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# Adaptive Antenna Arrays using Particle Swarm Optimization

Particle Swarm Optimization (PSO) is an algorithm first introduced in 1995 that was an outgrowth of a study of the flocking of birds. In PSO, we have “particles” which move in a semi-random manner in search of the optimum value of a function ƒ. The algorithm requires evaluation of ƒ at the position of each particle and then each particle’s position needs to be updated based on its own history and the history of the entire group. The particles end up swarming around the optimum value of ƒ.

Antenna arrays use the layout of their component antennas to create a desired radiation pattern in a technique known as beamforming. By applying different gains and phase shifts to each antenna, it is possible to point the main lobe, or lobes, of the antenna in a given direction, or directions, place nulls in certain directions, or maximize the overall efficiency of the array. For a fixed Antenna array, meaning that all of its parameters, i.e. its gains and phase shifts, are to be fixed in its design, the determination of the parameters is based on detailed analysis and computation. For an adaptive array, it is necessary for the antennas to be able to determine the optimal parameters in real time when a signal is detected, and adjust continuously if the signal changes.

PSO is a fast and robust optimization algorithm which is well suited to adaptive antenna arrays. The PSO algorithm can be applied to the objective function

 ƒ = w1max(min Pd) + w2min(max Pu) + w3(∑SINRd)

where Pd are the powers of the desired signals, the Pu are the powers of the undesired signals, SINRd are the SINR (Signal to Interference and Noise Ratio) of the desired signals, 0 ≤ wi ≤ 1, and w1+w2+w3=1. The choice of the wi depends on whether it is more important to aim at the desired signals (make w1 large), attenuate the undesired signals (make w2 large), or improve the efficiency (make w3 large). The speed of convergence allows for the array to quickly aim itself in the desired direction. Since the particles swarm around the optimum values after it is found, they will easily detect and adjust to changes that are not too abrupt. But, if an abrupt change is detected, for example if the signal strength or Signal to Noise Ratio (SNR) drops suddenly, the particles can be reseeded, and the algorithm restarted.

The use of PSO in adaptive antenna arrays has many applications due to the portability of so many of our modern antennas. It could be used in wireless ethernet cards to detect and aim the antenna pattern in the direction that provides the best network connection, while blocking the signals of nearby wireless ethernet cards. Similarly, it could be used in cell phones to achieve the best connection while blocking the signals of nearby cell phones.