6.1 Quantized time modulator (QTM)

For appropriate switching operation at pth element, a current pulse with a pulse width of t on <sup>p</sup> is required [2]. The proposed scheme for the periodical switching of the antenna array elements is shown in Figure 13. The QTM has two parts, namely, quantized pulse generator (QPG) and pulse width selector (PWS). In QPG, the consecutive tap delay output line, TAP<sup>i</sup> with i = 1, 2, ..Q, introduces an equal delay of "Tm/Q." The pulse output from the pulse generator (PG) is used to set the

#### Figure 13.

function as defined in Eq. (26), three multi-objective TMAA synthesis problems have been solved in Section 8. It is to be noted that, for different switching techniques, there is a trade-off between sideband level (SBL) and radiated total sideband power (SRp). Reducing the sideband level usually does not guarantee the power reduction. Hence, in that case a power term should be added into cost

In Eq. (26), all the objectives are added with different weighting factors to form a single cost function. In such techniques, it is tedious and difficult to select proper weighting factor for the optimal solution. Improper set of weighting factors strongly effect on achieving the final values of the desired synthesizing parameters and hence on the performance of the optimization algorithm. Generally, some selected best results are presented without mentioning such difficulties. However, these values of the weighting factors are obtained by trial and error method [4]. Though multi-objective evolutionary algorithm (MOEA) [35, 36] can be used to solve such problems, the researchers are not comfortable with it as it has been used rarely as

It is already discussed that time-modulated antenna array synthesis problems are non-convex as well as nonlinear. Therefore, stochastic, global computational techniques are required to solve such problems. In this regard, different populationbased global searching techniques such as DE, SA, GA, PSO, ABC, and multiobjective evolutionary algorithm (MOEA) have been applied successfully to synthesize the desired pattern at the center frequency by suppressing sideband radiation to satisfactorily low levels. However, here the working principle of ABC and its implementation have been presented, and a novel approach to synthesize TMAA is

6. A quantized time modulator (QTM) to synthesize different patterns

In Section 4.5, the quantized aperture size (QAS) time modulation or variable aperture size with quantize on-time duration has been explained. In this section first to realize such time-modulation approach, a time modulator, namely, quantized time modulator (QTM), is presented. Then it is shown that though the quantized on-time duration has been used, however, by selecting a suitable number of quantization levels, the effect of quantization errors on the synthesized patterns can be reduced. In order to select the best possible set of quantized on-time values, the potentiality of artificial bee colony algorithm (ABC) has been exploited as the global searching algorithm. Thus, for the desired patterns, ABC finds the optimum set of unknown parameter values from the discrete search space of QOT. The synthesized results as obtained by using this quantized on-time are compared with that achieved by using continuous search space of on-time [6, 33]. Finally, considering the discrete search space of QOT, a low side lobe level (SLL) flattop pattern with low dynamic range ratio (DRR) is synthesized by utilizing a fully digitally controlled QTM. The major advantage of this approach is that by implementing the "time modulator" either as a discrete component on a printed circuit board or in an integrated circuit (IC), it can generate different patterns in the TMAA system.

function.

discussed.

20

in TMAAs

5.5 Selection of weighting factors

Advances in Array Optimization

5.6 Evolutionary algorithms

compared to single-objective optimization approaches.

The proposed quantized time modulator (QTM).

#### Figure 14.

The wave form of the input and output pulses of different pulse widths that can be obtained at the outputs Oq∀q∈ð Þ 1, … , Q in Figure 13.

flip-flop (FFs) outputs to logic level 1, whereas the delayed pulses from the corresponding tap outputs of the delay line are applied to reset the flip-flop outputs to logic level 0. To avoid the simultaneous appearance of PG output and its delayed version at the S and R inputs of i th flip-flop, respectively, the pulse width less than Tm/Q can be used. The current waveforms of the input pulse applied to the set (S) inputs of the flip-flops and output pulses appeared at the outputs Oq with q = 1, 2, … Q of different flip-flops as shown in Figure 14. Therefore, the QPG, consisting of a pulse generator, simple tapped delay line, and flip-flops, provides the required current pulses with quantized values of t on p .

exploitation is carried out by EBs and OBs. Due to the presence of both exploration and exploitation, ABC becomes a robust search and optimization algorithm. It is to be noted that the objective of the bees in ABC is to find out the location of the best possible food sources within the search space. Hence, the possible locations of the food sources are the possible solutions to this process. But in other swarm intelligence algorithms, e.g., particle swarm optimization (PSO), the locations of the individual agents are the possible solution within the search space. It is assumed that the number of employed bees (NE) and number of onlooker bees are equal in the

In the following steps, the real bee colony behavior into the problem space is

a. Specifying objective: The objective is to synthesize far-field patterns at f0 by simultaneously minimizing SLL, SBLmax, and first null beamwidth (FNBW)

c. Defining the cost function: According to the design parameters discussed above and multiple objectives of the synthesis problem, the cost function is defined as

where δ<sup>h</sup> with h = 0, 1, and 2 are the instantaneous values of different parameters of the desired patterns, while δhd is the desired values of the specific parameters. For all examples as considered in Section 8, δ<sup>0</sup> is the maximum SLL (SLLmax) of the pattern at f0 and δ<sup>1</sup> is the value of SBLmax among the first five sidebands. But, for the first two examples, δ<sup>2</sup> represents FNBW, and, for the third case, it is the ripple level of the flattop pattern for which the positions of δhd and δ<sup>h</sup> are interchanged in the Heaviside step function Hð Þ� . "Wh" is the weighting factor for the corresponding terms. The cost function ψ in Eq. (27) depends on "D," the independent parameters of optimization parameter vector χ. A possible set of the parameter values may be considered as a point in the search space of D dimensional coordinate system. In ABC, the cost function ψ of the optimization problem has resembled with the food sources of the bees and each possible point as its location. The solutions of the optimization problem represent locations of the food sources, whereas the corresponding value of cost function ψ due to each point in its solution set is

d. Initialization: The possible solution,χi, where i = 1, 2 … FN, of an arbitrary number of food sources is generated randomly within the search space. With FN possible locations, each with D dimension is expressed in terms of a [FN � D] matrix.

e. Evaluating the quality of the food source: For all the possible solutions, the values of ψ and the corresponding fitness values, μi, are evaluated.

Wh � Hð Þ� j j� δhd j j δ<sup>h</sup> ð Þ δhd � δ<sup>h</sup>

<sup>2</sup> (27)

b. Parameters to be optimized: Depending on the requirement in an array synthesis problem, suitable independent parameters are chosen as the optimization parameter vector χ. The number of parameters in χ represents

the dimension (D) of the specific optimization problem.

<sup>ψ</sup>ð Þ¼ <sup>χ</sup> <sup>X</sup> h¼2

considered as the quality of the food source:

23

h¼0

colony and also these are equal to the number food sources (FN).

Pattern Synthesis in Time-Modulated Arrays Using Heuristic Approach

DOI: http://dx.doi.org/10.5772/intechopen.89479

7.2 Implementation of ABC

or ripple (R).

implemented:

One of the most important features in TMAAs is to reconfigure different antenna patterns just by changing the on-time sequence across each element. Such a feature can easily be obtained in the proposed QTM employing PWS. The PWS consists of N number of (Q 1) multiplexers and their outputs that are used to modulate antenna element using the quantized values of t on <sup>p</sup> . With appropriate bit combination at the select inputs I0, I1, ... IB of the multiplexers, one of the quantized pulses at the output of QPG is selected to time modulate the corresponding antenna element. Thus, just by using the appropriate combination of the select lines of multiplexers, it is very easy to reconfigure different patterns.
