Designing non-coherent massive SIMO systemsmainakch/talks/ciss_2014_talk.pdfMC, AM, AG (WSL)...
Transcript of 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
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 2 / 19
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
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 4 / 19
Prior work
Non-coherent receivers
Grassman manifold signaling [ZhengTse02]
Analysis of multiuser systems [ShamaiMarzetta02]
High SNR analysis, coherence time assumptions
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 4 / 19
Prior work
Non-coherent receivers
Grassman manifold signaling [ZhengTse02]
Analysis of multiuser systems [ShamaiMarzetta02]
High SNR analysis, coherence time assumptions
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 4 / 19
Our work
Question
How to design systems with large but finite number of antennas, with noCSI ?
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 5 / 19
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
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 6 / 19
Outline
1 Prior work
2 System model
3 Proof insights
4 Concluding thoughts
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 7 / 19
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)
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 8 / 19
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
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 9 / 19
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
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 9 / 19
Outline
1 Prior work
2 System model
3 Proof insights
4 Concluding thoughts
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 10 / 19
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)
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 11 / 19
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
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 12 / 19
Approx. hist. of ||y||2
n with increasing n (p , |x|2 + σ2)
p− d p p+ d0
10
20
30
40
50
60
70
80n = 10
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 12 / 19
Approx. hist. of ||y||2
n with increasing n (p , |x|2 + σ2)
p− d p p+ d0
20
40
60
80
100
120
140
160n = 50
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 12 / 19
Approx. hist. of ||y||2
n with increasing n (p , |x|2 + σ2)
p− d p p+ d0
50
100
150
200n = 100
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 12 / 19
Approx. hist. of ||y||2
n with increasing n (p , |x|2 + σ2)
p− d p p+ d0
50
100
150
200
250
300
350
400
450n = 500
Concentrates around p = |x|2 + σ2!
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 12 / 19
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
A minimum distance criterion gives a simple design and achievesasymptotically vanishing error probability
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 13 / 19
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 = 10
For fixed L, as n→∞, SER → 0. Result 1 established !
Result 1
A minimum distance criterion gives a simple design and achievesasymptotically vanishing error probability
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 13 / 19
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
50
100
150
200
250n = 50
For fixed L, as n→∞, SER → 0. Result 1 established !
Result 1
A minimum distance criterion gives a simple design and achievesasymptotically vanishing error probability
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 13 / 19
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
50
100
150
200
250
300
350n = 100
For fixed L, as n→∞, SER → 0. Result 1 established !
Result 1
A minimum distance criterion gives a simple design and achievesasymptotically vanishing error probability
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 13 / 19
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
100
200
300
400
500
600
700n = 500
For fixed L, as n→∞, SER → 0. Result 1 established !
Result 1
A minimum distance criterion gives a simple design and achievesasymptotically vanishing error probability
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 13 / 19
Design criterion
Idea
Given |C| = L, one can simply placethe symbols equispaced on a line,gives
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
For fixed L, as n→∞, SER → 0. Result 1 established !
Result 1
A minimum distance criterion gives a simple design and achievesasymptotically vanishing error probability
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 13 / 19
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
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 14 / 19
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)
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 15 / 19
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!
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 16 / 19
Outline
1 Prior work
2 System model
3 Proof insights
4 Concluding thoughts
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 17 / 19
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
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 18 / 19
Thank you!
Questions?
MC, AM, AG (WSL) Noncoherent massive SIMO March 20, 2014 19 / 19