Precoding aided spatial modulation (PSM) constitutes a flexible closed-loop multiple input multiple output transmission scheme, which benefits from both low cost and low complexity at the receiver side. In PSM, a single receive antenna is activated and a number of bits are conveyed by the index of the receiving antenna, in addition to the bits conveyed by a conventional amplitude-phase modulation symbol. In this paper, bit error rate (BER) of the PSM orthogonal frequency division multiplex (PSM-OFDM) system is investigated and the optimal power allocation between the data and the pilot symbols by minimizing the upper bound for the BER with imperfect channel estimation is derived. Furthermore, we prove that the proposed optimal power allocation scheme can be applied to all generalized linear interpolation techniques with the minimum mean square error channel estimation. Simulation results demonstrate that the proposed optimal power allocation scheme provides significant improvements in terms of the average BER performance for the PSM-OFDM system compared with its equal-power-allocation counterpart.
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