An Upper Bound on the Capacity of Vector Dirty Paper with Unknown Spin and Stretch

TL;DR

This paper derives a tighter upper bound on the capacity of a vector dirty paper channel with unknown channel effects, improving understanding of interference management under uncertainty.

Contribution

It introduces a novel upper bound for the capacity of a compound vector dirty paper channel with uncertain channel matrix, applicable to low-SIR and high-SNR regimes.

Findings

Tighter capacity bounds in low-SIR regime for scalar channels.

Established high-SNR behavior bounds.

Focus on the relationship between message and state dimensions.

Abstract

Dirty paper codes are a powerful tool for combating known interference. However, there is a significant difference between knowing the transmitted interference sequence and knowing the received interference sequence, especially when the channel modifying the interference is uncertain. We present an upper bound on the capacity of a compound vector dirty paper channel where although an additive Gaussian sequence is known to the transmitter, the channel matrix between the interferer and receiver is uncertain but known to lie within a bounded set. Our bound is tighter than previous bounds in the low-SIR regime for the scalar version of the compound dirty paper channel and employs a construction that focuses on the relationship between the dimension of the message-bearing signal and the dimension of the additive state sequence. Additionally, a bound on the high-SNR behavior of the system is established.