摘要： Orthogonal frequency division multiplexing (OFDM) and single-carrier frequency domain equalization (SC-FDE) are two commonly adopted modulation schemes for frequency-selective channels. Compared to SC-FDE, OFDM generally achieves higher data rates, but at the cost of higher transmit signal peak-to-average power ratio (PAPR) that leads to lower power amplifier efficiency. This paper studies a multi-group single-carrier modulation scheme, termed flexible multi-group single-carrier (FMG-SC), which encapsulates both OFDM and SC-FDE as special cases, thus achieving more flexible rate-PAPR trade-offs between them. Specifically, in FMG-SC, the total bandwidth is divided into a set of orthogonal subcarriers, which, based on the channel gains, are flexibly mapped to multiple non-overlapping groups, and SC-FDE is applied over each group independently to send multiple data streams in parallel. We investigate the joint subcarrier grouping and power allocation optimization problem to maximize the achievable rate of our proposed FMG-SC scheme for both the cases with Gaussian signaling and with practical modulation constellation (e.g., quadrature amplitude modulation (QAM)), respectively. For both cases, the optimization problem is non-convex in general, for which we propose a two-step approach for finding a high-quality approximate solution efficiently. First, with any given subcarrier grouping, we show that the optimal power allocation can be obtained via convex optimization techniques. Second, with fixed power allocation, we propose low-complexity algorithms for the subcarrier grouping design catering to the SC-FDE receiver. Numerical results show that our proposed algorithms perform close to the optimal solution obtained via exhaustive search over all subcarrier groupings, yet with substantially reduced complexity. Moreover, the achievable rate of our proposed FMG-SC scheme with Gaussian signaling approaches the OFDM channel capacity and significantly outperforms that of SC-FDE. Furthermore, with practical modulation constellation, numerical results show that our proposed FMG-SC scheme greatly outperforms the existing single-carrier frequency division multiple access (SC-FDMA) in terms of achievable rate, but with moderately increased PAPR.