Beamforming or spatial filtering is a signal processing technique used in sensor arrays for directional signal transmission or reception. This is achieved by combining elements in a phased array in such a way that signals at particular angles experience constructive interference while others experience destructive interference. Beamforming can be used at both the transmitting and receiving ends in order to achieve spatial selectivity. The improvement compared with omnidirectional reception/transmission is known as the receive/transmit gain (or loss).
Beamforming can be used for radio or sound waves. It has found numerous applications in radar, sonar, seismology, wireless communications, radio astronomy, acoustics, and biomedicine. Adaptive beamforming is used to detect and estimate the signal-of-interest at the output of a sensor array by means of optimal (e.g., least-squares) spatial filtering and interference rejection.
Beamforming techniques 
To change the directionality of the array when transmitting, a beamformer controls the phase and relative amplitude of the signal at each transmitter, in order to create a pattern of constructive and destructive interference in the wavefront. When receiving, information from different sensors is combined in a way where the expected pattern of radiation is preferentially observed.
For example in sonar, to send a sharp pulse of underwater sound towards a ship in the distance, simply transmitting that sharp pulse from every sonar projector in an array simultaneously fails because the ship will first hear the pulse from the speaker that happens to be nearest the ship, then later pulses from speakers that happen to be the further from the ship. The beamforming technique involves sending the pulse from each projector at slightly different times (the projector closest to the ship last), so that every pulse hits the ship at exactly the same time, producing the effect of a single strong pulse from a single powerful projector. The same thing can be carried out in air using loudspeakers, or in radar/radio using antennas.
In passive sonar, and in reception in active sonar, the beamforming technique involves combining delayed signals from each hydrophone at slightly different times (the hydrophone closest to the target will be combined after the longest delay), so that every signal reaches the output at exactly the same time, making one loud signal, as if the signal came from a single, very sensitive hydrophone. Receive beamforming can also be used with microphones or radar antennas.
With narrow-band systems the time delay is equivalent to a "phase shift", so in this case the array of antennas, each one shifted a slightly different amount, is called a phased array. A narrow band system, typical of radars, is one where the bandwidth is only a small fraction of the centre frequency. With wide band systems this approximation no longer holds, which is typical in sonars.
In the receive beamformer the signal from each antenna may be amplified by a different "weight." Different weighting patterns (e.g., Dolph-Chebyshev) can be used to achieve the desired sensitivity patterns. A main lobe is produced together with nulls and sidelobes. As well as controlling the main lobe width (the beam) and the sidelobe levels, the position of a null can be controlled. This is useful to ignore noise or jammers in one particular direction, while listening for events in other directions. A similar result can be obtained on transmission.
For the full mathematics on directing beams using amplitude and phase shifts, see the mathematical section in phased array.
Beamforming techniques can be broadly divided into two categories:
- conventional (fixed or switched beam) beamformers
- adaptive beamformers or phased array
- Desired signal maximization mode
- Interference signal minimization or cancellation mode
Conventional beamformers use a fixed set of weightings and time-delays (or phasings) to combine the signals from the sensors in the array, primarily using only information about the location of the sensors in space and the wave directions of interest. In contrast, adaptive beamforming techniques generally combine this information with properties of the signals actually received by the array, typically to improve rejection of unwanted signals from other directions. This process may be carried out in either the time or the frequency domain.
As the name indicates, an adaptive beamformer is able to automatically adapt its response to different situations. Some criterion has to be set up to allow the adaption to proceed such as minimising the total noise output. Because of the variation of noise with frequency, in wide band systems it may be desirable to carry out the process in the frequency domain.
Beamforming can be computationally intensive. Sonar phased array has a data rate low enough that it can be processed in real-time in software, which is flexible enough to transmit and/or receive in several directions at once. In contrast, radar phased array has a data rate so high that it usually requires dedicated hardware processing, which is hard-wired to transmit and/or receive in only one direction at a time. However, newer field programmable gate arrays are fast enough to handle radar data in real-time, and can be quickly re-programmed like software, blurring the hardware/software distinction.
Sonar beamforming requirements 
Sonar beamforming implementation is similar in general technique but varies significantly in detail compared to electromagnetic system beamforming implementation. Sonar applications vary from 1 Hz to as high as 2 MHz, and array elements may be few and large, or number in the hundreds yet very small. This will shift sonar beamforming design efforts significantly between demands of such system components as the "front end" (transducers, preamps and digitizers) and the actual beamformer computational hardware downstream. High frequency, focused beam, multi-element imaging-search sonars and acoustic cameras often implement fifth-order spatial processing that places strains equivalent to Aegis radar demands on the processors.
Many sonar systems, such as on torpedoes, are made up of arrays of up to 100 elements that must accomplish beam steering over a 100 degree field of view and work in both active and passive modes.
Sonar arrays are used both actively and passively in 1, 2, and 3 dimensional arrays.
- 1 dimensional "line" arrays are usually in multi-element passive systems towed behind ships and in single or multi-element side scan sonar.
