We demonstrate a simple technique to enhance the signal-to-noise ratio (SNR) in Brillouin optical time-domain analysis sensors by the addition of gain and loss processes. The technique is based on the shift of the pump pulse optical frequency in a double-sideband probe system, so that the gain and loss processes take place at different frequencies. In this manner, the loss and the gain do not cancel each other out, and it makes possible to take advantage of both informations at the same time, obtaining an improvement of 3 dB on the SNR. Furthermore, the technique does not need an optical filtering, so that larger improvement on SNR and a simplification of the setup are obtained. The method is experimentally demonstrated in a 101 km fiber spool, obtaining a measurement uncertainty of 2.6 MHz (2σ) at the worst-contrast position for 2 m spatial resolution. This leads, to the best of our knowledge, to the highest figure-of-merit in a BOTDA without using coding or raman amplification.