Beamforming - Wikiparency

# Beamforming **Beamforming**, also called spatial filtering, is a signal-processing technique that combines the outputs of several elements in a sensor array so that a signal arriving from one chosen direction adds up constructively while signals arriving from other directions are attenuated by destructive interference. The same combining can run in reverse on transmit, weighting what each element sends so that the array's radiated energy concentrates in one direction instead of spreading evenly in all of them. A three.js microsim elsewhere on this site renders a variant of the array-factor sketch built for [[Antenna_array|antenna arrays]], adding a deliberate interferer so the reader can watch a null, and not only the main beam, being steered onto a chosen angle. Because the underlying idea only needs an array of sensors and a way to combine their outputs with adjustable weights, beamforming appears wherever such an array exists: in [[Radar|radar]] and [[Sonar|sonar]] antennas and hydrophone arrays, in cellular and satellite radio links, in seismic arrays that locate the source of a tremor, in radio telescopes built from many small dishes, and in microphone arrays that isolate one talker's voice from the surrounding room. Adaptive beamforming extends the same principle by recomputing the weights from the data itself, most often to minimise output power subject to keeping the desired direction's gain fixed, which lets an array place a deep, narrow null exactly on a moving interferer rather than accepting whatever sidelobe level a fixed set of weights happens to leave there. ## Techniques Every beamformer is, at its core, a set of complex weights, one per element, that are multiplied onto that element's signal before all the weighted signals are summed. The simplest scheme, delay-and-sum beamforming, does nothing more than shift each element's signal in time by the amount a plane wave from the desired direction would take to reach it, so that the wanted signal lines up and adds coherently across the array while an interferer from another direction, having been shifted by the wrong amount for its own arrival angle, adds only partially or cancels. A narrowband version of the same idea uses a phase shift rather than a true time delay, since shifting a narrowband signal's phase is equivalent to shifting it in time by a fraction of one cycle; this is the same combining, expressed in the frequency domain rather than the time domain, that gives the array its overall [[Radiation_pattern|radiation pattern]]. The gain such combining adds over a single element, expressed as the array's [[Directivity|directivity]], is a standard antenna figure of merit equal to how much more power the array concentrates in its peak direction than an idealised source radiating equally in every direction would.[^ell-directivity] The same coherent-combination principle, applied not to many elements at one instant but to many positions a single moving antenna occupies over time, is the basis of [[Synthetic-aperture_radar|synthetic-aperture radar]], which synthesises a large effective aperture from a small one carried along a flight path. ## Sonar beamforming requirements Underwater sound travels roughly two hundred thousand times slower than radio waves, and that single fact changes what a beamformer must do. A sonar signal's bandwidth is often a large fraction of its centre frequency, so a phase shift computed at one frequency no longer approximates the true time delay across the rest of the band, and a sonar beamformer generally cannot take the phase-only shortcut a narrowband radio array relies on; it must apply an actual time delay to each channel instead, or accept the resulting loss of gain and resolution. Sonar arrays also tend to be physically large relative to the wavelengths they use, since a useful sonar wavelength in water is measured in centimetres to metres rather than millimetres, so a towed line array trailed behind a ship or [[Submarine|submarine]] can span many wavelengths and, in return for its length, resolve bearing far more finely than a compact array of the same element count could. Self-noise from the towing platform's own machinery and flow noise along the array further complicate the problem, since the interference a sonar beamformer must reject is often generated by the very vessel carrying the array rather than by an external jammer. ## Schemes Beamformers divide broadly into fixed and adaptive schemes. A fixed, or conventional, beamformer uses weights computed in advance from the array's geometry and the desired look direction alone, tapering the outer elements with a [[Window_function|window function]] to trade a wider main lobe for lower sidelobes in exactly the way a window trades frequency resolution for reduced spectral leakage in other signal-processing contexts. An adaptive beamformer instead recomputes its weights continuously from the received data, most commonly by minimising total output power subject to a constraint that the gain toward the desired direction