Abstract: A method for generating minimum shift keying (MSK) modulation signals with relatively reduced energy sidelobes relative to known methods. In one embodiment, a second derivative of the phase waveform is taken and convolved with a selectable smoothing function and integrated twice to generate a smooth phase waveform S2D.sub.-- MSK (i)=where .o slashed. (i)=.pi. i d(i)/2T. In the alternate embodiment, the sidelobe energy can be varied by simply changing the smoothing function, which can be stored in a lookup table. In the embodiment, the MSK modulation signal has a constant amplitude envelope allowing it to be transmitted using class C amplifiers. Since the embodiment provides continuous phase derivatives, the frequency and thus the sidelobe energy is sufficiently reduced to minimize interference with cosite equipment and nearby communication channels bands.

Abstract: An input signal is multiplied by a reference and quadrature signal and the two output signals are integrated and multiplied by a ramp signal, having a period equal to the maximum period of the input signal, and integrated to provide four output signals. The integrated product of the input, reference and ramp signals is multiplied by the integrated product of the input and quadrature signals and the product is subtracted from the product signal of the integrated product of the input and reference signals multiplied by the integrated product of the input, quadrature and ramp signals. The difference output signal is the gradient of the envelope of the maximum posterior-probability estimate of the frequency of the input signal.

Abstract: A system for virtual time base direct synchronization in which a hopping sequence signal grossly synchronized with a received hopped base band has a fine synchronization correction performed by a virtual time shift of the hopping reference through first derivative subtraction of the phase of a hopped carrier signal, which in effect brings the hopping sequence signal into time alignment with the received hopped base band.

Abstract: An array of signals is adapted and dithered by use of a weight signal, a gradient signal with a carrier at a first frequency and an orthogonal sequence signal with a carrier at a second frequency, the dithered signals are then operated on to extract an output signal, a gradient signal, and a weight signal, which gradient and weight signals along with a generated orthogonal sequence signal, are then fed back for use in the dithering process. The carriers at different frequencies provide separability of predetermined components during the operation.

Abstract: An adaptive antenna array including a main antenna and at least one auxiliary antenna with a plurality of weight adjusting channels and circuitry for adjusting the gain of each channel periodically switched into each channel, and each channel further including memory means for continued gradient control during period that the circuit is connected to other channels.