The proportional relationship between the adaptive array under directional constraint and the adaptive array under least-mean-square-error criterion is proved for narrow-banded signal under the condition that the incident direction of the desired signal is identical with the constraint direction.

In this paper, we analyze the convergence behavior of the CMA (Constant Modulus Algorithm) adaptive array working under the steepest decent method, and investigate how to achieve the highest possible output SINR (Signal to Interference plus Noise Ratio). In multipath radio environments, CMA sometimes suppresses the desired signal (stronger one) and selects to receive the interference (the weaker one) resulting in the low output SINR. This is one of the problems met in an optimization system under a nonlinear control equation where there are two or more local minima of the cost function and the final state depends on the initial condition. The study can be done only numerically by starting from various initial values. In our analysis of the CMA adaptive array in multipath radio environments, we will assume that there are two waves which are radiated from the same source and try to find out what conditions may affect the convergence behavior. In this process, we discover the effect of the neglected factor by the previous papers and revise the initial condition to guarantee the reception of the desirable wave. In conclusion, we propose the prescription of the initial weights of the array elements as well as the choice of preferable arrays.

The authors implemented a directionally-constrained adaptive array system in an audio-frequency range. This system has a good prospect of applications since it does not require a rigorous a priori knowledge of the desired signal. Its algorithm contains matrix calculation, for which some technique has to be devised in implementation. For this, data are sampled and A-D converted so that the necessary processing for feedback control may be done by a microcomputer in digital form. The signal path remains in analog form, which will allow us to extend the system to higher frequency range. The performance of the system is demonstrated through the experiments. Effects of hardware errors are found: (1) Nulling behavior against the interference is not affected at all by virtue of the feedback control. (2) A little deviation from the constrained response to the desired signal is perceived. The behavior against a wideband interference is investigated analytically and experimentally. It was found that the final SIR becomes lower with wider frequency bandwidth.

A symptotic equivalency between the adaptive array under directional constraint and the synthesized array with maximum directive gain subject to null constraint is proved analytically. (The analytical expression of the solution of the latter which has only been treated numerically is derived here.) Method of analysis is based on the orthogonal projection of a vector in the multidimensional space with properly chosen base. The results of adaptive and conventional methods are given in closed forms and their proportional relationship is shown obviously. Based on the characteristics of the adaptive array which gives the maximum output signal-to-noise ratio, its application to the pattern synthesis problem is investigated for the environment of various combinations of the interference and internal noise. Special emphasis is laid upon the case of super-gain phenomenon, where the angular separation between the desired signal and interference is very close. Even in this case, the adaptive technique does not require any introduction of additional parameters like Q-factor, but guarantees the optimum solution by virtue of its guiding principle. It is also shown that the adaptive technique always gives higher output signal-to-noise ratio than the conventional synthesis method. Some numerical examples are presented to prove the discussions clearly.

An adaptive antenna array system with phase-only control and under the principle of DCMP (directionally constrained minimization of power) is discussed. A new penalty function is introduced for the system in order to take into consideration the protection of the desired signal while minimizing the unwanted interference and/or noise. Because of the analytical limitation, computer simulation experiments are extensively carried out. The constraint coefficient that is the most important factor of the penalty function is especially investigated, and the optimum choice is given. It is also shown that the theoretical consideration leads to the same value. Finally, the quantization of phaseshifters is attempted, and the limit of its performance is shown.

The adaptive array under the principle of directionally constrained minimization of power (DCMP) operates to minimize the output power under the constraint to maintain the specified response to the direction of the desired signal. This constraint depends on the a priori knowledge of the relation of the output at each element of the array with respect to the desired signal. If this setting contains some error, the desired signal will be taken for the unwanted one and hence become a target of suppression. To prevent this malfunction, we introduce a modified system of DCMP, which is named the tamed adaptive array, and demonstrate its effectiveness against such imperfect constraint. We consider two examples that cause such effects, i.e., the mutual coupling and random input errors, and numerical results show that the tamed system is robust against those influences.