Beam Steering Improvements Using Non-ideal Phase Fronts with a Minimal Number of Control Bits

As active electronically steerable arrays (AESAs) become more prominent, a new paradigm of assigning bits to a set of digital phase shifters is proposed. It is well known that a modern day digital phase shifter which is associated with each transmit/receive (TR) module typically relies on four to six bits. Each of these phase shifters provide a desired resolution of 22.5 degrees to 5.625 degrees, respectively. When an array is steered in one of the canonical angles of the phase shifters, the error between the desired angle and the actual angle is essentially zero. For example, steering 11.25 degrees with the family of six bit phase shifters would be ideal. However, when an array is requested to steer in a non-canonical direction, say 15 degrees, then errors will occur. These errors occur because each of the phase shifters receive the same bit assignments. In other words, the shifters operate independently and improvements will occur if the set of shifters operate collectively. In particular this letter seeks the solution for this problem: for a set of N phase shifters, each defined by B bits, an optimal approach could be derived to distribute the N*B bits so that the array performance is maximized. In order to achieve this, the simulated annealing algorithm is used to search for a nonlinear phase gradient solution that optimizes the maximum sidelobe level performance given a certain beamsteering angle. Properties of a phased array antenna can be derived from the AF, which is a model of an array's electric field pattern in the far field. The AF is derived from a “phase front”. The phase front results in a set of phase offsets across the array in which the values would be assigned to a real phased array system's set of digital phase shifters. Given a phase shifter's finite degrees of freedom (i.e. bits), the phase front will be quantized and errors will ensue when phase offsets are rounded to the nearest acceptable value. By modifying the error function of the quantized phase gradient, a new phase front can be developed to create nonlineararities that can be shown to remove the periodic property of the quantized phase front and therefore mitigate quantization lobes. The theoretical phase front is a reflection about the center of the array. It will be shown in this letter that maximum sidelobe levels can be reduced by modifying this phase gradient, thereby removing the symmetric property. Disrupting this attribute will also increase sidelobe levels for angles far away from the steering angle. Nonetheless, this allows a possible phase gradient solution that sacrifices higher average sidelobe levels for lower maximum sidelobe levels. In order to test this approach, a method has been developed that searches the space of all valid phase offset combinations. The simulated annealing algorithm is used here to search for a nonlinear phase gradient solution that optimizes the maximum sidelobe level performance given a certain beamsteering angle. The optimal phase gradient searching algorithm is shown to perform well when quantized phase fronts for a given steering angle do not produce maximum sidelobe levels near the theoretical maximum of 13.2 dB down (a result of the rectangular amplitude window function). It has been shown that the linear, quantized phase front will incur errors that are dependent on beam steering angle. The pointing errors created with the optimal, non-linear, quantized phase fronts are not dependent on steering angle and are controlled by the randomly introduced phase offsets. Additionally, these errors can be dependent on the number of elements in the array, N. The beam steering capability of phase array radars has been analyzed and improved. A new method of assigning phase shifter values in phased array radars was developed by analyzing the array factor for multiple steering angles. It has been shown that array sidelobe levels can be reduced when using a minimal number of phase shifter degrees of freedom (i.e. bits) while the average sidelobe levels are increased. The real beam steering angle error can increase as well with small array sizes. The main beam width was shown to not be affected by the technique. This paper's proposed approach can always achieve an improvement greater than or equal to traditional beamsteering methods. The proposed method is appealing due to the software controlled architecture that assigns values to digital phase shifter hardware. Therefore, the cost of implementation into existing systems would be minimal.