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We analytically approximate the expected sum capacity loss between theoptimal downlink precoding technique of dirty paper coding (DPC), and thesub-optimal technique of zero-forcing precoding, for multiuser channels. Wealso consider the most general case of multi-stream transmission to multipleusers, where we evaluate the expected sum capacity loss between DPC and blockdiagonalization precoding. Unlike previously, assuming heterogeneous Riceanfading, we utilize the well known affine approximation to predict the expectedsum capacity difference between both precoder types (optimal and sub-optimal)over a wide range of system and propagation parameters. Furthermore, forsingle-stream transmission, we consider the problem of weighted sum capacitymaximization, where a similar quantification of the sum capacity differencebetween the two precoder types is presented. In doing so, we disclose thatpower allocation to different users proportional to their individual weightsasymptotically maximizes the weighted sum capacity. Numerical simulations arepresented to demonstrate the tightness of the developed expressions relative totheir simulated counterparts.

Sum Capacity Loss Quantification With Optimal and Sub-Optimal Precoding in Heterogeneous Multiuser Channels