By Raphael Hunger

ISBN-10: 3642316913

ISBN-13: 9783642316913

ISBN-10: 3642316921

ISBN-13: 9783642316920

This publication bargains with the optimization-based joint layout of the transmit and obtain filters in MIMO broadcast channel within which the consumer terminals might be outfitted with numerous antenna parts. in addition, the utmost functionality of the approach within the excessive strength regime in addition to the set of all possible quality-of-service requisites is analyzed.

First, a basic duality is derived that holds among the MIMO broadcast channel and digital MIMO a number of entry channel. This duality build allows the effective answer of difficulties initially posed within the broadcast channel within the twin area the place a most likely hidden convexity can frequently be printed.

On the root of the proven duality outcome, the gradient-projection set of rules is brought as a device to unravel limited optimization difficulties to worldwide optimality below definite stipulations. The gradient-projection device is then utilized to fixing the weighted sum fee maximization challenge that's a principal optimization that arises in any community application maximization.

In the excessive energy regime, an easy characterization of the bought 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 cost loss that linear transceivers need to face with appreciate to soiled paper coding.

In the final half, we solution the basic query of feasibility in quality-of-service dependent optimizations with inelastic site visitors that includes strict hold up constraints. below the belief of linear transceivers, now not each set of quality-of-service necessities can be possible making the facility minimization challenge with given decrease sure constraints at the fee for instance infeasible in those instances. We derive a whole description of the quality-of-service feasibility zone for arbitrary channel matrices.

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**Additional info for Analysis and Transceiver Design for the MIMO Broadcast Channel**

**Example text**

2K ,L K T = Z −1 · ¯t 1,1 22 , . . 78) The L × L matrix Z reads as ⎤ Z 1,1 · · · Z 1,K ⎥ ⎢ Z := ⎣ ... . ... 79) with off-diagonal blocks ¯ iMF H k T¯ k Z k,i := − G ¯ iMF H k T¯ k G ∗ T ∈ R L k ×L i for k = i. All diagonal blocks are diagonal matrices, and the kth block reads as ¯ MF,H ¯ MF Z k,k := G k Gk IL k − i =k diag{1TL i Zi,k } ∀k. 80) Again, zero rows and columns representing passive streams have to be removed and after this removal, Z is a nonsingular M-Matrix (see Appendix A1) such that there is a positive solution for the scaling factors of all active streams.

Equating εBC k and εk K scaling factors ψ1 , . . , ψ K (that can be chosen to be positive) instead of a single one as in the level one duality conversion. 9), the dual MIMO MAC filter parametrization is set to H T k = ψk AH k Bk G k = ψk−1 P H k ∀k ∈ {1, . . , K }. 7), we obtain K = L k + tr εMAC k i=1 ψi2 ψk2 −2 H H H H PH k H i Ai B i B i Ai H i P k + ψk P k P k H H H − tr P H k H k Ak B k − tr B k Ak H k P k . 3) are identical, if [cf. 11)] ∀k ∈ {1, . . , K }. 17) and the identity tr(X H X) = tr(X X H ) = X 2F : MAC ⇔ ψk2 εBC k = εk B k H BC k Pi 2 F + tr(B k C ηk B H k) i =k ψi2 B i H iBC P k − 2 F = Pk 2 F i =k Above equation must hold for all users k ∈ {1, .

1 with given precoders P 1 , . . 52), we construct a dual MIMO MAC with precoders T 1 , . . , T K achieving at least the same mutual information using the same amount of transmit power. In addition, we derive receive filters G 1 , . . , G K in this dual MAC for which exactly the user-wise BC mutual information is obtained in the dual MAC by means of separate decoding. This way, one direction of the duality statement is proven, and it will be possible to tackle a rate-based optimization problem stated in the MIMO BC in its dual MIMO MAC which offers better mathematical properties, see Sect.

### Analysis and Transceiver Design for the MIMO Broadcast Channel by Raphael Hunger

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