Design of antenna arrays for present day requirements has to take into account both mechanical and electrical aspects. Mechanical aspects demand the antennas to have low profile, non-protruding structures, structures compatible to aerodynamic require­ments and so on. Electrical aspects may introduce several constraints either due to. technical reasons or due to readability conditions in practice. Thus, arrays of modern requirements may not fall into the category of linear or planar arrays. Further, due to the nearby environment, the elements will generate complicated individual patterns. These issues necessitate the analysis and synthesis of antenna arrays which are arbi­trary as far as the orientation, position or the element pattern are concerned. Such arrays which may be called arbitrary arrays are being investigated in this thesis. These investigations have been discussed as different aspects as indicated below: Radiation Characteristics of Arbitrary Arrays Radiation fields of an arbitrarily oriented dipole are obtained. Such fields are plotted for typical cases. Further, methods for transforming the electromagnetic fields are discussed. Having obtained the field due to an arbitrary element, the fields due to an arbitrary array are obtained. Factors controlling the radiation fields, like, the curvature in the array and element pattern are investigated. Radiation patterns of circular and cylindrical arrays are plotted. Synthesis of a Side Lobe Topography Requirements of a narrow beam pattern generated by an antenna array are identified. A problem of synthesizing such a pattern using an arbitrary array is formulated. The envelope of the side lobe region which may be called, the side lobe topography (sit), is included in the computation of the covariance matrix. This problem which has been formulated as a problem of minimizing a quadratic function subjected to a system of linear constraints is solved by the method of Lagrangian multipliers. An iterative procedure is used to satisfy all the requirements of the pattern synthesis. The procedure has been validated by synthesizing linear arrays and is used to synthesize circular and parabolic arrays. Patterns with tapered sit, Taylor-like sit have been synthesized. Asymmetric patterns are also synthesized. Role of sit is brought out. Shaped Beam Synthesis Synthesis of shaped broad beams is discussed. Amplitude constraints are formulated. Phase distribution is linked with the phase centre. Quadratic problems thus formu­lated are solved by the Lagrangian method of undetermined multipliers. An iterative procedure is made use of to synthesize flat topped beams as well as cosecant squared-patterns using linear arrays as well as circular arrays. Reasonable excitation dynamic has been obtained. Optimum phase centres obtained by trial and error are made use of. Effects of the Frequency and Excitation on the Synthesized Patterns In general, synthesized patterns can be sensitive towards any specific parameter either excitation or to frequency or any such parameter. Several methods can be used to observe these issues. In this thesis, these effects are also studied. Using a specific array configuration, to synthesize a specified radiation pattern, frequency is changed by 10% from the design frequency and the pattern is computed. Similarly, excitation phase distribution is rounded to the nearest available phase distribution using a digital phase shifter (say 8 bit) and the resulting pattern is computed. Further, excitation dynamic is also controlled by boosting the amplitudes of the array elements which are less than the permissible (i.e. the maximum excitation/allowed dynamic). Effects of these variations are also recorded. It appears that reasonable patterns can be obtained, in spite of significant variations in these parameters in most of the cases. Reconfigurable Arbitrary Arrays It would be very useful if a single array configuration can be used for different ap- plications. This may be either for the different phases of a single application or for different applications that may be required at different times. Attempts are made to synthesize a variety of patterns from a single array. Such arrays which may be called as reconfigurable arrays can be of much use. Obviously, the excitations are different for different patterns. Both narrow beams, as well as shaped broad beams, with different side lobe topographies have been synthesized using a single array.