Practical analysis of codebook design and frequency offset estimation for virtual-multiple-input–multiple-output systems

A virtual-multiple-input-multiple-output (MIMO) wireless system using the receiver-side cooperation with the compress-and-forward (CF) protocol, is an alternative to a point-to-point MIMO system, when a single receiver is not equipped with multiple antennas. It is evident that the practicality of CF cooperation will be greatly enhanced if an efficient source coding technique can be used at the relay. It is even more desirable that CF cooperation should not be unduly sensitive to carrier frequency offsets (CFOs). This study presents a practical study of these two issues. Firstly, codebook designs of the Voronoi vector quantisation (VQ) and the tree-structure VQ (TSVQ) to enable CF cooperation at the relay are described. A comparison in terms of the codebook design and encoding complexity is analysed. It is shown that the TSVQ is much simpler to design and operate, and can achieve a favourable performance-complexity tradeoff. Furthermore, this study demonstrates that CFO can lead to significant performance degradation for the virtual-MIMO system. To overcome this, it is proposed to maintain clock synchronisation and jointly estimate the CFO between the relay and the destination. This approach is shown to provide a significant performance improvement