A signal processing antenna consisting of an array of modulated scatter elements is described. Time-modulation of array elements for radiation pattern and sidelobe control was initially described more than a half-century ago. Recent decades have produced many advances and extensive documentation for both transmit and receive arrays with time modulated elements. The new article presented here includes both receive and transmit functions in an array of modulated scattering elements. This new approach to time-modulated array experiments greatly simplifies both the physical array elements and the measurement apparatus. An incoming continuous wave (CW) signal in space arrives at the array, is time-modulated by the elements, and then re-radiated in space. The only electrical connections to the individual array elements are low-frequency time-modulation signals. The measurement apparatus consists of a spectrally pure and frequency stable CW source, an audio sine wave modulator with different phases for each element, a microwave receives down-converter to a baseband IF from dc to 24 kHz, and an audio frequency power spectrum analyzer running on a laptop computer. Models that incorporate both the CW signal arrival angle and radiation angles for each modulation and distortion product are presented, along with measurements of 16 element arrays in the anechoic chamber at 2.3 GHz using time-modulation frequencies near 1 kHz. The individual array element time-modulators are nearly ideal RF switches, and the agreement between the new time-modulated scatter array models and measurements is remarkable.