Millimeter Wave Hybrid Beamforming with DFT-MUB Aided Precoder - - PowerPoint PPT Presentation

Millimeter Wave Hybrid Beamforming with DFT-MUB Aided Precoder Codebook Design

• K. Satyanarayana

∗University of Southampton

&

†InterDigital

Supervisors: Mohammed El-Hajjar∗, Ping-Heng Kuo†, Alain Mourad†, Lajos Hanzo∗ ks1r15@soton.ac.uk www.satyanarayana.xyz

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Overview

1

mmWave Challenges

2

mmWave Architectures

3

Hybrid Architecture Conceived

4

DFT-MUB Precoder Codebook Design

5

Results

6

Conclusions

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mmWave Challenges

10-4

2 5

10-3

2 5

10

• 2

2 5

10-1

2 5

1

2 5

10

2 5

102

Specific Attenuation (dB/km)

50 100 150 200 250 300

Frequency (GHz) Oxygen (O2) Water Vapour (H2O), = 7.5 g.m

• 3

Light Rain (2 mm/hr) Heavy Rain (50 mm/hr)

Wall mmWave transmitter sub-3 GHz transmitter

mmWave transmitter Attenuation

Receiver Diffraction Transmitter Blocked Reflection

• I. A. Hemadeh, K. Satyanarayana, M. El-Hajjar, L. Hanzo “Millimeter-Wave

Communications: Physical Channel Models, Design Considerations, Antenna Constructions and Link-Budget” IEEE Communications Surveys & Tutorials submitted.

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mmWave Challenges

Directional transmission is employed to mitigate the losses Conventional MIMO heavily relies on digital signal processing

◮ Dedicated RF chains (ADCs) for every antenna element

Large number of antennas can be accommodate in compact space at mmWave frequencies

◮ Employing RF chains per antenna would incur more cost and

complexity

Analog signal processing combined with digital processing, termed hybrid beamforming is a plausible solution State-of-the-art hybrid beamforming designs include fully-connected architecture and sub-array-connected architecture

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Fully-Connected Architecture

. . . . . . + + + . . . . . .

• mmWave

Channel

WBB

+ + +

Nt FRF N RF

t

Nr FBB N RF

r

y WRF Ns s H Nray Nc

The phase shifters of each RF chain are connected to all the transmit antennas Number of phase shifters required is equal to NtNRF

t

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Sub-Array-Connected Architecture

. . . . . .

mmWave Channel

. .

.

.

.

. . . . . .

.

. .

λ/2 λ/2 s

Ns

N RF

t

Nt Nr

y WRF FRF Nc,Nray H WBB FBB N RF

r

The phase shifters of each RF chain are connected to only a subset of transmit antennas Number of phase shifters required is equal to Nt Thus, the sub-array based architecture is more energy-efficient and cost-efficient than the fully-connected architecture

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Hybrid Design Conceived

. . . . . . .

mmWave Channel mmWave

. . .

. . .

d

Cluster 1 Channel mmWave Cluster 2 Channel Cluster H1 H2 Nray

Nt Nsub

Ns Nsub NRF r

s

FBB FRF

Nt HNsub Nr Nray

y

Nray Nsub

WRF WBB

In contrast to state-of-the-art sub-array design, in this design, the sub-arrays are separated by a sufficiently large distance d, so that the they experience independent fading Thus, this design is capable of providing both diversity and BF gains

• K. Satyanarayana, et al.”Dual-Function Hybrid Beamforming and Transmit Diversity

Aided Millimeter Wave Architecture” in IEEE Trans. Veh. Technol. 2017

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Hybrid Design Conceived

1 2 3 4 5 6 7 8 9 10 Achievable Rate (bps/Hz)

• 40
• 35
• 30
• 25
• 20
• 15
• 10
• 5

SNR [dB]

Full-connected 2 sub-arrays connected (proposed) 4 sub-arrays connected (proposed) 8 sub-arrays connected (proposed) 2 sub-arrays connected (state-of-the-art)

Parameters Values Nc 4 Nray 6 Nt 64 Nr 32 Ns 2 NRF

t

2 NRF

r

2 φnray

nc

∼ U[0, 2π)

Proposed design performs superior to fully-connected design However, the performance begins to degrade when the number of sub-arrays is larger than 2

• K. Satyanarayana, et al.”Dual-Function Hybrid Beamforming and Transmit Diversity

Aided Millimeter Wave Architecture” in IEEE Trans. Veh. Technol. 2017

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Conceived Hybrid Design

This result is independent of the precoder and the combiner used at the transmitter and the receiver, respectively!

• K. Satyanarayana, et al.”Dual-Function Hybrid Beamforming and Transmit Diversity

Aided Millimeter Wave Architecture” in IEEE Trans. Veh. Technol. 2017

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System Model

. . . . . . + + + . . . . . .

