ADC Bit Optimization for Spectrum- and Energy-Efficient Millimeter Wave Communications

Jinseok Choi, Junmo Sung, Brian Evans, and Alan Gatherer*Electrical and Computer Engineering, The University of Texas at Austin

*Huawei TechnologiesadsdGlobecom 2017

December, 2017

Motivation

2

Millimeter Wave Massive MIMO§ Large bandwidth to achieve multi-gigabit data rates§ Small antenna sizes due to high carrier frequency§ Large antenna arrays to compensate large pathloss

Approach§ Exploit sparsity in mmWave MIMO channels

- Apply analog processing (beamspace projection)

Goal§ Reduce uplink power consumption at base station

Need to reduce power consumption at ADCs

Millimeter Wave Spectrum [Pi & Khan,11]

§ ADC bit allocation subject to a total power constraint- Some ADCs/RF chains will be turned off to save power- Other ADCs will have a variable number of bits

System Model

3

§ Nu users, each with single antenna

§ Nr ULA* antennas at base station (Nr >> Nu)

§ Narrowband channel

§ Known channel state information at receivers

§ Received signals after analog combining

Multiuser Massive MIMO Uplink

H

y =ppuF

H

RFHs+ FH

RFn

Tx power User symbols

AWGN Analog combiner: DFT** matrix

Hybrid receiver with adaptive-resolution ADCs

*Uniform Linear Array**Discrete Fourier Transform

Digital BasebandProcessing

y

System Model

4

4

§ L major propagation paths

§ Array response vector under ULA

Millimeter Wave Channel

a(✓) =1pNr

h1, e�j2⇡#, e�j4⇡#, . . . , e�j2(Nr�1)⇡#

i|

# =d

�sin(✓)where

Angle of arrival

hk =p�k

LX

`=1

!k` a(✓

k` ) 2 CNr

Pathloss Complex path gain

Array response vector§ Linear gain plus noise model

§ Variable number of quantization bits

Quantization Model

W↵ = diag(↵1, · · · ,↵N )

yq = Q(y) = W↵ y + nq

=ppuW↵Hbs+W↵n+ nq

wherevariance of nq:

Quantization noiseQuantization gain matrix

Beamspace channel FH

RFnF

H

RFH

[Fletcher et al., 07]

Rqq = W↵(I�W↵)diag(puHbHH

b + I)

Problem Formulation

5

Minimum Mean Squared Quantization Error (MMSQE)Eh|xi � xqi|2

i=

⇡p3

2�2xi2�2biMSQE:

Ptot =NrPLNA +Nact(NrPPS + PRFchain) + 2NRFX

i=1

⇣PADC(bi) + PSW(bi)

⌘+ PBBwhere

cfs2bADC power

consumption

PSW(b) = csw��2b � 2b

prev ��

Resolution switchingpower consumption

# of activeRF chains

ChallengesNact

PSW(bi)

NrX

i=1

1bi 6=0

PADC(bi)

functions of quantization bits ( involves nonlinearity)

�2xi

= k[Hb]i,:k2where

b? = argminb2ZNRF

+

NRFX

i=1

Ei(bi) s.t. Ptot p [Choi, Evans & Gatherer, 17]

Nact, PSW

Step 0. Estimate switching power as a function of power constraint p,

Step 1. Sort aggregated channel gain to be

Step 2. Derive a MMSQE solution assuming first M RF chains used

Step 3. Find optimal that provides smallest quantization error

Step 4. Final solution:

PSW(b) ! PSW(p)PSW(bi)

�2xi

�2x1

� �2x2

� · · · � �2xNRF

(Nact = M)

M? 2 {1, 2, . . . , NRF}

b?M

b?M?

General Approach

6

To consider RF chains with larger channel gains first

Through binary search

Closed form bit allocation solution for M* active RF chains

Closed form bit allocation solution for given M active RF chains

Switching power becomes fixed value for given power constraint

O(Nr) ! O(logNr)

X

i

Ei(b?M,i)

Offline processing ( )

Joint search ( , )Nact b?

PSW(bi)

Joint Binary Search

7

Bit allocation solution at binary search stage s

bs = argminb2RMs

MsX

i=1

Ei(bi) s.t. 2MsX

i=1

PADC(bi) p

# of activated RF chains at stage sConvex optimization problem

Closed-form optimal solution

Real number relaxation

KK

T*

cond

itio

n

p� Ptotal\ADC

bsi = log2p

2c fs+ log2

k[Hb]i,:k2/3PMs

j=1 k[Hb]j,:k2/3

!, i = 1, · · · ,Ms.

