By Raphael Hunger

This booklet bargains with the optimization-based joint layout of the transmit and obtain filters in MIMO broadcast channel within which the consumer terminals could be outfitted with a number of antenna components. in addition, the utmost functionality of the approach within the excessive energy regime in addition to the set of all possible quality-of-service requisites 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 printed.

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

In the excessive strength regime, an easy characterization of the acquired functionality turns into attainable in view that the weighted sum price 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 price loss that linear transceivers need to face with recognize to soiled paper coding.

In the final half, we solution the elemental query of feasibility in quality-of-service established 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 will be possible making the ability minimization challenge with given decrease sure constraints at the cost for instance infeasible in those circumstances. We derive an entire description of the quality-of-service feasibility quarter for arbitrary channel matrices.

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

**Sample text**

Apart from representing one direction of the duality proof, the conversion rules from the BC to the MAC are usually not applied in practice since the problem setting can completely be solved in the dual MAC and then be converted back to the original BC given the conversion rules deduced now. Nonetheless, some iterative algorithms exist that repeatedly switch between the BC and the MAC such that the BC to MAC conversion really has to be implemented, see for example [47, 48]. 2 For any set of linear transceivers in the dual MIMO MAC, there exist linear precoding and equalizer filters in the MIMO BC such that the same overall sum MSE, the same user-wise MSEs, and the same stream-wise MSEs can be achieved with the same amount of transmit power.

3 Rate Duality for Linear Transceivers Under Gaussian Signaling Another, probably even more important metric is the Shannon capacity that is defined as the maximum rate of transmission over a system with arbitrarily small error probability [50, 51]. Given a proper encoding and decoding scheme, the frequency of error can be made as small as desired by increasing the length of the encoding sequences. 43) which is a special case of the MIMO BC in Sect. 1, Shannon showed that the rate of transmission RSISO corresponds to the difference of the input entropy and the equivocation: RSISO = H(y1 ) − H(y1 |s1 ) Here, H(·) denotes the differential entropy function.

3 Rate Duality for Linear Transceivers Under Gaussian Signaling 41 the unitary rotations W 1 , . . , W K as additional degrees of freedom. Although W k does not influence the interference covariance matrix experienced by any other user i = k, it can be used as a spatial decorrelation filter for the point-to-point link from the transmitter to user k. 50). 53) can be rewritten to ⎪ ⎪ ⎪ MMSE BC ⎪ ¯ = − log2⎪ H k P k W k⎪ IkBC ( P) = IkBC ( P) ⎪I L k − W H ⎪. k Bk Choosing W k as the unitary eigenbasis of B MMSE H BC k k P k for all k ∈ {1, .