• mmWave

Channel

WBB

+ + +

Nt FRF N RF

t

Nr FBB N RF

r

y WRF Ns s H Nray Nc

The received signal vector y after hybrid precoding and combining is given by

Received Signal Vector

y = √ PWH

BBWH RFHFRFFBBs + WH BBWH RFn

(1)

Channel Model

H =

• NrNt

NcNray

Nc

• nc=1

Nray

• nray=1

αnray

nc ar(φnray nc )aT t (φnray nc ),

(2)

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DFT-MUB Precoder Codebook Design

We have H = UΣVH

RF Beamformer using Discrete Fourier Transform (DFT) at the Tx

FRF(:, i) = max

i

<DFTNt(:, i), vj >, 1 ≤ i ≤ NRF

t ; 1 ≤ j ≤ Nt

(3) where vj is the jth vector of the right singular matrix of the channel matrix H and DFTNt(:, i) is the ith column of the Nt × Nt DFT matrix.

RF Combiner (DFT) at the Rx

WRF(:, i) = max

i

<DFTNr (:, i), uj >, 1 ≤ i ≤ NRF

r

, 1 ≤ j ≤ Nt (4) where uj is the jth vector of the left singular matrix of the channel and DFTNr (:, i) is the ith column of the Nr × Nr DFT matrix.

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DFT-MUB Precoder Codebook Design

The baseband precoder FBB is constructed from the mutually unbiased bases (MUBs).

Motivation

The motivation behind the choice of an MUB assisted codebook is that the entries of the matrix constructed from MUBs for powers of 2 are

• bserved to be composed of finite alphabets i.e.,{1, −1, i, −i}, which

would significantly reduce the computational complexity. The total number of MUBs for a given dimension N is limited and is equal to N+1.

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DFT-MUB Precoder Codebook Design

For example, we consider the scenario where the transmitter is equipped with NRF

t = 4 RF chains. For NRF t

= 4, the MUBs are given by A = 1 2     1 1 1 1 1 1 −1 −1 1 −1 −1 1 1 −1 1 −1     B = 1 2     1 1 1 1 −1 −1 1 1 −i i i −i −i i −i i     , C = 1 2     1 1 1 1 −i −i i i −i i i −i −1 1 −1 1     , D = 1 2     1 1 1 1 i i −i −i 1 −1 −1 1 −i i −i i     . Thus 5 MUBs are obtained along with Identity matrix, which is also an MUB.

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DFT-MUB Precoder Codebook Design

Baseband Precoder FBB

The baseband precoder FBB is chosen from the codebook F = {A0, A1, A2, A3, B0, B1, B2, B3, C0, C1, C2, C3, D0, D1, D2, D3}, which maximizes the minimum SNR and it is given by Fdesired

BB

= arg max

FBB∈F Λmin{HeffFBB},

(5) where Heff = WH

RFHFRF.

Baseband Combiner WBB

The baseband combiner is chosen as the linear minimum mean squared error (LMMSE).

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Simulation Results

1 2 3 4 5 6 7 Achievable Rate (bps/Hz)

• 40
• 35
• 30
• 25
• 20
• 15
• 10
• 5

SNR [dB]

Unconstrained Precoding (SVD) Orthogonal Matching Pursuit DFT-MUB Codebook DFT-Identity Solid line: 32 16 MIMO Dashed line: 8 8 MIMO 32 16 MIMO 8 8 MIMO

Parameters Values Nc 4 Nray 6 Nt 32, 8 Nr 16, 8 Ns 2 NRF

t

4 NRF

r

2 φnray

nc

∼ U[0, 2π)

• Fig. Fully-connected architecture. DFT-MUB based codebook design with

4-bit feedback and different other methods relying on perfect CSI for 32 × 16 and 8 × 8 MIMO, and Ns = 2 and NRF

t

= 4, NRF

r

= 2.

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Simulation Results

1 2 3 4 5 6 7 8 9 10

Achievable Rate (bps/Hz)

• 40
• 35
• 30
• 25
• 20
• 15
• 10
• 5

SNR [dB]

Optimal Unconstrained Precoding (SVD) DFT-MUB Aided Codebook Unconstrained SIC-based Beamforming DFT-Identity Aided Beamforming

Parameters Values Nc 4 Nray 6 Nt 64 Nr 32 Ns 2 NRF

t

2 NRF

r

2 φnray

nc

∼ U[0, 2π)

• Fig. Proposed 2-sub-array-connected for 64 × 32 MIMO, using DFT-MUB

based codebook design with 4-bit feedback using Ns = 1, NRF

sub = 1,

Nsub = 2.

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Conclusions

Proposed a new architecture where we analyzed that 2-sub-array-connected design is the optimal in terms of achievable rate Further, we have proposed a low-complexity hybrid precoder codebook design that performs close to the optimal precoder

• K. Satyanarayana, et al.”Dual-Function Hybrid Beamforming and Transmit Diversity

Aided Millimeter Wave Architecture” in IEEE Trans. Veh. Technol. 2017

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ks1r15@soton.ac.uk www.satyanarayana.xyz

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