error (EMSE) above the minimum mean square
error (MMSE) in large linear systems where the posterior mean estimator (PME)
is evaluated with a postulated prior that differs from the true prior of the
input signal. We focus on large linear systems where the measurements are
acquired via an independent and identically distributed random matrix, and are
corrupted by additive white Gaussian noise (AWGN). The relationship between the
EMSE in large linear systems and EMSE in scalar channels is derived, and closed
form approximations are provided. Our analysis is based on the decoupling
principle, which links scalar channels to large linear system analyses.
Numerical examples demonstrate that our closed form approximations are
accurate.Comment: 5 pages, 2 figure
A Geometric View on Constrained M-Estimators
We study the estimation error of constrained M-estimators, and derive
explicit upper bounds on the expected estimation error determined by the
Gaussian width of the constraint set. Both of the cases where the true
parameter is on the boundary of the constraint set (matched constraint), and
where the true parameter is strictly in the constraint set (mismatched
constraint) are considered. For both cases, we derive novel universal
estimation error bounds for regression in a generalized linear model with the
canonical link function. Our error bound for the mismatched constraint case is
minimax optimal in terms of its dependence on the sample size, for Gaussian
linear regression by the Lasso
On the Performance of Mismatched Data Detection in Large MIMO Systems
We investigate the performance of mismatched data detection in large
multiple-input multiple-output (MIMO) systems, where the prior distribution of
the transmit signal used in the data detector differs from the true prior. To
minimize the performance loss caused by this prior mismatch, we include a
tuning stage into our recently-proposed large MIMO approximate message passing
(LAMA) algorithm, which allows us to develop mismatched LAMA algorithms with
optimal as well as sub-optimal tuning. We show that carefully-selected priors
often enable simpler and computationally more efficient algorithms compared to
LAMA with the true prior while achieving near-optimal performance. A
performance analysis of our algorithms for a Gaussian prior and a uniform prior
within a hypercube covering the QAM constellation recovers classical and recent
results on linear and non-linear MIMO data detection, respectively.Comment: Will be presented at the 2016 IEEE International Symposium on
Information Theor
Impact of Channel Estimation Errors on Multiuser Detection via the Replica Method
For practical wireless DS-CDMA systems, channel estimation is imperfect due
to noise and interference. In this paper, the impact of channel estimation
errors on multiuser detection (MUD) is analyzed under the framework of the
replica method. System performance is obtained in the large system limit for
optimal MUD, linear MUD and turbo MUD, and is validated by numerical results
for finite systems.Comment: To appear in the EURASIP Journal on Wireless Communication and
Networking - Special Issue on Advanced Signal Processing Algorithms for
Wireless Communication
Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)
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