Pilot-aided Direction of Arrival Estimation for mmWave Cellular - PowerPoint PPT Presentation

Pilot-aided Direction of Arrival Estimation for mmWave Cellular Systems Mahbuba Sheba Ullah Dr. Ahmed Tewfik University of Texas at Austin March 23, 2016

Outline • Motivation • Prior work • Pilot assisted, sub-sample based MUSIC algorithm • Simulation results

Motivation Problem formulation: Concurrent DoA estimation of mmWave primary and secondary beams. § Dynamic mmWave channel is susceptible to blockage § 5G requires ultra low latency Challenges: 5G Requirements: § Bandwidth § Latency § Energy efficiency § Reliability Solution: All-digital Evolution of peak Spurious Free Dynamic Range (SFDR) for ADCs

Prior work & challenges Sparse Large-scale High-speed Ultra Channel Antenna ADCs wideband Analog Responder Baseband One • low cost, τ • low resolution, . . . + RF ADC • high latency τ - sweep search Few Hybrid Responder τ . . . • reduced cost, + ADC RF Baseband τ • low resolution, Initiator • moderate latency τ - sweep search (large scale antenna) . . . + ADC RF [Ayach’14][Desai’14] τ Digital Responder Power Complexity ? efficiency? • flexible , • performance , Cost ? • low latency Relax using sparsity - concurrent search ADC RF Baseband [Barati’14] . . . . . . . . . Subsample enabled by pilot ADC RF Many

Sparse channel model Received signal mmWave sparse channel model can reduce complexity. y ( t ) = ABx ( t ) + n ( t ) at antenna array ! # a ( θ 1 ) ! a ( θ p ) A = " $ Millimeter Wave " % 1 Multi-path Channel ULA direction i ( m − 1) $ ' e i ψ ψ a ( θ ) = e 2 vector $ ' ! $ ' e i ( m − 1) ψ # & ψ = − 2 π d cos( θ ) λ ! $ 0 β 1 β 2 x ( t − τ 2 ) β 1 x ( t − τ 1 ) # & ! B = # & TX 0 θ 2 β p # & " % Uniform linear array θ 1 " % x ( t − τ 1 ) Delayed pilot $ ' ! x ( t ) = signals $ ' x ( t − τ p ) $ ' # & Assumptions d • Number of multipath components, p is small. • All p multi-paths have distinct delays. RX • Maximum delay-spread is a known parameter and is small for Uniform linear array mmWave propagation channel.

Subspace based DoA estimation y ( t ) = ABx ( t ) + n ( t ) Channel Model: Decomposed into p ¡ dimensional } = ABPB H A H + σ 2 Ι signal-subspace and ( m-p ) R yy = E y ( t ) y ( t ) H { Covariance matrices: dimensional noise subspace . P = E x ( t ) x ( t ) H { } The covariance matrix P is non-singular if: Accurate estimation requires • The propagation delays are distinct. ( p+1 ) high speed ADC s • Pilot signals have good autocorrelation properties. Large number ( p+1 ) of RF chains with high speed ADC s are impractical to implement in terms of cost and power consumption.

Pilot assisted sub-sample based MUSIC-like algorithms Pilot design can assist an all digital solution. Subsequences maintain good circular correlation Cyclic Prefix ( CP ) properties Reduced complexity Sub-Nyquist rate sampling frequency domain algorithms

Proposed pilot design ( N , D ) : positive integers Energy Efficient (constant amplitude) Zero circular correlation D : decimation factor ND > delay_spread Zadoff Chu (ZC) sequence ( L=ND 2 ) Decimated by D , subsequence ’s properties: I. Zero circular cross-correlations . II. Zero circular auto-correlation within N lags.

Proof outline of property I & II ZC sequence of length L " − i π un 2 L , $ The root parameter u is e for L even s [ n ] = # relatively prime to L . − i π un ( n + 1) $ e , for L odd L % Decimated subsequence with the j th phase offset. s j [ k ] = s [ j + Dk ], k = 0, ! , ND − 1 j = 0,..,D-1 Decompose Second term First term Third term Linear Linear Constant phase term frequency term phase term Does not affect the Adds circular shift to the ND -point DFT of the third term. A ZC sequence with circular correlation Each subsequence’s circular shift amount is distinct and length N and root u properties from the set { 0,..,D-1 } repeated D times

Proof outline An Example of the ND - point DFT of the subsequences with phase offsets , j=0,…,D-1 Even length ZC example, N=48, D=10, u=17, => L=4800 70 The ND - point DFT of the subsequence Magnitude of DFT of the decimated sequences m=0,...,D − 1 offsets with phase offsets j=0 . 60 (Also the DFT of the third term) 50 40 The ND - point DFT of another 30 subsequence which is a circular shifted 20 version the DFT of the third term. 10 0 5 10 15 20 Example shows: frequency I. Subsequences have zero circular cross-correlations . II. Each subsequence have zero circular auto- correlations within N lags.

Algorithm description ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ Ultra wideband signal at the antenna array y ( t ) = ABx ( t ) + n ( t ) Subsample by a factor D Enabled by pilot design ADC working at sub-Nyquist rate ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ y ( Dt ) = ABx ( Dt ) + n ( Dt ) Few due to sparsity ND -point DFT of the received samples at each antenna The phases of the dominant multipaths can be identified from the DFT of the received vector: ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ Y Y Circular correlation by the pilot subsequence with the j th phase Circular correlation decouples the contribution of ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ! ¡ each subsequence of the pilot due to property II Y Apply MUSIC algorithm on Circular autocorrelation of the correlation output frequency domain signal will be zero within maximum delay spread, as long as: DOA ¡es(mates ¡for ¡the ¡pilot ¡ ¡ (property I) τ max < ND signal ¡with ¡the ¡( j+kD) th ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ phase ¡offsets. ¡ k = 0, ! , τ max D ! # " $ Reduces antenna size

Simulation Results (Pilot = ZC(4096,11), decimation factor = 16) Root MUSIC on all 4096 symbols Pilot aided root MUSIC on 256 symbols (Antenna size = 4) (Antenna size = 2) 8 8 Detected multi-paths: 7 7 § Strongest delay = 2.1 § 2 nd strongest gain = 1.5 § 3 rd strongest 6 6 peak from the weakest beam 5 5 root MUSIC spectrum root MUSIC spectrum delay = 7.7 4 4 gain = 0.75 delay = 10.8 gain = 0.7 3 3 2 2 1 1 0 0 -1 -1 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 DoA (deg) DoA (deg) 16 10 14 8 12 Histogram Histogram 10 6 8 4 6 4 2 2 0 0 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 DoA (deg) DoA (deg) Unable to resolve Finds DoA of each multipath (strongest to weakest) 4x4 covariance matrix 2x2 covariance matrices

Conclusion • Low complexity all digital solution. – Eliminates high speed ADC without performance degradation. • Sub-Nyquist rate sampling using ZC based pilot design. • Reduced antenna size requirements.