Zero-Forcing Precoding and Generalized Inverses

Abstract

Abstract-We consider the problem of linear zero forcing precoding design, and discuss its relation to the theory of generalized inverses in linear algebra. Special attention is given to a specific generalized inverse known as the pseudo-inverse. We begin with the standard design under the assumption of a total power constraint and prove that precoders based on the pseudo-inverse are optimal in this setting. Then, we proceed to examine individual per-antenna power constraints. In this case, the pseudo-inverse is not necessarily the optimal generalized inverse. In fact, finding the optimal inverse is non-trivial and depends on the specific performance measure. We address two common criteria, fairness and throughput, and show that the optimal matrices may be found using standard convex optimization methods. We demonstrate the improved performance offered by our approach using computer simulations.

Robust multibeam satellite systems for underlay licensed shared access

“…This paper takes the suboptimal approach identified in [8] and assumes that ZF precoding is employed. Under this context, the transmit power can be optimized as follows…”

Physical Layer Network Coding Based on Integer Forcing Precoded Compute and Forward

“…It is well known that zero forcing (ZF) precoding is a standard suboptimal approach for precoding, which is known to provide a promising trade-off between complexity and performance [11]. The traditional zero forcing precoder is designed to eliminate the effect of the channel fading, while satisfying constraints of power optimally as per certain performance measures.…”

Linear Precoded Cooperative Transmission Protocol for Wireless Broadcast Channels

“…The null space precoding well known as ZFBF is able to multiplex M stream of messages simultaneously and eliminate the interference among destinations. At the mth destination, the observation is Ym(2) == JE:"lhmlsm(2)+ JE:"gR I,mPR I,m sm(l) +nm (2). (6) Although the remaining relays also receive a mixture of the messages, they will be able to decode the source messages using simple successive decoding since they satisfy the qualification criterion in eq.…”

“…However, the high computation cost and complexity make it less attractive if compared to suboptimal methods such as linear precoding. An example is the zeroforcing beamforming (ZFBF) which cancels the co-channel interference among multiple users [2]. Linear precoded broadcast transmission protocol can achieve the optimal sum-rate by utilising the multi-user diversity [3] in scheduling.…”