1. Quantized Angular Beamforming for mmWave Channels
with Limited Training
Hao Zhou, Dongning Guo, Michael L. Honig
Department of Electrical Engineering and Computer Science, Northwestern University
Background, Problem Setup
Main Results
Example: 2-D FFT With Zero Padding
For ML estimation, the outage probability is minimized with one pilot per beam pair (S = Mt Mr).
For MP estimation, the outage probability is minimized with multiple pilots per beam pair (S > Mt Mr).
Given S, ML has lower outage probability than MP.
High-resolution implementation of ML using FFT.
mmWave channel characteristics, challenges:
High path loss, small number of propagation paths.
Large antenna arrays focus energy.
Beam searching requires training overhead.
System Model:
Mt, Mr are number of quantized transmit/receive beams.
Access point (AP) and user equipment (UE) exhaustively sweep all possible MtMr beam pairs with S > MtMr pilots.
16 Point
128 Point
Average Received SNR (dB) Nt Nr
Digital Baseband Unit
RF Chain … Mr Mt
Numerical Example
Uniform linear array (ULA) with Nt = Nr = 8.
Total pilots S = 4096.
SNR threshold is 3.5 dB.
How much training do we need?
MP: Solid
ML: dashed
Pr(Received SNR < Threshold)
Number of pilots per beam pair S/(Mt Mr) , Log-scale
Estimation Methods
The TX/RX beamspace is quantized according to the pair of arrival/departure angles
Max Power (MP): Choose that maximizes received signal power.
Maximum Likelihood (ML): Choose that maximizes
Incorporates beam patterns.
Decision statistic: output of the receiver beam correlator.
Normalized Gaussian random variable.
Mean depends on: SNR and
S/(Mt Mr) for max power.
S/(Nt Nr) for maximum likelihood.
Increasing number of pilots S or SNR increases “distance” between received signals, which reduces outage probability.
Outage Prob.
Improving Resolution with the FFT
Conclusions
Can compute decision statistics at any angle pair, not just the quantized angles:
Using an FFT, the complexity is O(Q2logQ)
Q is number of FFT points (estimation resolution).
True
Path
ML versus MP trades off performance versus complexity.
Can compute outage probability as a function of number of antennas, beams, pilots, and power.
Can improve angular resolution using FFT to compute decision statistics of ML.
Going from 16- to 256-point FFT gives 1.5 dB gain in received SNR with S = 100 pilots.
DFT vector
DFT vector