- 2 dimensional "planar" arrays are common in active/passive ship hull mounted sonars and some side-scan sonar.
- 3 dimensional spherical and cylindrical arrays are used in 'sonar domes' in the modern submarine and ships.
Sonar differs from radar in that in some applications such as wide-area-search all directions often need to be listened to, and in some applications broadcast to, simultaneously. Thus a multibeam system is needed. In a narrowband sonar receiver the phases for each beam can be manipulated entirely by signal processing software, as compared to present radar systems that use hardware to 'listen' in a single direction at a time.
Sonar also uses beamforming to compensate for the significant problem of the slower propagation speed of sound as compared to that of electromagnetic radiation. In side-look-sonars, the speed of the towing system or vehicle carrying the sonar is moving at sufficient speed to move the sonar out of the field of the returning sound "ping". In addition to focusing algorithms intended to improve reception, many side scan sonars also employ beam steering to look forward and backward to "catch" incoming pulses that would have been missed by a single sidelooking beam.
Beamforming schemes 
- A conventional beamformer can be a simple beamformer also known as delay-and-sum beamformer. All the weights of the antenna elements can have equal magnitudes. The beamformer is steered to a specified direction only by selecting appropriate phases for each antenna. If the noise is uncorrelated and there are no directional interferences, the signal-to-noise ratio of a beamformer with antennas receiving a signal of power is , where is Noise variance or Noise power.
- Null-steering beamformer
- Frequency domain beamformer
Beamforming history in cellular standards 
- Passive mode: (almost) non-standardized solutions
- Active mode: mandatory standardized solutions
- 2G — Transmit antenna selection as an elementary beamforming
- 3G — WCDMA: Transmit antenna array (TxAA) beamforming
- 3G evolution — LTE/UMB: Multiple-input multiple-output (MIMO) precoding based beamforming with partial Space-Division Multiple Access (SDMA)
- Beyond 3G (4G, 5G, …) — More advanced beamforming solutions to support SDMA such as closed loop beamforming and multi-dimensional beamforming are expected
Beamforming for speech audio 
Beamforming can be used to try to extract sound sources in a room, such as multiple speakers in the cocktail party problem. This requires the locations of the speakers to be known in advance, for example by using the time of arrival from the sources to mics in the array, and inferring the locations from the distances.
It is useful to use specialized filter banks to separate frequency bands prior to beamforming. This is because different frequencies have different optimal beamform filters, so can be treated as separate problems. (i.e. run many filters in parallel, then recombine the bands.) Standard filters such as FFT bands are suboptimal for this purpose because they are not designed to isolate bands. For example, the FFT assumes implicitly that the only frequencies present in the signal are exactly those harmonics present as FFT harmonics. Frequencies which lie between these harmonics will typically activate all of the FFT channels, which is not what is wanted in a beamform analysis. Instead, filters can be designed in which only local frequencies are detected by each channel. The recombination property is also required: there must be enough information in these receptive field to reconstruct the signal. These basis are typically non-orthogonal, unlike the FFT basis.
See also 
Beamforming solutions 
- Aperture synthesis
- Inverse synthetic aperture radar (ISAR)
- Phased array antennas, which uses beamforming to steer the beam
- Sonar, side-scan sonar
- Synthetic aperture radar
- Synthetic aperture sonar
- Thinned array curse
- Window function
- Magnetoencephalography (SAM)
- Microphone array
- Zero-forcing precoding
- Multibeam echosounder
Related issues 
- Spatial multiplexing
- Antenna diversity
- Channel state information
- Space–time code
- Space–time block code
- Dirty paper coding (DPC)
- Smart antennas
- Space-division multiple access
- Wideband Space Division Multiple Access
- Golomb ruler
- Van Veen, B.D.; Buckley, K.M. (1988). "Beamforming: A versatile approach to spatial filtering". IEEE ASSP Magazine 5 (2): 4. doi:10.1109/53.665.
- Louay M.A. Jalloul and Sam. P. Alex, "Evaluation Methodology and Performance of an IEEE 802.16e System", Presented to the IEEE Communications and Signal Processing Society, Orange County Joint Chapter (ComSig), December 7, 2006. Available at: http://chapters.comsoc.org/comsig/meet.html
- H. L. Van Trees, Optimum Array Processing, Wiley, NY, 2002.
- "A Primer on Digital Beamforming" by Toby Haynes, March 26, 1998
- "What Is Beamforming?", an introduction to sonar beamforming by Greg Allen.
- "Two Decades of Array Signal Processing Research" by Hamid Krim and Mats Viberg in IEEE Signal Processing Magazine, July 1996
- "Dolph-Chebyshev Weights" antenna-theory.com
- Acoustic Beamforming Literature
- An introduction to Acoustic Beamforming
- An introduction to Sound Source Localization
- A collection of pages providing a simple introduction to microphone array beamforming
- "Beamforming Narrowband and Broadband Signals" by John E. Piper in Sonar Systems, InTech, Sept. 2011