Interpolation Filter (802.11n/ac/ax/be)

The Interpolation Filter parameter applies filtering to the channel to reduce signal noise or smooth frequency response.

Channel frequency response values are computed separately for each subcarrier. Since, typically, there is noise on each subcarrier that is independent of noise on other subcarriers, we can perform some kind of averaging to reduce the noise power in the frequency response, and consequently, reduce the EVM Error vector magnitude (EVM): A quality metric in digital communication systems. See the EVM metric in the Error Summary Table topic in each demodulator for more information on how EVM is calculated for that modulation format. in the demodulation measurement. This assumes that the true transmitter frequency response is smooth enough, which is usually (though not always) a valid assumption.

However, there is a trade-off: channel smoothing makes the equalizer less able to track real frequency-domain roughness in the transmitter, sometimes making EVM worse on signals with low noise or signals with more roughness in the transmitter frequency response.

There are three Interpolation Filter choices:

None/Linear: No interpolation filter is applied.
Triangular: A simple triangular-weighted moving average, with special handling at the ends of the channel response to avoid biasing the end points , is applied to the channel response estimate before equalization.

The triangular weights applied to the subcarrier and adjacent subcarriers are as follows: 1 2 ... (N-1)/2 ... 2 1

Example: for a smoothing Length of 5, to following is a calculation of the smoothed value of subcarrier n's channel frequency response coefficients ch'_n and its equalizer values eq'_n:

w = [1 2 3 2 1]

ch'_n = 1/sum(w) * w * [ch_-2 ch_-1 ch₀ ch₁ ch₂]'

eq'_n = 1/ch_n

Near the endpoints, where there are not enough channel frequency response values to apply the specified smoothing value, the smoothing algorithm makes the smoothing window narrower in order to keep the window symmetrical. For example, the smoothed coefficient ch'₁ is calculated from ch₀, ch₁, and ch₂ regardless of the smoothing length.
Wiener (default): a Wiener filter is applied to the channel response estimate before equalization. The procedure is as follows:
1. Calculate a least-squares estimate of the channel response H_LS from the appropriate training field (divide received subcarrier with known subcarrier). This is the same method used regardless of Interpolation filter.
  
  Compute the Wiener filter coefficients based on MMSE criteria (minimum error between filtered channel frequency response and actual channel frequency response).
2. Note that the Wiener filter coefficient is determined by the Est. Channel Delay Spread parameter because auto-correlation matrix and cross-correlation matrix in Wiener-Hopf equation is determined based on the Est. Channel Delay Spread parameter.
3. Filter HLS using calculated Wiener filter coefficients H_Wiener = Wiener(H_LS).
4. Perform zero-forcing equalization on the data symbols using the H_Wiener channel frequency response coefficients.