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DFE Online Simulator


QPSK + Multipath + Decision Feedback Equalizer (DFE)

20 BER Before: 0 | BER After: 0

Simulator Workflow & Mathematics

1 The Signal Path

  1. QPSK Modulation Random bits are grouped into pairs and mapped to complex symbols: s = exp(j * (Ļ€/4 + kĻ€/2)).
  2. Multipath Channel The signal is convolved with a multi-tap impulse response, simulating reflections that cause Inter-Symbol Interference (ISI).
  3. DFE Equalization A Feedforward Filter (FFF) suppresses precursor ISI, while a Feedback Filter (FBF) subtracts post-cursor ISI using previous symbol decisions.

2 The DFE Equations

// 1. Equalizer Output

y[n] = Ī£(w_f[k] * x[n-k]) - Ī£(w_b[k] * d[n-k])

(Feedforward Output - Feedback Correction)

// 2. Error Calculation

e[n] = d_known[n] - y[n]

// 3. LMS Weight Update

w_f[k] = w_f[k] + Ī¼ * e[n] * x*[n-k]

w_b[k] = w_b[k] - Ī¼ * e[n] * d*[n-k-1]

Where Ī¼ is the step size, x* is the conjugate of the received signal, and d are previous decisions.

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