Channel Estimation (pilot-aided wireless channel identification) L1-389
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.
Forward model E
A transmitted OFDM/MIMO waveform passes through a multipath fading channel with impulse response h[tau, nu] in delay-Doppler space; the receiver collects y_k = sum_l h_l * x_{k-l} + n_k and uses known pilot symbols to estimate h.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- when pilot spacing satisfies Nyquist (delta_f <= 1/tau_max, delta_t <= 1/(2 f_d))
- Stability:
- conditional
- κ:
- 500
Well-posed under Nyquist pilot spacing; sub-Nyquist recoverable via sparse CS when channel is sparse in delay-Doppler. Mismatch: CFO, phase noise, non-ideal pilot power allocation.
Solvability C
- Solver class:
- LS, MMSE, DFT-based, LMMSE-interpolation, sparse (OMP, LASSO), Bayesian (message-passing), deep (ChannelNet, DeepRx)
- Convergence rate q:
- 2
- Complexity:
- LS: O(N_pilot^3) or FFT O(N*log(N)); MMSE: O(N_pilot^3); OMP: O(k*N_pilot*L_ch)