Tight PEP Lower Bound for Constellation-Rotated Vector-OFDM Under Carrier Frequency Offset and Fast Fading

In this paper, we study pairwise error probability (PEP) of a system employing constellation-rotated vector orthogonal frequency-division multiplexing (CRV-OFDM), which is an enhancement of vector OFDM (V-OFDM) with enhanced diversity, over a frequency-selective channel with both carrier frequency offset (CFO) and Doppler frequency spread. First, we extend the work of Rugini and Banelli, which is known to give a good bit-error rate (BER) approximation for the standard OFDM system only with CFO, to PEP evaluation for CRV-OFDM and discuss its limitations. Then, we discuss the conditionally Gaussian characteristi2cs of the Doppler-induced interference and propose a conditionally Gaussian PEP approximation. Confirming a good match of the conditionally Gaussian PEP approximation and with simulation results, we propose a new semianalytical PEP lower bound. The new lower bound is computationally feasible and is shown by simulation to be tight for small to moderate CFO. Finally, a computationally more feasible approximation of the lower bound is also proposed. Our discussion reveals, as a by-product, why the Gaussian assumption for the Doppler-induced interference works for standard OFDM systems although the assumption is actually incorrect.