1. Introduction

In any wireless communication system, the antenna is an essential component to transmit or receive a message signal. In many applications such as satellite communication, point-to-point communication, military communication, surveillance, radar, sonar, aircraft, etc., the antenna gain and directivity should be sufficiently high so as to direct most of the antenna-radiated power along a particular direction by reducing the power level (side lobe power) at other directions. A single radiator may not meet such requirements due to its omnidirectional power pattern and high side lobe level (SLL) in the far-field region. Moreover, radiation of huge amount of

transmitter power from a single antenna element needs high-power amplification in the feed network. The high-power amplifier is not easy to design and safe to handle. Therefore, a number of antenna elements are arranged along a line, called linear antenna array (LAA), or in a plane called planer antenna array (PAA). The use of multiple antenna elements in the transmission and reception systems simplifies the power amplifier design problem by reducing the power level per transmitting antenna elements of the arrays. Some other advantages of using antenna arrays are to improve signal fading resistance or deliberately exploit the signal fading; mitigate the interfering signal coming from other directions, adaptive beam forming, and null steering at both transmitter and receiver; and increase system capacity. Due to its high gain and narrow beamwidth, the large antenna arrays also find applications in weather forecast, astronomy, image processing, and biomedical imaging.

2. Theory of time-modulated antenna array (TMAA)

Pattern Synthesis in Time-Modulated Arrays Using Heuristic Approach

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

AF<sup>c</sup> <sup>¼</sup> <sup>X</sup> N

the x-axis as shown in Figure 1.

on

f max

time duration only; otherwise, it will be inactive.

Basic antenna array of N element with inter-element spacing of d0.

sequence t

fm = <sup>1</sup>=

Figure 1.

5

on <sup>p</sup> (0≤ t

fmax (Hz), T<sup>0</sup> < <Tm ≤ <sup>1</sup>

the array factor expression of CAAs can be obtained as in Eq. (1) [1]:

p¼1

Ape <sup>j</sup>Φ<sup>p</sup> e

where ω<sup>0</sup> = 2πf0 = 2π/T0 is the angular frequency in rad/sec for the operating signal of frequency f0 in Hz; T0 is the time period of the operating signal; β = 2π/λ is the wave number with λ being the wavelength; p = 1, … … , N represents the element number of the antenna array; Ap and Ф<sup>p</sup> ∀p ∈½ � 1, N stand for the normalized static excitation amplitudes and phases of the array elements, respectively; and θ is the angle made by the line joining the observing point and the origin with

In order to control the antenna pattern by using the additional degree of freedom, namely, "time," periodically the static excitation amplitudes of the antenna element are time-modulated. The commonly used and simplest way of doing that is to insert high-speed radio-frequency (RF) switches in the feed network, just prior to radiating sources as shown in Figure 2. Each array element is assumed to be connected to the RF switches with individually controlled switching circuits. The switches are periodically "on" and "off" according to a predetermined on-time

Tm, is selected such that if the maximum frequency of the message signal is

which a switch is on, the array element connected to that switch is active for that

<sup>p</sup> ≤Tm)∀p∈½ � 1, N , with time period,Tm. The switching rate,

[14]. Thus, during each period, the on-time duration by

<sup>j</sup>½ � <sup>ω</sup>0tþð Þ <sup>p</sup>�<sup>1</sup> <sup>β</sup>d<sup>0</sup> cos <sup>θ</sup> (1)

Let us consider a linear antenna array of N number of mutually uncoupled isotropic radiators with inter-element spacing d0. The antenna elements are placed along the x-axis with the first element at the origin of the geometrical coordinate system as shown in Figure 1. In the XZ plane (one of the vertical principle plane),

Although the antenna array with uniform excitation amplitude and equally spaced antenna elements is the simplest one for practical implementation and also can be used to synthesize different patterns, due to the high value of peak SLL, it is impractical to use in such applications. In conventional antenna array (CAA) system, the low side lobe pattern is obtained by tapering the static excitation amplitudes. The well-known analytical techniques to taper amplitude distributions in nonuniformly excited antenna arrays are Dolph-Chebyshev (DC) and Taylor series [1]. However, the high dynamic range ratio (DRR) and complex excitation of the antenna elements are the major drawbacks of such CAA synthesis method with nonuniform excitation, because the complex excitation is practically difficult to realize and designing the practical antenna with high DRR of static amplitude tapering provides various errors such as systematic errors and random errors.

Conversely, the ultralow SLL pattern in the far-field of the antenna array can be realized even in uniform amplitude antenna arrays by exploiting "time" as a fourth dimension [2, 3]. The introduction of the additional dimension "time," into the antenna array system, results in time-modulated antenna array (TMAA). By using the fourth degree of freedom, "time" in antenna array system, various errors in realizing the low SLL pattern can be drastically reduced, and error tolerance levels become equivalent to those obtained in conventional antenna array system for the patterns of ordinary SLLs [4, 5]. Yet, the main disadvantage in TMAA is the generation of sideband signals which appeared due to the time modulation of the antenna signals by periodically commutating the antenna elements with the specified modulation frequency. Therefore, time modulation involves with the radiation or reception of electromagnetic energy at different harmonics of the modulation frequency that are termed as sidebands. In some applications where the antenna array is synthesized at center (operating) frequency, sideband signals are not useful. In such cases, sideband signals and associated power losses are suppressed to improve the radiation efficiency at the operating frequency of the antenna array [5, 6]. Presently, it is investigated that sideband signals are also effective in synthesizing multiple patterns and researchers are interested to exploit the same in some specific applications of the modern-day communication systems like harmonic beam forming [7], generation of multibeam radiation pattern [8], beam steering [9, 10], direction finding [11], wireless power transmission [12], etc. The interested readers may refer to Reference [13] for the stateof-the-art overview, applications, and present research trend on time-modulation theory and techniques.

This chapter explains about the fundamental theory and techniques of different time-modulation strategies and such antenna array synthesis methods using optimization algorithms. The parameters involved with the use of optimization techniques and TMAA synthesis problem have also been presented.

Pattern Synthesis in Time-Modulated Arrays Using Heuristic Approach DOI: http://dx.doi.org/10.5772/intechopen.89479
