Comments on: Overview of MIMO Broadcast Channel Capacity Results http://windowsil.org/2008/02/12/overwiew-of-mimo-broadcast-channel-capacity-result/ Your window into the Wireless Systems Innovation Laboratory Sun, 27 May 2012 13:11:51 +0000 http://wordpress.org/?v=2.0.3 by: Rahul Vaze http://windowsil.org/2008/02/12/overwiew-of-mimo-broadcast-channel-capacity-result/#comment-33341 Tue, 18 Mar 2008 04:13:17 +0000 http://windowsil.org/2008/02/12/overwiew-of-mimo-broadcast-channel-capacity-result/#comment-33341 Thanks Caleb for pointing out the typos. Thanks Caleb for pointing out the typos.

]]> by: Caleb Lo http://windowsil.org/2008/02/12/overwiew-of-mimo-broadcast-channel-capacity-result/#comment-33113 Fri, 14 Mar 2008 17:50:49 +0000 http://windowsil.org/2008/02/12/overwiew-of-mimo-broadcast-channel-capacity-result/#comment-33113 Rahul - thanks for this writeup. Sometimes I find it difficult to get a handle on information-theoretic results, but this writeup illustrates the key proof mechanisms at a relatively accessible level (MIMO-BC -> AMIMO-BC -> DAMIMO-BC -> enhanced DAMIMO-BC, which is where I guess Bergman's proof becomes quite useful). It would be interesting to compare the proof employed here with that in the paper by Mohseni and Cioffi. A few comments on the nuts and bolts of this writeup: 1) Throughout the writeup we see that the governing system equation has user $n$ receiving $y_n = H_nx_n+v_n$. It seems, though, that the transmitter would send $x$ to user $n$, not just $x_n$ (which is what user $n$ wants to decode). 2) There seems to be a mistake in the achieved rate for user 2 in the case where DPC encoding entails encoding user 2's signal first. The determinant in the denominator should have $S_1$, not $S_2$ (since user 1's signal would interfere with user 2's signal). 3) The definition of the enhanced DAMIMO-BC is somewhat confusing. It would seem more straightforward to have the constraint $cov(\hat{v}_i)\leq cov(v_i^{*})$ for $i = 1,2$. Currently, $cov(\hat{v}_1)$ is compared with $cov(v_2^{*})$, but how is this an improvement over the DAMIMO-BC? I wonder if the accompanying sum constraint on the covariances is the key to understanding this. Rahul - thanks for this writeup. Sometimes I find it difficult to get a handle on information-theoretic results, but this writeup illustrates the key proof mechanisms at a relatively accessible level (MIMO-BC -> AMIMO-BC -> DAMIMO-BC -> enhanced DAMIMO-BC, which is where I guess Bergman’s proof becomes quite useful).

It would be interesting to compare the proof employed here with that in the paper by Mohseni and Cioffi.

A few comments on the nuts and bolts of this writeup:
1) Throughout the writeup we see that the governing system equation has user $n$ receiving $y_n = H_nx_n+v_n$. It seems, though, that the transmitter would send $x$ to user $n$, not just $x_n$ (which is what user $n$ wants to decode).
2) There seems to be a mistake in the achieved rate for user 2 in the case where DPC encoding entails encoding user 2’s signal first. The determinant in the denominator should have $S_1$, not $S_2$ (since user 1’s signal would interfere with user 2’s signal).
3) The definition of the enhanced DAMIMO-BC is somewhat confusing. It would seem more straightforward to have the constraint $cov(\hat{v}_i)\leq cov(v_i^{*})$ for $i = 1,2$. Currently, $cov(\hat{v}_1)$ is compared with $cov(v_2^{*})$, but how is this an improvement over the DAMIMO-BC? I wonder if the accompanying sum constraint on the covariances is the key to understanding this.

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