MIMO beamforming means adjusting the phase and amplitude of each antenna’s signal so that the signals add up at the intended receiver instead of arriving out of step. Beamforming in MIMO systems turns several weak signals into one stronger one, with up to 10 log10(N) dB of SNR gain from N antennas. It relies on knowing the channel, which is why channel state information comes up so often in this topic.
This is a beginner’s route into the subject. It uses small numbers and few equations, and it does not need any array theory. For the array factor, grating lobes, sidelobes, hardware limits and a full 28 GHz example, go to the main beamforming article after this one.
MIMO beamforming in one idea
Two ripples in a pond make a bigger ripple if their peaks meet, and flat water if a peak meets a trough. Radio waves behave the same way. Suppose two antennas each send half of the available power. If the signals arrive in phase, the amplitudes add and the received power is twice what one antenna would deliver with all of the power. If they arrive 180 degrees out of phase, they cancel completely.
Nothing here creates energy. The power that is missing from the nulls appears in the peaks. Beamforming simply controls where the peaks land, by setting the phase at each antenna.
How beamforming works in a MIMO system
Beamforming has a simple cycle, whatever the system:
- Measure. The radios send known pilot signals and estimate the channel from each antenna.
- Compute. The transmitter works out one complex weight per antenna, which is a phase shift and a gain.
- Transmit. Each antenna sends the same data multiplied by its own weight.
- Repeat. The channel changes as things move, so the weights must be refreshed.
Two ways to think about the channel
In free space or at millimetre-wave frequencies, there may be one strong path, so a beam points in a real direction. For antennas spaced d apart, steering to angle θ takes a phase step between neighbouring antennas of (360° × d/λ) × sin θ. At half-wavelength spacing, a 30° steer takes a 90° step.
Indoors or in a city, the signal arrives by many reflected paths, and there is no single direction to point at. The transmitter still applies one weight per antenna, but it computes the weights from the measured channel so that the many paths add up at the receiver. The energy forms a hot spot around the receiver and not a narrow beam. Both cases are beamforming, and MIMO systems use the second kind as readily as the first.
CSI-based beamforming
The weights come from channel state information. Consider a transmitter with N antennas and a single receive antenna, where the channel to antenna n is a complex number hn. The best weights are the maximum ratio transmission (MRT) weights:
wn = hn* / ||h||
The conjugate reverses each channel’s phase, so that all paths arrive with zero phase. The amplitude term puts more power on the stronger paths. The receive SNR becomes ρ||h||2, the same as a SIMO receiver using MRC.
TDD systems can get this CSI by measuring the reverse link, and FDD systems usually have the receiver feed it back, often as an index into a codebook. Channel state information explains these methods and how quickly CSI ages.
Worked example: four antennas, one receiver
Take a 3.5 GHz transmitter with four antennas and fixed total power. A reference SNR of 5 dB is what a single antenna of channel gain 1 would give with all of the power. The channel to each antenna has been measured:
| Antenna | Gain |hn| | Phase of hn | MRT weight magnitude | MRT weight phase |
|---|---|---|---|---|
| 1 | 1.0 | 20° | 0.517 | -20° |
| 2 | 0.7 | -110° | 0.362 | 110° |
| 3 | 1.2 | 75° | 0.621 | -75° |
| 4 | 0.9 | 160° | 0.465 | -160° |
Each weight cancels the phase of its channel, and the weight powers add up to 1. The result, compared with some simpler options, uses the same total power in all cases.
| Method | Power gain on the 5 dB reference | Receive SNR | Capacity | Rate in 20 MHz |
|---|---|---|---|---|
| All antennas, no weights | -4.7 dB | 0.3 dB | 1.05 b/s/Hz | 21 Mb/s |
| One average antenna | -0.3 dB | 4.7 dB | 1.98 b/s/Hz | 40 Mb/s |
| Strongest antenna only | 1.6 dB | 6.6 dB | 2.47 b/s/Hz | 49 Mb/s |
| Phase-only beamforming | 5.6 dB | 10.6 dB | 3.63 b/s/Hz | 73 Mb/s |
| Full MRT beamforming | 5.7 dB | 10.7 dB | 3.68 b/s/Hz | 74 Mb/s |
Three lessons follow from these numbers:
- MRT is 6.02 dB above the average antenna, which is exactly 10 log10(4). That is the array gain.
