Channel state information (CSI) is what a radio knows about how the channel changes a signal between each transmit antenna and each receive antenna, usually as a complex gain per subcarrier. CSI in wireless communication lets the receiver undo the channel and lets the transmitter adapt its rate or point its energy. Its accuracy and age often set how close a real MIMO link gets to its theoretical performance.
This page covers what CSI is, how it is estimated, fed back and aged, and how to simulate it. For what is done with it afterwards, see MIMO precoding and beamforming.
What is channel state information?
In a narrowband MIMO link, the received vector is:
y = H x + n
H is the channel matrix and entry hij is the complex gain from transmit antenna j to receive antenna i. CSI is an estimate of H, or some reduced form of it. In OFDM, each subcarrier has its own H, so CSI for a 4×2 link on 52 subcarriers is a set of 52 matrices, each 2×4.
Several kinds of CSI are in use:
- Instantaneous CSI is the current channel, including its phase. It is the most useful and has the shortest life.
- Statistical CSI holds long-term properties, such as the mean path gain, delay spread, correlation and angular spread. It stays valid for far longer.
- CSIR is CSI at the receiver, which is nearly always available because coherent detection needs it.
- CSIT is CSI at the transmitter, which has to be obtained through feedback or reciprocity and is much harder to come by.
- Partial CSI is a compressed form, such as an SNR report or a precoder index.
Why CSI matters
CSIR lets a receiver equalise and combine, and CSIT lets the transmitter do something about the channel before the signal is sent. A MISO link shows the size of the prize: with two transmit antennas at 10 dB SNR, capacity is 3.16 b/s/Hz without CSIT and 4.06 b/s/Hz with it.
Errors in CSI behave like extra noise. If the receiver’s channel estimate has normalised error variance σe2, a common approximation for the effective SNR is:
γeff = ρ(1 – σe2) / (1 + ρ σe2)
At 20 dB SNR this gives:
| CSI error variance | Effective SNR |
|---|---|
| 0.001 | 19.6 dB |
| 0.01 | 16.9 dB |
| 0.03 | 13.8 dB |
| 0.1 | 9.1 dB |
High-order modulation is the most exposed. A channel error of 0.03 costs more than 6 dB here, which is the gap between adjacent QAM orders.
CSI estimation with pilots
Pilots, or reference signals, are symbols known to the receiver. If pilot symbol s is received as y = hs + n, the least-squares (LS) estimate is ĥ = y/s. It needs no statistics, and its error variance is simply 1/SNR at the pilot.
Linear MMSE (LMMSE) estimation adds knowledge of the channel’s frequency correlation R and the noise level. It weights the pilots as:
ĥ = Rhp (Rpp + σn2 I)-1 yp
Blind and decision-directed methods use the data symbols themselves. They can lower pilot overhead but are slower to converge and more sensitive to errors.
Pilot spacing follows from the channel. The rule of thumb for coherence bandwidth is Bc ≈ 1/(5στ), so a 100 ns RMS delay spread gives about 2 MHz. Pilots must be closer than this in frequency, and closer than the coherence time in time.
Channel state information simulation
A short simulation is the best way to see how CSI quality behaves. The following procedure was used for Figures 1 and 2, and works in any numerical language.
- Build a tapped delay line. Here it has 16 taps at 50 ns spacing with an exponential power profile and 100 ns RMS delay spread, normalised to unit total power.
- Draw each tap as a complex Gaussian with that tap’s variance, for Rayleigh fading.
- Take a 64-point FFT of the taps to get the true H on each subcarrier, here with 312.5 kHz spacing in 20 MHz.
- Place a pilot on every sixth subcarrier (11 pilots, 1.875 MHz apart) and add complex noise at the chosen SNR.
- Form the LS estimate at the pilots and interpolate linearly between them, then form the LMMSE estimate from the known correlation matrix.
- Compute the normalised mean square error against the true H, averaged over thousands of channels. This run used 4,000.
The table gives the resulting errors, also plotted in Figure 2.
| Pilot SNR | LS with interpolation | LMMSE |
|---|---|---|
| 0 dB | 0.765 | 0.345 |
| 10 dB | 0.156 | 0.078 |
| 20 dB | 0.094 | 0.017 |
| 30 dB | 0.088 | 0.0088 |
LS with interpolation stops improving near 0.09, however strong the pilots are. That error floor comes from interpolating between pilots spaced almost a full coherence bandwidth apart. LMMSE continues to improve but also flattens, since it has limited pilots to work from. Using the effective SNR formula at 20 dB, LS with interpolation leaves 9.4 dB and LMMSE leaves 15.6 dB, which is 6 dB gained from better processing with no extra pilot power.
