Complexity analysis of multicarrier and single-carrier systems for very high-speed digital subscriber line

A complexity analysis of discrete multitone (DMT) and single-carrier modulation (SCM) in the context of a very high-speed digital subscriber line (VDSL) is presented in this paper. In addition to the traditional arithmetic complexity measures such as the number of multiply-and-accumulate (MAC) operations, we also compute the memory requirements. Furthermore, we normalize these metrics with respect to the number of information bits transmitted (rate normalized) and scale with respect to data path precision (precision scaled) in order to obtain more comprehensive metrics. The analysis shows that the number of MAC's per transmitted information bit (N_MACb) for SCM is greater than that for DMT for all distances of interest in VDSL. The number of MACs per information bit and scaled with respect to precision (B_MAC), i.e., NB_MACb = N_MACb B_MAC, was found to be clearly smaller for SCM in loops shorter than approximately 2 kft. This metric was found to be clearly smaller for DMT in loops longer than approximately 3.25 kft. At all lengths, DMT was found to have smaller memory requirements per information bit, as well as smaller precision-scaled memory requirements.