Cyclic delay transmission achieves full diversity without (Pre)coding

Cyclic Delay Diversity (CDD) is a simple method that converts transmit antenna diversity into frequency selectivity, thus allowing simple operation and use of conventional receivers to capture the diversity. This paper shows that single-carrier CDD methods are capable of producing diversity without channel coding or linear precoding, and that this is made possible via the appropriate design and use of linear equalizers. At the heart of our result is the establishment of a functional equivalence between effective channels seen by the CDD MISO system and the cyclic-prefix SISO ISI system. Specifically, we show that in an M×1 CDD MSIO system, the MMSE receiver achieves maximum diversity for rate values R ≤ log L/M(ν+1)-1, where L is the data block length, R the spectral efficiency in b/s/Hz, and ν is the channel memory. The equivalence between the delay diversity (DD) system and a zero-padding single-carrier system can be also established (as long as the DD delay taps are carefully chosen) for which linear equalizers can achieve maximum diversity with no constraint on rate.