stay fixed, which automatically steers a deep null toward whatever interference is actually present rather than toward wherever a designer guessed it might appear. That adaptivity is essential to [[Passive_radar|passive radar]], which listens for a target's echo of a broadcast transmitter it does not control and must null the much stronger signal arriving directly from that transmitter before the faint echo can be seen at all. Frequency-domain implementations typically split the incoming signal into narrow sub-bands with a [[Fast_Fourier_transform|fast Fourier transform]] and apply an independent, narrowband set of weights in each sub-band, recombining the results afterward. ## Evolved beamformer Some array geometries and design goals, particularly irregular or sparse arrays and beamformers required to satisfy several competing goals such as a narrow main lobe, a deep null at a specific angle and a low general sidelobe floor all at once, do not reduce to a closed-form solution for the weights. Treating the weight vector as a candidate solution and searching for one that scores well against all the stated goals together turns the design problem into an optimisation that a [[Genetic_algorithm|genetic algorithm]] or a related evolutionary search can attack directly, evaluating many candidate weight sets, keeping and recombining the better performers, and repeating until the population converges on weights no closed-form design would have produced as directly. Such an evolved beamformer trades the guarantee of an analytic method for the ability to target an arbitrary, hand-specified combination of pattern requirements. ## History in wireless communication standards Cellular systems moved from sectorised, fixed-pattern base-station antennas toward antennas capable of forming a narrower beam per user only gradually. Early smart-antenna proposals for second- and third-generation networks promised more capacity per cell but saw limited deployment, held back by the cost of the extra radio hardware every additional antenna element demanded.[^cn-3g-smart-antenna] Beamforming became a mainstream feature only once standards began to specify it directly: successive releases of the Long-Term Evolution standard added transmit modes that steer energy toward a specific handset, and fifth-generation networks operating at millimetre-wave frequencies rely on beamforming as a practical necessity rather than an optional enhancement, since the path loss at those frequencies would otherwise leave too little signal to detect at any useful range.[^cn-5g-standard] The same pressure that pushed wireless standards toward beamforming, more antennas doing more signal processing rather than more transmitter power, is the same trend behind [[MIMO|MIMO]] systems, which use an array's multiple elements to carry independent data streams rather than, or in addition to, a single steered beam. ## Digital, analog, and hybrid An array can form its beam in three different places in the signal chain. Analog beamforming applies a phase shift to each element in the radio-frequency hardware itself, before the signals are combined and passed to a single [[Analog-to-digital_converter|analog-to-digital converter]]; it needs only one receiver chain regardless of element count, which keeps cost and power low, at the price of forming only one beam at a time. Digital beamforming instead gives every element its own receiver chain and its own converter, so that combining happens entirely in software after every element's signal is already a stream of numbers; this is far more flexible, since the same digitised data can be combined many different ways at once to form several simultaneous beams, but the hardware cost and power draw scale with the number of elements rather than staying fixed. Hybrid beamforming splits the difference, grouping elements into sub-arrays that are combined by analog phase shifters and then digitising only the smaller number of sub-array outputs, and it is the architecture most large millimetre-wave [[Phased_array|phased arrays]] use for exactly that reason: full digital beamforming at hundreds of elements and multi-gigahertz bandwidths would need more converters and more power than is practical, while a purely analog array could not form the several simultaneous beams a base station or a [[Radio_receiver|radio receiver]] serving many users at once requires. ## For speech audio A small array of microphones can beamform on a talker's voice in exactly the same way a much larger array beamforms on a radio or sonar source, steering a spatial null toward a competing talker or a noise source and a peak toward the microphone array's target direction. Hands-free telephones, video-conferencing units and voice-controlled smart speakers commonly use this to improve the signal reaching a speech recogniser or a remote listener in a noisy or reverberant room, and hearing aids use a small, tightly spaced microphone array on the same principle to improve a wearer's ability to follow one voice in a crowded space, a benefit audiology studies have reported as measurably improving speech understanding in noise for many users.