Abstract
Abstract The block diagonalization (BD) is a linear precoding technique for multi-user multi-input multi-output (MIMO) broadcast channels, which is able to completely eliminate the multi-user interference (MUI), but it is not computationally efficient. In this paper, we propose the block diagonal Jacket matrix decomposition, which is able not only to extend the conventional block diagonal channel decomposition but also to achieve the MIMO broadcast channel capacity. We also prove that the QR algorithm achieves the same sum rate as that of the conventional BD scheme. The complexity analysis shows that our proposal is more efficient than the conventional BD method in terms of the number of the required computation.
Highlights
The research of the capacity region of the multi-user multi-input multi-output (MIMO) broadcast channels (BC) has been of concern
We show that the new method has the lower complexity than the conventional block diagonalization (BD) method through complexity analysis, and the efficiency improvement becomes significant when the base station or users have a large number of transmit antennas
These results show that the QR decomposition algorithm requires much less complexity than the conventional BD method
Summary
The research of the capacity region of the multi-user multi-input multi-output (MIMO) broadcast channels (BC) has been of concern. In [1], the authors proposed the MIMO channel precoding/decoding based on the Jacket matrix decomposition where we believe that the required computational complexity in obtaining diagonal-similar matrices is smaller than that required in the conventional EVD. We consider the channel matrix decomposition based on QR and Jacket matrices for the case where each user has multiple antennas. The aforementioned problem is categorized as a convex optimization problem It can be solved optimally and efficiently by using the water filling algorithm, which is proposed for the multi-user transmit optimization for broadcast channels. To maximize the sum rate under a total power constraint at the BS, where the power allocation matrix is the solution to the following optimization, with TBD chosen, the capacity of the BD [10,15] is CBD max. A summary of the BD algorithm [10] in Algorithm 1
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