* Karush–Kuhn–Tucker conditions

: Fixed value

: function of channel gains

Bit Optimization Algorithm

8

1) Set power constraint p2) Sort channel gains to be3) Compute Mmax

4) Set 5) Binary Search at stage s with

a)b) For

c) compare total quantization error for d) If Ms has minimum total quantization error

i. compute bs

ii. compute

i. map of Ms to nearest integer, thenii. return

e) else go to smaller half

Ms 2 S

Mmax = min

✓�p�NrPLNA � 2NRFPSW(p)� PBB

NrPPS + PRFchain

⌫,NRFX

i=1

1{hi 6=0}

◆.

S = {1, 2, . . . ,Mmax}

MLs = max(1,Ms � 1), MR

s = min(Mmax,Ms + 1)ML

s , Ms, MRs

b| =⇥max(bs,0)|,0|⇤ 2 R1⇥NRF

Enforce positivity & append zeros

MLs , Ms, M

Rs

bb

�2x1

� �2x2

� · · · � �2xNRF

determines Psw

bsi = log2p

2c fs+ log2

k[Hb]i,:k2/3PMs

j=1 k[Hb]j,:k2/3

!

Joint binary search

Offline Average Switching Power Modeling

9

§ Training for given power constraint p

§ Modeling trained data Tp

Use least-squares polynomial to model average switching power using training data Tp

Resolution switching power estimation: estimate average switching power as a function of total power constraint p

Step 1. Set estimated average switching power Step 2. Perform Algorithm over different channel realizations

and calculate actual switching powerStep 3. Repeat Step 1 and 2 for differentStep 4. Find best estimate of average switching power

Step 5. Set (training data for power constraint p)

Pest

Pact

Pest

P ?est = argminPest(i) |Pact(i)� Pest(i)|

Tp = P ?est

Simulation

10

System Parameters

Cell radius

Min dist.

Noise fig.

Carrier freq. fc

Bandwidth

# Rx ant.

# RF chains

# users

# paths

Tx Power

200 m

30 m

5 dB

28 GHz

1 GHz

256

128

10

13

20 dBm

Environment• Proposed bit allocation (BA) algorithm

• Infinite resolution ADCs ( )

• Fixed ADCs ( -bit ADCs)

• revMMSQE-BA*: Solves MMSQE subject to total ADC power constraint

b1 = 12

b = argminb

NRFX

i=1

Exi(bi)

s.t.NRFX

i=1

PADC(bi) NRFPADC(b)

b = argminb

NRFX

i=1

Exi(bi)

s.t.NRFX

i=1

PADC(bi) NRFPADC(b)

Setting

Total ADC power(not receiver power)

Fixed ADC bits

Resulting total receiver power from revMMSQE-BAPower constraint for proposed BA algorithm

b

[Choi, Evans & Gatherer, 17]

*Bit Allocation

Simulation

11

1 2 3 4 5 6 7 8Quantization Bits b

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

Sum

SpectralEfficiency

R[bps/Hz]

Infinite Resolution b∞

Fixed ADC

revMMSQE-BA

Proposed BA

Spectral Efficiency with MRC

§ Highest spectral efficiency§ Comparable to infinite-resolution at§ Almost no quantization distortion at

§ Highest energy efficiency § is effective region

(already comparable to infinite bits)

1 2 3 4 5 6 7 8Quantization Bits b

1

2

3

4

5

6

7

8

9

Energy

Efficiency

[Mbits/J]

Infinite Resolution b∞Fixed ADCrevMMSQE-BAProposed BA

Energy Efficiency

b < 4b = 1

Proposed Method

Total receiver power consumption

Proposed BA = revMMSQE-BA < Fixed ADC

⌘EE =RW

Ptotbits/Joule

b = 1

Conclusion

12

§ Proposes bit optimization algorithm that solves MMSQE problem:

§ Achieves highest spectral/energy efficiency for low-resolution ADCs

§ Eliminates most of quantization distortion with small power consumption

§ Enables existing state-of-the-art digital combiners to be employed

§ Allows more power for downlink communication

b = argminb2ZNRF

+

NRFX

i=1

Ei(bi) s.t. Ptot p

Contributions

13

Thank you

References

14

[1] Pi, Zhouyue, and Khan, Farooq. "An introduction to millimeter-wave mobile broadband systems." IEEE communications magazine 49.6 (2011).

[2] Fletcher, Alyson K., et al. "Robust predictive quantization: Analysis and design via convex optimization." IEEE Journal of selected topics in signal processing 1.4 (2007): 618-632.

[3] J. Choi, B. L. Evans and A. Gatherer, "Resolution-Adaptive Hybrid MIMO Architectures for Millimeter Wave Communications," in IEEE Transactions on Signal Processing, vol. 65, no. 23, pp. 6201-6216, Dec.1, 1 2017.