On the Convexity of the MSE Region of Single-Antenna Users

Details On the Convexity of the MSE Region of Single-Antenna Users On the Convexity of the MSE Region of Single-Antenna Users

2008-04-02

arxiv.org/abs/0804.0337v2

Computer Science

Information Theory

submitted to Globecom 2008; fixed definition of matrix S, added 2 KKT conditions, and few minor changes

Scientific paper

We prove convexity of the sum-power constrained mean square error (MSE) region in case of two single-antenna users communicating with a multi-antenna base station. Due to the MSE duality this holds both for the vector broadcast channel and the dual multiple access channel. Increasing the number of users to more than two, we show by means of a simple counter-example that the resulting MSE region is not necessarily convex any longer, even under the assumption of single-antenna users. In conjunction with our former observation that the two user MSE region is not necessarily convex for two multi-antenna users, this extends and corrects the hitherto existing notion of the MSE region geometry.

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