- Sending the same signal on all four antennas without weights is the worst option. The channel phases happen to cancel here, leaving the receiver about 4.4 dB worse off than a single average antenna.
- Phase does most of the work. Phase-only weights come within 0.15 dB of full MRT here, which is why simple phase shifters are so widely used.
What a beam looks like
With a line of four half-wavelength antennas at 3.5 GHz, the wavelength is 85.7 mm and the spacing is 42.8 mm. Equal phases send the main beam straight ahead, with a half-power width of 26.3°. A 90° phase step moves the beam to 30° from broadside, and it widens to 30.9° because the array looks narrower from that angle.
More antennas give a narrower beam and more gain. Doubling N adds 3 dB and halves the width. Sixteen antennas give 12.0 dB, and 64 give 18.1 dB. On the transmit side, EIRP can grow by twice as many decibels if each antenna has its own PA, as the beamforming page shows with a worked 28 GHz example.
Beamforming and the other uses of MIMO
Antennas in a MIMO system can be used in three main ways, and beamforming is only one:
| Use | What it does | Best at |
|---|---|---|
| Beamforming | Sends one stream with maximum SNR | Low SNR, long range |
| Diversity | Sends one stream through independent fades | Reliability, no CSI needed |
| Spatial multiplexing | Sends several streams at once | High SNR, rich scattering |
A real link often mixes these. Multi-user systems also beamform a separate stream to each of several users, and suppress the interference between them. That topic is called MIMO precoding, of which single-stream beamforming is the simplest case.
Analog, digital and hybrid beamforming in brief
The weights can be applied in different places:
- Digital beamforming applies weights in baseband, with one complete RF chain per antenna. It is the most flexible and the most power-hungry.
- Analog beamforming uses phase shifters in the RF path. It is cheap per antenna, but it forms only one beam per chain.
- Hybrid beamforming combines the two. Massive MIMO and millimetre-wave arrays, with tens or hundreds of antennas, use it to reach large gain without a full chain per element.
The MIMO, Beamforming and Phased-Array Architectures article compares these in hardware terms, and phased array design covers array practice.
Where to go next in beamforming
Once these basics are clear, a sensible order of reading is:
- Beamforming: array factor, steering limits, tapering, nulling and hardware errors.
- Channel state information: how the transmitter learns the channel, and how fast that goes stale.
- MIMO precoding: beamforming to several users at once.
- MIMO and multiple antenna systems: how array gain, diversity and multiplexing fit together.
Frequently asked questions
What is the difference between MIMO and beamforming?
MIMO is the antenna arrangement, with several antennas at each end. Beamforming is one way of using those antennas, by weighting them to focus a signal on a receiver. A MIMO system can beamform, multiplex streams or provide diversity.
How much gain does MIMO beamforming give?
Up to 10 log10(N) dB of SNR for N transmit antennas: 3 dB for two, 6 dB for four and 9 dB for eight. Real gain is lower when CSI is old or imperfect, or when the hardware has phase errors.
Does beamforming need channel state information?
Yes. Some knowledge of the channel is essential, whether a full measurement, a codebook index or just a direction. Without any of these, the transmitter cannot tell which phases will add up at the receiver, as the unweighted row of the example shows.
Does beamforming work with only two antennas?
Yes. Two antennas give up to 3 dB of gain, and many Wi-Fi devices use that. The beam is broad and the benefit is modest, but it is real.
Related topics
The natural next step is the full beamforming article. See also MIMO and multiple antenna systems, SISO, SIMO, MISO and MIMO systems, and link budgets for how array gain fits into a radio design. The antennas hub has more background.