Analysis and Transceiver Design for the MIMO Broadcast by Raphael Hunger

By Raphael Hunger

This ebook offers with the optimization-based joint layout of the transmit and obtain filters in MIMO broadcast channel during which the consumer terminals could be outfitted with numerous antenna components. moreover, the utmost functionality of the approach within the excessive strength regime in addition to the set of all possible quality-of-service necessities 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 most likely hidden convexity can usually be published.

On the root of the demonstrated duality end result, the gradient-projection set of rules is brought as a device to resolve restricted optimization difficulties to international optimality less than convinced stipulations. The gradient-projection software is then utilized to fixing the weighted sum price maximization challenge that is a significant optimization that arises in any community software maximization.

In the excessive strength regime, an easy characterization of the received functionality turns into attainable due to the fact the weighted sum price application converges to an affine asymptote within the logarithmic strength 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 appreciate to soiled paper coding.

In the final half, we resolution the basic query of feasibility in quality-of-service dependent optimizations with inelastic site visitors that includes strict hold up constraints. lower than the idea of linear transceivers, now not each set of quality-of-service standards could be possible making the ability minimization challenge with given decrease certain constraints at the cost for instance infeasible in those instances. We derive an entire description of the quality-of-service feasibility zone for arbitrary channel matrices.

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63) j=1 Having removed the intra-user interference from every user, we can create a dual MIMO MAC that offers at least the same data rates per user by simply applying the level three duality conversion on the rotated transmit and receive filters P¯ 1 , . . , P¯ K ¯ 1, . . , B ¯ K , respectively, see Sect. 3. In particular, we make use of the and B SINR conservation in order to be able to express the rates in the dual domain in terms of the SINRs. Indeed, the MSEs are also preserved but the MSEs in the dual MAC cannot easily be mapped to data rate since they are not the minimum MSEs in general.

If, by chance, the dual MAC precoders are chosen such that the obtained mutual information tuple lies on the boundary of the mutual information region for a given power constraint, then the duality conversion will deliver filter pairs that diagonalize the error covariance matrix and achieve the BC mutual information. Synopsis: Given precoders T 1 , . . , T K in the dual MIMO MAC achieving mutual information expressions I1MAC (T ), . . , I KMAC (T ), it is possible to derive transmit and receive filters P and B, respectively, such that the same or larger data rates can be obtained in the MIMO BC using the same amount of transmit power.

13) Ak = C η2 k 1 1 ,H that satisfies C η2 k C η2 k = C ηk . 11), the channel matrices of the dual MIMO MAC have to be chosen such that − 1 ,H H k = H kBC,H C ηk2 . 14) For uncorrelated noise terms η 1 , . . , η K in the BC with identity covariance matrix, the MAC channels are simply the Hermitian BC channels. 9). BC Synopsis: For any MIMO BC with channel matrices H BC 1 , . . , H K and arbitrary linear transmit and receive filters there exists a dual MIMO MAC with channel matrices − 1 ,H H k = H kBC,H C ηk2 ∀k such that if an overall sum MSE in the BC is feasible, it is also achievable in the dual MAC with the same amount of total transmit power.

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