Abstract: A system and method are disclosed for synchronizning the linear PN sequences contained in a received spread spectrum signal, characterized by the provision of a resident PN generator that is responsive to the chip rate clock for producing a replica of the PN sequence with arbitrary phase, a running matrix inverse of the matrix (R) formed by n successive observations of the register of the resident generator, and a matrix vector product device for multiplying the running inverse by a column vector of noisy chips, thereby to obtain a plurality of estimates of the phase vector. These estimates are smoothed and averaged to produce the smoothed phase vector (c.sub.j) that is applied to one input of a dot product device that operates in conjunction with the contents of the shift register of the resident generator to produce the properly phased PN sequence, which sequence is then supplied to despreading means for combining the noisy chips with the properly phased PN sequence.

Abstract: A method of transmitting binary data from one station to another via a troposcatter medium, characterized in that the data is converted to parallel form so that the bits produce distinctive pairs of sine and cosine harmonics having different frequencies, which harmonics are summed in two separated channels that are modulated by rf sine and cosine modulating signals that are combined and transmitted to the receiver, together with a test signal that was periodically inserted in the parallel bits. The receiver supplies the signals to banks of matched filters that produce a first set of signal estimates from which the test signal is detected. A matrix system responsive to the test signal produces from the first set of estimates a second set of signal estimates having lower distortion than the first set.