[^cn-hearing-aid] Because a room's reflections scatter sound back toward the array from many directions besides the true one, acoustic beamforming for speech is generally combined with separate noise-suppression and echo-cancellation stages rather than relied on alone, a layering also common in the [[Acoustics|acoustics]] of active noise control. ## Microsims No sketch of this article's own runs on this page. The three.js microsim named above adapts the array-factor sketch built for antenna arrays, adding a fixed interferer so the reader can watch the array's null, not only its main lobe, track onto a chosen angle as the weights change, the adaptive scheme described above. Two neighbouring sketches on the site show pieces of the same physics from a single-element point of view rather than an array's. The Sonar sketch draws the outward ping and returning echo of a single active sonar and computes the sonar equation's detection budget for one target at a time, the same range and detection problem an array of hydrophones beamforms to improve by adding gain against self-noise and interference. The Radar sketch shows a single rotating beam rather than an electronically steered one, and prints the Doppler shift of a moving target directly in its diagnostics panel. *Try:* In the [[Sonar]] sketch, lengthen the ping and watch the detection flag in the sonar equation's readout change as the transmission-loss budget shifts, the same signal-to-noise budget that a beamformer's array gain, not modelled in that single-element sketch, is added to improve. *Try:* In the [[Radar]] sketch, note how one antenna beam sweeps mechanically through every bearing in turn; an electronically beamformed array instead points several such beams at once, with no motor and no sweep to wait for. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Beamforming) : [Wikitube](https://en.wikitube.io/wiki/Beamforming) Skeleton mirrored at revision 1365970552. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Antenna_array]] - [[Phased_array]] - [[MIMO]] - [[Radar]] - [[Sonar]] - [[Monopulse_radar]] - [[Synthetic-aperture_radar]] - [[Passive_radar]] ## References The array-factor combining that underlies delay-and-sum and phase-shift beamforming, the trade between window tapering and sidelobe level, and the split between analog, digital and hybrid architectures are standard antenna and signal-processing material and are not separately footnoted here, per the Wikitube style guide's §6.1. Page numbers in the footnotes below are PDF pages of the open editions listed under Further reading. [^ell-directivity]: Ellingson, S. *Radio Systems Engineering, Revised First Edition*. 2023, pp. 104-105 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^cn-3g-smart-antenna]: Citation needed: a named second- or third-generation cellular standard's smart-antenna option and its documented deployment history would support the specific claim of limited uptake made here. [^cn-5g-standard]: Citation needed: the specific 3GPP release introducing beamformed transmit modes for LTE, and the millimetre-wave link-budget analysis motivating mandatory beamforming in fifth-generation New Radio, would support the dates and the necessity claimed here. [^cn-hearing-aid]: Citation needed: a specific peer-reviewed audiology study quantifying the speech-in-noise benefit of microphone-array beamforming in hearing aids would support the claim made here. **Further reading** — the open textbooks this article draws on, since the pair carries no separate Further reading heading of its own: - Christian Tiberius; Max Mulder. *Engineering Signal Analysis: From Fourier to filtering: Theory*. 2026. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/engineering-signal-analysis-from-fourier-to-filtering-theory . CC BY. - Don Johnson. *Fundamentals of Electrical Engineering I*. 2014. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 . CC BY. - Michael Stiber; Bilin Stiber; Eric Larson. *Signal Computing: Digital Signals in the Software Domain*. 2020. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/signal-computing-digital-signals-in-the-software-domain . CC BY-SA. - Allen Downey. *Think DSP: Digital Signal Processing in Python*. 2012. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/think-dsp-digital-signal-processing-in-python . CC BY-NC. - Steven Ellingson. *Radio Systems Engineering, Revised First Edition*. 2023. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. - John Dyer; Chad Davis. *Measurement and Instrumentation: An Introduction to Concepts and Methods, 1st Edition*. 2020. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/measurement-and-instrumentation-an-introduction-to-concepts-and-methods . CC BY-NC-SA. ## External links This article carries no p5.js or three.js sketch of its own in this pass; the three.js microsim described under Microsims is built and linked separately as part of the Radar portal's shared framework build, not hosted by this article.