Field Guide · algorithm

Also known as: beamforming, spatial filtering, phased-array combining

Beamforming is the technique of combining the outputs of several antenna elements — each with its own phase and amplitude weight — so that signals from a chosen direction add coherently while signals from other directions partly cancel, synthesising a steerable, directional beam from an array of otherwise omnidirectional elements.1 The same weights can place nulls on interferers, so beamforming is spatial filtering: it selects by direction the way a bandpass filter selects by frequency.

wavefront w₁·e^jφ w₂·e^jφ w₃·e^jφ w₄·e^jφ Σ main beamsteered gain
Beamforming applies a phase/amplitude weight to each element and sums them; the weights that align the wavefront's staggered arrivals build a main beam toward the source.

How it works

A plane wave reaches the elements of an array at slightly different times, so each element sees the same signal with a direction-dependent phase shift. Beamforming applies a complex weight wₙ to each element and sums the results. Choose the weights to undo the phase shifts for a target direction and those copies add in phase (array gain ≈ number of elements), while other directions stay misaligned and partially cancel. Steering is just a matter of changing the weights — electronic, instantaneous, and with no moving parts, which is why it is called a phased array.

Variants

  • Delay-and-sum (conventional). Fixed weights that are just the conjugate steering vector for the desired angle. Simple and robust, but its nulls fall wherever the array geometry puts them, not on the interference.
  • Adaptive — MVDR / Capon. Minimum-variance distortionless response computes the weights from the measured covariance matrix: hold unit gain toward the target while minimising total output power, which automatically steers deep nulls onto interferers. Sharper and far better at rejection than delay-and-sum, but sensitive to steering errors and needs a good covariance estimate.
  • Digital vs analog / hybrid. Weights applied in RF phase shifters (analog), fully in DSP after per-element ADCs (digital, most flexible), or a mix (hybrid) as used in millimetre-wave 5G to limit the number of expensive RF chains.
  • Transmit beamforming. The same principle in reverse concentrates radiated power toward a receiver — the basis of massive MIMO.

Relevance to SDR

Beamforming underpins radar, sonar, 5G NR and Wi-Fi massive MIMO, satellite ground stations, and the front end of direction-finding systems, where it complements subspace estimators like MUSIC and ESPRIT that share the same array data. It can also null a strong multipath reflection or a jammer. All of this requires a coherent multi-element array with synchronised per-channel receivers — hardware GopherTrunk does not have. GT is a single-front-end trunking receiver and does no beamforming; the concept is covered here for the broader RF context and its close ties to antenna gain and array processing.

Sources

  1. Beamforming — Wikipedia, on phased combining of array elements to steer gain and nulls. ↩

See also