ANALOG BS + UE · ONE RF STREAM AT EACH END

Beam sweeping and measurement bounds

One OFDM pilot symbol per tested beam pair. A full 100 × 32 sweep is 3,200 sequential symbols.

Observation budget

Joint marginal standard-deviation bounds

Unknown parameterLower bound

Conditional, local noise bounds for one static coherent path. A small value is not predicted hardware accuracy. Missing rank is reported as unidentifiable, not as a zero from a pseudoinverse.

Full Fisher information and model

μmnk = sk α exp(−j2π fk τa) (wnHar) (atHvm)
J = 2 Re(DHC−1D)

Normalized derivative similarity Jᵢⱼ/√(JᵢᵢJⱼⱼ), not estimator correlation. Export contains the unnormalized matrix. Order: delay, AoA az/el, AoD az/el, loss, phase.

Unit-modulus steering vectors; unit-norm analog weights. Spatially white pre-combining noise. Equal-power contiguous pilot tones. Narrowband array steering at the carrier; ideal phase shifters; known calibration. All complex I/Q is retained. No CP, switching gaps, motion, beam squint, phase drift or extra RF losses are simulated. The gain and phase are unknown nuisance parameters. Apparent delay includes receiver clock bias.

Changing beam density at fixed transmit power increases total acquisition energy and duration; it is not a fixed-energy comparison.