Prediction of Fading Broadband Wireless Channels Torbjörn Ekman UniK-University Graduate Center Oslo, Norway JOINT BEATS/Wireless IP seminar, Loen

Contents Motivation Noise Reduction Linear Prediction of Channels Delay Spacing, Sub-sampling Results Power Prediction Results Recommendations

With channels known in advance the problem with fast fading can be turned into an advantage Adaptive resource allocation Fast link adaptation The multi-user diversity can be exploited Why?

Noise Reduction of Estimated Channels The same noise floor is seen in the power delay profile. The estimated Doppler spectrum is low pass and has a noise floor.

IIR smoothers

FIR or IIR Wiener-smoother? IIR smoothers 1.based on a low pass ARMA-model 2.can be numerically sensitive 3.need few parameters FIR smoothers 1.based on a model for the covariance 2.need many parameters Both have similar performance. Both use estimates of the variance of the estimation error and the Doppler frequency.

Linear Prediction of Mobile Radio Channels Model for the tap The FIR-predictor The MSE-optimal coefficients A step towards power prediction Can produce prediction of the frequency response

Linear prediction with noise reduction

Model Based Prediction

Delay Spacing

The MSE optimal delay spacing for the Jakes model depends on the variance of the estimation error. The NMSE has many local minima.

Sub-sampling and aliasing OSR 50 Sub-sampling rate 13 Jakes model SNR 10dB 16 predictor coefficients FIR Wiener smoother (128)

Prediction performance on a Jakes model OSR 50 (100 samples per ) FIR predictor, 8 coefficients FIR Wiener smoother (128) Dashed lines: no smoother

The Measurements Channel sounder measurements in urban and suburban Stockholm Carrier frequency 1880MHz Baseband sampling rate 6.4MHz Channel update rate 9.1kHz Vehicle speeds 30-90km/h 1430 consecutive impulse responses at each location Data from 41 measurement locations

Prediction performance on the taps

Channel prediction performance

Power Prediction The power of a tap A biased quadratic predictor An unbiased quadratic predictor Rayleigh fading taps: the optimal  for the complex tap prediction is optimal also for the power prediction.

Biased and unbiased NMSE

Observed power or complex regressors? AR2-process Approx. Jakes FIR predictor (2) Dash-dotted line for observed power in the regressors.

Power prediction performance

Median tap prediction performance

Channel prediction

Compare average predictor with unbiased predictor

Predictor Design Estimate the channel with uttermost care. Noise reduction using Wiener smoothers. Estimate sub-sampled AR-models or use a direct FIR-predictor. Estimate as few parameters as possible. Design Kalman predictor using a noise model that compensates for estimation errors Power prediction: Squared magnitude of tap prediction with added bias compensation.