(7) have all made suggestions to remedy this problem. Their solutions are complicated and require much extra hardware in the already very complicated phase conjugation circuitry. In this paper, new designs of two-tone and multitone uplink signals with frequencies situated at one side of the downlink frequency are suggested. This method removes the abovementioned difficulties and does not require extra components in the phase conjugation circuit. We shall review in our next section the basic principle of phase conjugation and where the problems are in a symmetrically situated two- tone uplink signal. In Sec. Ill, we show how these problems can be circumvented with these new designs. II. DIFFICULTIES WITH SYMMETRICALLY SITUATED TWO-TONE UPLINK SIGNAL A retrodirective array electronically transmits a microwave beam back to the apparent source of a coherent pilot signal. The beam radiated by self-phasing antenna may or may not be coherent across the aperture, but it is coherent when it arrives back at the source. Retrodirectivity is the result of phase conjugation of the pilot signal received by each element of the array. Let the phase of the pilot signal of angular frequency co received by the Ath element of the array at time t be <f>k(t) = o>(t — rk/c), where rfcis the distance from the Ath element to the source. We define the conjugate of <f>k to be Thus the contributions to the field at r = 0 from various elements of the array are all in phase at that point. In the above simple example, the uplink frequency was chosen to be the same as the downlink frequency. This restriction is neither necessary nor desirable and is usually avoided because of input-output isolation problems. When these two frequencies are different, a phase-locked receiver is used. Retrodirectivity can still be achieved — provided that the propagating medium is nondispersive. Due to the fact that single-tone phase-locked receivers are expensive and the ionosphere and transmission lines are dispersive, a two-tone uplink signal with frequencies symmetrically situated around the downlink frequency was suggested with the average of the phases of the uplink tones taken as a good estimate of the phase at the downlink frequency. Such a system lowers the cost and partially removes the difference between the uplink and downlink phases but it also introduces a new problem known as the 77-ambiguity. We shall review these problems here. We shall use the ionosphere as an example to study the effect on the phase conjugation due to the dispersive property of the propagating medium. The dispersion relation for ionosphere with co>>wp is
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