Multicarrier transmission over a frequency selective channel implies large differences between the signal to noise ratios (SNR) on the transmitted tones. For independently detected tones, the best performance in terms of average bit error rate (BER) is obtained when conditions are equally good on all subcarriers, as proved by Jensen's inequality. In the case of blindly precoded orthogonal frequency division multiplexing (OFDM), independent minimum square error (MSE) detection over each tone and joint-maximum-likelihood (ML) detections are not equivalent, as tones are no longer independent. Jensen's bound, which is reached by MSE detection, can then be outperformed. However, the computational complexity of joint-ML detection makes it unrealistic in practical systems, In this paper we present a low complexity detection scheme based on Bernoulli-Gaussian (B-G) evaluation over the complex field that outperforms Jensen's MSE bound typically by several dB, without the need for feedback to the transmitter.