designing non-coherent massive simo systemsmainakch/talks/ciss_2014_talk.pdfmc, am, ag (wsl)...

Designing non-coherent massive SIMO systems

Mainak Chowdhury, Alexandros Manolakos, and Andrea Goldsmith

Wireless Systems LabStanford University

March 20, 2014

MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 1 / 19

Outline

1 Prior work

2 System model

3 Proof insights

4 Concluding thoughts


Prior work

Coherent receivers with infinite antennas

High beamforming gain, simple receiver design [Marzetta10]

Small decorrelation distance, large number of antennas

Infinite number of receive antennas, pilot contaminationMC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 3 / 19

Prior work

Non-coherent receivers

Grassman manifold signaling [ZhengTse02]

Analysis of multiuser systems [ShamaiMarzetta02]

High SNR analysis, coherence time assumptions


Our work

Question

How to design systems with large but finite number of antennas, with noCSI ?


Our work

Assumptions

Single antenna transmitter

Knowledge of channel statistics

No instantaneous CSI at transmitter or receiver

Finite transmit SNR, delay and large number of receive antennas

Energy detectors at the receiver

Results

Non-coherent low complexity receivers

Same scaling law as coherent receivers with increasing number ofantennas


Outline

1 Prior work

2 System model

3 Proof insights



Single user system

y = hx+ ν

Assume that hi and νi are i.i.d, y ∈ Rn , E[h∗ihi] = 1, E[ν∗i νi] = σ2

Transmitter

Given a constellation C, transmitter sends x ∈ C

Receiver

Given a decoding function f(·), receiver computes

x̂(y) = f

( ||y||2n

)

Goal

Given channel statistics and transmit power constraints, chooseconstellation C and a decoding function f(·) to get a low Pr(x̂ 6= x)


Results

Constellation design (Result 1)

A minimum distance criterion gives a simple design and achievesasymptotically vanishing error probability

Scaling law optimality (Result 2)

As the number of receiver antennas increases, the scaling law of theachievable rate without CSI is the same as that with perfect CSI

C.= Cnocsi log(n) ≤ Ccsi log(n)

E.g. Cnocsi = 0.5− ε is achievable


Outline

1 Prior work

2 System model

3 Proof insights



Simplified system model

We have

||y||2n

=

∑ni=1 |hix+ νi|2

n= |x|2 + σ2 + ν̃(x)

Idea

Use results from large deviation theory to characterize noise ν̃(x)


Approx. hist. of ||y||2

n with increasing n (p , |x|2 + σ2)

p− d p p+ d0

10

20

30

40

50

60

70n = 5




p− d p p+ d0

10

20

30

40

50

60

70

80n = 10




p− d p p+ d0

20

40

60

80

100

120

140

160n = 50




p− d p p+ d0

50

100

150

200n = 100




p− d p p+ d0

50

100

150

200

250

300

350

400

450n = 500

Concentrates around p = |x|2 + σ2!


Design criterion

Idea

Given |C| = L, one can simply placethe symbols equispaced on a line,gives

dmin =2

L− 1

dmin0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

20

40

60

80

100

120n = 5

For fixed L, as n→∞, SER → 0. Result 1 established !

Result 1



Design criterion

Idea


dmin =2

L− 1

dmin0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

20

40

60

80

100

120n = 10


Result 1



Design criterion

Idea


dmin =2

L− 1

dmin0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

50

100

150

200

250n = 50


Result 1



Design criterion

Idea


dmin =2

L− 1

dmin0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

50

100

150

200

250

300

350n = 100


Result 1



Design criterion

Idea


dmin =2

L− 1

dmin0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

100

200

300

400

500

600

700n = 500


Result 1



Design criterion

Idea


dmin =2

L− 1

dmin 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

100

200

300

400

500

600

700

800

900n = 1000


Result 1



Rate function

Pr

( ||y||2n− |x|2 − σ2 > d

)≤ e−nI1(d),

Pr

( ||y||2n− |x|2 − σ2 < −d

)≤ e−nI2(d)

I1(d), I2(d) are monotonicallyincreasing with positive d

If I(d) , I1(d)1d>0 + I2(−d)1d<0,I(0) = 0, I(d) ≈ w(x)d2

−1.0 −0.5 0.0 0.5 1.00.00

0.05

0.10

0.15

0.20Rate function I


Symbol error rate (SER) of scheme

SER / maxx

e−nw(x)d2min/4 ≈ e−nC/(L−1)2

Choosing L = nt, t = 0.5− ε, can achieve SER = e−Cn2ε → 0

Rate achieved is log(nt) = (0.5− ε) log(n)Symmetric rate of coherent system is also log(n) for large n

Result 2 established !

Result 2

As the number of receiver antennas increases, the scaling law of theachievable rate without CSI is the same as that with perfect CSI

C.= Cnocsi log(n)


Numerical evaluation (UL refers to upper bound)

101 102 103 104

Number of receiver antennas n

10-6

10-5

10-4

10-3

10-2

10-1

100

Pe

L=2,K=0

L=4,K=0

L=8,K=0

L=16,K=0

UL for L=2,K=0

UL for L=4,K=0

UL for L=8,K=0

UL for L=16,K=0

Number of antennas can be brought down (e.g. to 50 for SER10−4, L = 4) by optimizing constellations!


Outline

1 Prior work

2 System model

3 Proof insights



Concluding thoughts

Multiple antenna communication without CSIR (or CSIT) possible byexploiting independent channel realizations!

Scaling law same as that of coherent schemes

Current work:I Extension to multiuser systemsI Optimal and robust constellation designsI Optimal time codes trading off rate and reliability

F For N = 3, error exponent improves from 4 to 4.7

I Comparison of error exponents of coherent and non coherent schemes


Thank you!

Questions?


designing non-coherent massive simo systemsmainakch/talks/ciss_2014_talk.pdfmc, am, ag (wsl)...

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