CSI feedback and channel reciprocity
A transmitter can obtain CSIT in two ways.
Feedback. The receiver measures the channel and reports it. Uncompressed feedback is costly. For a 4×2 link on 52 subcarriers at 8 bits each for I and Q, one report is 6,656 bits, and sending that every 10 ms takes about 666 kb/s. Grouping subcarriers by four cuts that to about 166 kb/s. Real systems therefore compress CSI, often sending an index into a shared codebook.
Reciprocity. In TDD, both directions use the same frequency, so the over-the-air channel is the same each way. The transmitter can estimate the channel from the reverse link’s pilots. The catch is that the RF chains are not reciprocal. PAs, LNAs and filters add different gains and phases, so the array needs calibration.
Cellular standards use both routes. In LTE and 5G NR, devices typically report a channel quality indicator (CQI), rank indicator (RI) and precoding matrix indicator (PMI) from downlink reference signals such as CSI-RS, while TDD base stations can also use uplink sounding reference signals (SRS).
CSI in Wi-Fi
Wi-Fi CSI is the per-subcarrier amplitude and phase between each antenna pair, measured from training fields in the preamble. For transmit beamforming, the access point sends a sounding frame, a null data packet that has training fields but no data, and the client returns a compressed beamforming report. This exchange costs airtime, so it is repeated only as often as the channel needs.
CSI has a second use in Wi-Fi. Because people and objects disturb multipath, changes in CSI over time can reveal motion or presence, and this has become a research field known as Wi-Fi sensing. Consumer chipsets generally do not expose raw CSI, so that work tends to rely on specific hardware and tools. The raw values also contain phase offsets from sampling and carrier frequency errors, which have to be removed before use.
CSI ageing: Doppler and coherence time
CSI goes stale as the device or its surroundings move. For Clarke’s model of scattering, correlation after delay τ is J0(2πfDτ), where fD = vf/c is the maximum Doppler shift. A common estimate of coherence time is Tc ≈ 0.423/fD.
Consider a 3.5 GHz link at 30 km/h. The Doppler shift is 97.3 Hz and Tc is about 4.3 ms. If a transmitter beamforms with CSI that has correlation r with the true channel, the SNR gain for N antennas in Rayleigh fading is r2N + 1 – r2.
| CSI age | Correlation r | Gain, 4 antennas | Gain, 64 antennas |
|---|---|---|---|
| 0.25 ms | 0.994 | 5.98 dB | 18.01 dB |
| 0.5 ms | 0.977 | 5.87 dB | 17.86 dB |
| 1 ms | 0.909 | 5.41 dB | 17.24 dB |
| 2 ms | 0.660 | 3.63 dB | 14.54 dB |
| 3 ms | 0.320 | 1.17 dB | 8.73 dB |
With 2 ms of delay, the 4-antenna link has lost 2.4 dB and the 64-antenna link 3.5 dB. For fast users, a system can fall back on statistical CSI or open-loop diversity instead, which is one reason why open-loop and closed-loop modes both exist.
Frequently asked questions
What is CSI in wireless communication?
CSI, or channel state information, is knowledge of the gain and phase of the radio channel between each pair of transmit and receive antennas. It may be a full matrix for each subcarrier or a compressed report. Radios use it for equalisation, rate adaptation, precoding and beamforming.
What is the difference between CSIT and CSIR?
CSIR is channel knowledge at the receiver, and it is usually obtained directly from pilots. CSIT is channel knowledge at the transmitter, which needs feedback from the receiver or channel reciprocity in TDD. CSIT is harder to get and usually older by the time it is used.
What is CSI in Wi-Fi?
It is the set of complex channel values across subcarriers and antenna pairs, measured from Wi-Fi training fields. Access points use it for beamforming, and researchers use its changes over time for Wi-Fi sensing.
How often does CSI need updating?
It should be refreshed well inside the coherence time. At 3.5 GHz and 30 km/h that is about 4.3 ms, so an update every 1 ms or so keeps nearly all of the beamforming gain. A stationary device in a quiet room can go for much longer.
Related topics
CSI feeds MIMO precoding and beamforming, and it is central to MIMO and multiple antenna systems. OFDM explains subcarriers and pilots, SNR and Eb/N0 gives required SNR by modulation, and measuring radio performance covers test methods. More is on the RF design hub.