Name
Abstract | ||
|---|---|---|
Suppose a linear model ${\\bf y}={\\bf H}{\\bf x}+{\\bf n}$, where inputs ${\\bf x,n}$ are independent Gaussian mixtures. The problem is to design the transfer matrix ${\\bf H}$ so as to minimize the mean square error (MSE) when estimating ${\\bf x}$ from ${\\bf y}$. This problem has important applications, but faces at least three hurdles. Firstly, even for a fixed ${\\bf H}$, the minimum MSE (MMSE) has no analytical form. Secondly, the MMSE is generally not convex in ${\\bf H}$. Thirdly, derivatives of the MMSE w.r.t. ${\\bf H}$ are hard to obtain. This paper casts the problem as a stochastic program and invokes gradient methods. The study is motivated by two applications in signal processing. One concerns the choice of error-reducing precoders; the other deals with selection of pilot matrices for channel estimation. In either setting, our numerical results indicate improved estimation accuracy—markedly better than those obtained by optimal design based on standard linear estimators. Some implications of the non-convexities of the MMSE are noteworthy, yet, to our knowledge, not well known. For example, there are cases in which more pilot power is detrimental for channel estimation. This paper explains why. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/TSP.2013.2278812 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
Gaussian processes,gradient methods,matrix algebra,mean square error methods,signal processing,MMSE,channel estimation,gradient methods,independent Gaussian mixtures,linear model under mixed Gaussian inputs,mean square error,minimum MSE,signal processing,stochastic program,transfer matrix design,Gaussian mixtures,estimation,minimum mean square error (MMSE) | Mathematical optimization,Linear model,Matrix (mathematics),Minimum mean square error,Mean squared error,Optimal design,Gaussian,Gaussian process,Mathematics,Estimator | Journal |
Volume | Issue | ISSN |
61 | 21 | 1053-587X |
Citations | PageRank | References |
0 | 0.34 | 20 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| John T. Flåm | 1 | 35 | 4.68 |
| Dave Zachariah | 2 | 159 | 24.28 |
| Mikko Vehkaperä | 3 | 103 | 15.36 |
| Saikat Chatterjee | 4 | 320 | 40.34 |