Channel Equalisation Calculator

Real RF channels are not flat. Multipath reflections produce frequency selective fading and inter symbol interference, where each transmitted symbol smears into its neighbours and the receiver cannot decide which symbol was sent. Equalisation is the process of estimating the channel and applying a compensating filter at the receiver before symbol decisions are made. Without equalisation, wideband digital communication over multipath channels falls apart at the higher modulation orders (256 QAM, 1024 QAM, 4096 QAM) where the symbol decision regions are smallest.

Zero Forcing inverts the channel completely. It is ideal at very high SNR with no spectral nulls but suffers severe noise enhancement at frequencies where the channel response approaches zero. MMSE balances ISI cancellation and noise enhancement and is optimal across all SNR regimes. It is the standard choice for most modems. DFE adds a feedback filter that cancels post cursor ISI from past decisions, approaching the Shannon capacity bound on severe multipath channels at the cost of error propagation when wrong decisions feed back. The calculator computes all three simultaneously so the trade off is visible.

Up to six multipath taps with fractional delays handled via exact sinc interpolation in the frequency domain. Channel transfer function H[k] equals sum over n of h[n] times exp of (minus j 2 pi k tau[n] divided by N), evaluated across 256 frequency points. Each tap has independent delay (in fractional symbol periods), magnitude, and phase. Built in presets cover the common reference channels including the ITU Pedestrian A.

LMS (Least Mean Squares) updates the equaliser tap weights with a small step toward the gradient of the error each symbol. Simple, low complexity, slow convergence. RLS (Recursive Least Squares) maintains an estimate of the inverse correlation matrix using a Kalman gain update. Faster convergence at O(N squared) complexity per symbol. DD (Decision Directed) uses the receiver decisions as the reference signal once initial convergence is achieved, useful for tracking slow channel variations after the training preamble ends.

In OFDM the cyclic prefix removes ISI between OFDM symbols entirely, so the equaliser only needs to compensate per tone amplitude and phase distortion. This reduces equaliser complexity from O(K times N equaliser) for single carrier time domain equalisation to O(K) for OFDM per subcarrier equalisation. The MMSE per subcarrier weight is W[k] equals H conjugate of [k] divided by (magnitude H squared plus sigma squared). LTE, 5G NR, and WiFi all use this approach because of the complexity advantage on wideband channels.

The Forney bound. SNR DFE equals exp of ((1 over N) times sum over k of ln of (1 plus SNR times magnitude H squared)) minus 1. This is the theoretical SNR achievable by an ideal infinite length DFE assuming no decision errors. Real DFE implementations approach this bound on severe multipath channels but suffer error propagation when wrong decisions feed back, so the practical performance sits below the bound by a small margin.

Yes. Output SNR and EVM are checked against minimum receiver SNR thresholds for BPSK, QPSK, 64 QAM (LTE), 256 QAM (DVB T2 and 5G NR FR1), 1024 QAM (WiFi 6), and 4096 QAM (DOCSIS 3.1). Pass or fail status updates as channel or equaliser parameters change. Useful for confirming whether a candidate receiver design will achieve the target modulation order on a given channel.

No. The calculator runs entirely in your browser. No channel models, equaliser configurations, or design data are submitted to a server. Useful for commercially confidential modem design work, defence and intelligence communications development, and environments where information security policy prohibits sending engineering data to third party services.