Adaptive Beam Forming

An adaptive beam former is a device that is able to separate signals co-located in the frequency band but separated in the spatial domain. This provides a means for separating the desired signal from interfering signals. An adaptive beam former is able to automatically optimise the array pattern by adjusting the elemental control weights until a prescribed objective function is satisfied. An algorithm designed for that purpose specifies the means by which the optimisation is achieved. These devices use far more of the information available at the antenna aperture than does a conventional beamformer.

Figure 7.4: A two element adaptive array for interference suppression. The array simultaneously accepts a signal coming from the zenith, while rejecting an interfering signal $30^o$ from the zenith by a suitable choice of the weights $W_i$.

The procedure used for steering and modifying an array's beam pattern in order to enhance the reception of a desired signal, while simultaneously suppressing interfering signals through complex weight selection is illustrated by the following example. Let us consider the array shown in Figure 7.4. The array consists of two antennas with a spacing of $\lambda/2$. Let the signal $S(t)$ arriving from a radio source at zenith is the desired signal. Let $I(t)$ be an interfering signal arriving from a direction $\theta = \pi/6$ radians. The signal from each element is multiplied by a variable complex weight $(w_1, w_2)$ and the weighted signals are then summed to form the array output. The array output due to the desired signal is

$$Y(t) = A~e^{j2\pi ft} [w_1+w_2].$$ (7.6.1)

For the $Y(t)$ to be equal to $S(t)$, it is necessary that

$$RP [w_1] + RP [w_2] = 1$$ (7.6.2)

and

$$IP [w_1] + IP [w_2] = 0.$$ (7.6.3)

Where RP and IP denote real and imaginary parts of the complex weights. The interfering signal arrives at the element 2 with a phase lead of $\pi/2$ with respect to the element 1. Consequently the array output due to the interfering signal is given by

$$Y_i(t) = [N e^{j2\pi ft}] w_1+[N e^{j2\pi ft + \pi/2}] w_2.$$ (7.6.4)

For the array response to the interference to be zero, it is necessary that

$$RP [w_1] + RP [jw_2] = 0$$ (7.6.5)

and

$$IP [w_2] + IP [jw_2] = 0.$$ (7.6.6)

The requirement that the array has to respond to only the radio source and not to the interfering signal leads to the solution

$$w_1 = 1/2 - j 1/2$$ (7.6.7)

and

$$w_2 = 1/2 + j 1/2.$$ (7.6.8)

With these weights, the array will accept the desired signal while simultaneously rejecting the interference.

The method used in the above example exploits the fact that there is only one directional interference source and uses the a priori information concerning the frequency and the directions of both of the signals. A more practical processor should not require such a detailed a priori information about the location, number and nature of sources. But this example has demonstrated that a system consisting of an array, which is configured with complex weights, provides numerous possibilities for realising array system objectives. We need to only develop a practical processor for carrying out the complex weight adjustment. In such a processor the choice of the weighting will be based on the statistics of the signal of interest received at the array. Basically the objective is to optimise the beamformer response with respect to a prescribed criterion, so that the output contains minimal contribution from the interfering signal.

There can be no doubt about the worsening observing situation in radio astronomy due to the increased use of frequency space for communications. But a pragmatic view is that it is hopeless to resist the increased use of frequency space by others and we must learn to live with it. The saving grace is that the requirements of mobile cellular, satellite and personal communication services systems are pushing the advancement in technology to provide increasingly faster and less expensive digital hardware. The present trend is to replace the analog functions of a radio receiver with software or digital hardware. The ultimate goal is to directly digitise the RF signal at the output of the receiving antenna and then implement the rest of the radio functions in either digital hardware or software. Trends have evolved toward this goal by incorporating digitisation closer and closer to the antenna at increasingly higher frequencies and wider bandwidths. It is appropriate that the radio astronomer uses this emerging technology to make the future radio telescopes interference free. Adaptive arrays hold the key to this endeavour.