An Analysis of Adaptive Retransmission Arrays in a Fading Environment

Adaptive antenna arrays have been the subject of numerous investigations. 1 - 3 In an adaptive transmitting array, the individual element is excited according to information derived from the incident pilot field. For example, in a complex conjugate system, the excitation currents are proportional to the complex conjugate of the incident voltages while the total power radiated is kept constant. In a phase conjugate system, the currents are kept constant while the phases are adjusted according to the conjugate phase of the incident voltages. 1811 1812 T H E BELL SYSTEM T E C H N I C A L J O U R N A L , OCTOBER 1970 In a free-space environment, that is, plane wave incident from a particular direction, it is well known that phase reversal would steer the radiated beam toward the source antenna. Cutler and others 2 have shown how phase reversal can be achieved by frequency conversion of the pilot signal. The role of adaptive retransmission in a multipath fading environment, for example, mobile radio, tropscatter communication, and so on, has received far less attention. Still unanswered is the question of whether the phase conjugate or the complex conjugate retransmission schemes could improve the communication link and reach a stable state. In his work, S. P. Morgan has shown that, in a stationary arbitrary environment, stable state and maximal power transfer can be achieved by complex conjugate retransmission. 3 In this paper, we show that the much simpler phase conjugate system will also reach a stable state.