Block diagram of the proposed technique for a 4-element array. The antennas are sampled in a nonsequential order and the information is digitized and transferred to a processing unit. 

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... stands for the unit vector in the direction of the incoming signal and is the velocity of light in free space. According to the traditional phased array theory, it is possible to align the phase of signals received from each antenna, such that a constructive interference is produced. In other words, after alignment, all the signals present the same propagation delay. The economic sampling technique introduced in [7] is based on this principle, but instead of simultaneously sampling all the antennas, only one antenna is considered at a time. The idea is to sample the th antenna during a RF cycle, ( seconds), wait for seconds and continue with the th antenna, wait for seconds, and so forth. A scheme of the sampling process and its transmission to the processing unit is depicted in Fig. 2. The waiting time between the th and th antenna is computed as (2) where stands for the unit vector of the scanned angle. Equation (2) guarantees that the waiting time is positive but shorter than a RF cycle. The variable indicates the number of full cycles that should be subtracted or added in order to assure causality , as well as to avoid sampling the same cycle twice . As a result, cycles are lost between the th and th antenna if is positive, while we would need to wait extra full cycles if it is negative (a lost cycle does not trans- late into information loss since the transmitted signal can be re- covered by applying a LPF ...