By Raphael Hunger
This ebook bargains with the optimization-based joint layout of the transmit and obtain filters in MIMO broadcast channel during which the person terminals might be built with a number of antenna parts. in addition, the utmost functionality of the procedure within the excessive strength regime in addition to the set of all possible quality-of-service standards is analyzed.
First, a primary duality is derived that holds among the MIMO broadcast channel and digital MIMO a number of entry channel. This duality build permits the effective answer of difficulties initially posed within the broadcast channel within the twin area the place a in all probability hidden convexity can frequently be published.
On the foundation of the validated duality outcome, the gradient-projection set of rules is brought as a device to resolve limited optimization difficulties to worldwide optimality below sure stipulations. The gradient-projection instrument is then utilized to fixing the weighted sum price maximization challenge that's a critical optimization that arises in any community application maximization.
In the excessive energy regime, an easy characterization of the got functionality turns into attainable on account that the weighted sum expense software converges to an affine asymptote within the logarithmic energy area. we discover closed shape expressions for those asymptotes which permits for a quantification of the asymptotic expense loss that linear transceivers need to face with recognize to soiled paper coding.
In the final half, we resolution the basic query of feasibility in quality-of-service established optimizations with inelastic site visitors that includes strict hold up constraints. lower than the belief of linear transceivers, now not each set of quality-of-service requisites may be possible making the ability minimization challenge with given reduce certain constraints at the cost for instance infeasible in those situations. We derive a whole description of the quality-of-service feasibility sector for arbitrary channel matrices.
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Additional resources for Analysis and Transceiver Design for the MIMO Broadcast Channel
If the noise covariance matrix in the dual MAC is chosen to be the identity matrix, the channel matrices in the dual MAC result from the channel matrices and the noise covariance matrices in the BC as shown in Corollary 1. As a consequence of Theorem 1, it is possible to tackle an MSE-based problem in the dual MIMO MAC that is originally stated in the MIMO BC where it usually has a complicated structure due to the inexistent indices alignment of the precoders and the channel matrices (see the discussion in Sect.
Hence, we are able to use standard gradient-based algorithms and are not reliant on optimization packages. Due to the indices alignment in the dual MIMO MAC, iterative algorithms can be implemented very efficiently. Using the rate-based duality, we were able to derive a close-to-optimum (weighted) sum rate maximization algorithm  that will be derived in Sect. 3. Moreover, we were able to further explore the properties of linear multi-antenna transceivers.
2 In the K user MIMO BC with linear transceivers, the K mutual information expressions between the transmitter and each receiver can be achieved by separate stream decoding using MSE receivers followed by appropriate decorrelation matrices applied at all transmit and receive filters. This also holds for the MIMO MAC. The proof of Theorem 2 for the MIMO MAC follows from the BC to MAC conversion in Sect. 1 and the MAC to BC conversion in Sect. 2. Synopsis The rate duality between the MIMO MAC and the MIMO BC with linear transceivers was so far deduced from the stream-wise SINR duality in the literature.