Several methods and corresponding apparatus reduce peak to average power in signals transmitted in a wireless communications system, particularly with respect to pilot symbols transmitted from a base station to several user stations. A large peak to average amplitude of inserted pilot symbols has been found to result from a common sign chip position that exists in orthogonal codes, such as Walsh codes. In a first embodiment, the Walsh codes are multiplied by a random value of ±1. Under a second embodiment, the common sign chip position is eliminated in each Walsh code. The user station then inserts the missing chip position to regain orthogonality. In a third embodiment, the base station transmits pilot symbols, on a separate pilot channel, in only symbol positions that user stations expect to find pilot symbols. Under a fourth embodiment, each Walsh code is randomly shifted.