Let’s learn more about beamforming. We dig into some of the key assumptions and terminology, including the difference between time delay and phase shift.
To summarize, beamforming is a method that creates antenna radiation patterns. Arrays constructively add signals in a direction of interest, while cancelling signals in the direction of interference. While a time-based filter combines energy over time, a spatial filter combines or removes energy over its aperture.
Does beamforming work at all distances? Technically, no. Beamforming assumes that signals arrive in a plane rather than a curved wave. This assumes the signal arriving is “far field”, which is typically more than 10 wavelengths from the source. So, on HF, if an interfering signal is less than a half a kilometer away, its wave front will have some curve and beamforming will need some compensation.
Does spacing between array elements really matter? Yes. If spacing is less than λ/4 arrays become inefficient. Patterns become more isotropic and mutual coupling destroys control. If spacing is much more than λ/2, too many side lobes are formed. For most of us, the spacing between antennas used from coherent reception on a city lot will be just fine.
Why is it best to do SDR spatial filtering at baseband? Two reasons. First, you are generally processing only a reduced size bandwidth, so their is less effort. Second, baseband normally uses quadrature data, where phase shifting with complex numbers is relatively straightforward.
Do arrays have to be linear, i.e. elements lined up in a row? No. They can be circular, two-dimensional or three-dimensional.
More About Beamforming – Time Delay versus Phase Shift
Time delay is generally used for larger, wideband arrays. Adjustable time delay steps are independent from operating frequency and bandwidth. This is why you will hear folks who use wideband loop arrays talking about phasing with time delays. For smaller, narrow band systems, however, you use phase shifts to approximate timing differences at a particular frequency. This is called the “narrow band assumption”. (The math shows that phase shift and timing delay are not exactly the same, but close enough for most uses. By narrow band, we mean that bandwidth is only a small fraction of the tuned frequency.)
If you have an SDR processing signals from a wideband array, you must use buffers to compensate for frames of data arriving at a noticeably different time. On the other hand, phase shifting can be accomplished just by multiplying the sample by a complex number which contains amplitude and phase weights. Since audio signals are typically wideband, audio spatial filtering uses time delays. At higher frequencies, phase shifting is more common.
So, if you have your SDR processing signals from two coherent receivers, you can normally do spatial filtering with just mathematics. If you want a deeper experience in learning more about beamforming, read this Digital Beamforming Primer.