In this paper we investigate the use of bipolar Barker sequences for high-speed wireless communication systems based on Parallel Sequence Spread Spectrum (PSSS) modulation. To improve bit error rate (BER) performance for PSSS, we propose the use of either median detection at the receiver or DC-offset correction at the transmitter. Both techniques cancel the influence of cyclic-autocorrelation sidelobes that occur in the correlator at the receiver. The simulation results reveal that PSSS based on Barker codes of length 13 outperforms PSSS with m-sequences by 2.5 dB, if one of the abovementioned techniques is applied. The novelty of the proposed DC-correction method lies in a simple hardware realization and very low complexity. All modifications are performed in the PSSS transmitter, which is significantly less complex than the PSSS receiver. Thus, this algorithm improves PSSS BER and keeps the balance between the transmitter and receiver complexity.