Precoding: Difference between revisions

Revision as of 07:06, 5 September 2010

Revision as of 02:07, 12 May 2011

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:<math>\underset{\{\mathbf{w}_k\}:\sum_i \|\mathbf{w}_i\|^2 \leq P}{\mathrm{maximize}} \sum_{k=1}^K a_k \log_2(1+\textrm{SINR}_k)</math>

for some positive weights <math>a_k</math> that represent the user priority. The weighted sum rate is maximized by MMSE precoding that selects

:<math>\mathbf{w}^{\textrm{MMSE}}_i_k = \sqrt{p_ip_k} \frac{( \mathbf{I} + \sum_{i \neq k} q_i \mathbf{h}_i \mathbf{h}_i^H )^{-1} \mathbf{h}_k}{\|( \mathbf{I} + \sum_{i \neq k} q_i \mathbf{h}_i \mathbf{h}_i^H )^{-1} \mathbf{h}_k\|} </math>

for some positive coefficients <math>q_1,\ldots,q_K</math> (related to the user weights) that satisfy <math>\sum_{i=1}^K q_i = P</math> and <math>p_i</math> is the optimal power allocation<ref name=bjornson />.