1. Design and Performance of a Noncoherent SIMO MAC System
Alexandros Manolakos, Mainak Chowdhury, Andrea Goldsmith
Electrical Engineering, Stanford University
November 26, 2013
AM, MC, AG (EE, Stanford)
Noncoherent massive mimo
November 26, 2013

2. Motivation for large number of antennas
The good Q
High carrier frequencies make larger number of antennas possible More the number of antennas n, more the number of spatial streams
The bad Q
Channel estimation overhead is huge (even at receiver)
Our question
How well do we do with no CSIR (channel state info at receiver) ?
We show
Positive rate achievable schemes with vanishing BER and no CSIR
Low encoding and decoding complexity
Scaling law (with n) of the symmetric rate supported is same as that of the coherent case for 2 users
AM, MC, AG (EE, Stanford)
Noncoherent massive mimo
November 26, 2013

3. System model
Multiuser model with 1 n-antenna receiver and 2 transmitters
y = Hx + n,
y ∈ Rn, H ∈ Rn×m, Hi ,j ∼ N (0, 1), ni is i.i.d. N (0, σ2), x1 ∈ C1, x2 ∈ C2
Idea
We don’t know the channel, let’s look at the received energy !
Simplified system model
||y||2
||h1x1 + h2x2 + n||2 = n n
= x 2 + x 2 + σ2 + ν for n large
1 2
AM, MC, AG (EE, Stanford)
Noncoherent massive mimo
November 26, 2013

4. dmin = BER performance Some facts about ν
Is non zero even if σ2 is zero
By large deviation bound, the following holds
P(|ν| > c) ≤ e−nI (c), ∼
For large n, BER in the system dominated by I (c) for c = “minimum
distance”
where I (c) is the rate function, and I (c) ∝ c2 for small c
dmin =
min |c2 + c2 − c2 − c2 |
1,i 2,j 1,k 2,l
i ,j ,k,l :(i ,j )I=(k,l )
Objective of “constellation” design for small BER
Maximize dmin
Non convex in general, symmetry critical to solving it efficiently
AM, MC, AG (EE, Stanford)
Noncoherent massive mimo
November 26, 2013

5. Comparison with perfect CSI
Perfect CSIR
With CSIR known perfectly, an upper bound on the symmetric capacity of the system is given by
Csym = log(I + HH H) ≈ log n for large n
Scaling law optimality for 2 users
If optimal dmin can be shown to be decaying polynomially with |C1|, |C2|,
i.e. dmin = 1
, the BER is dominated by
|C1|a |C2|b
BER � e−n/(|C1|2a |C2|2b ), for a > 0, b > 0
AM, MC, AG (EE, Stanford)
Noncoherent massive mimo
November 26, 2013
5 / 7

6. Comparison with perfect CSI
Perfect CSIR
With CSIR known perfectly, an upper bound on the symmetric capacity of the system is given by
Csym = log(I + HH H) ≈ log n for large n
Scaling law optimality for 2 users
If optimal dmin can be shown to be decaying polynomially with |C1|, |C2|,
i.e. dmin = 1
, the BER is dominated by
|C1|a |C2|b
BER � e−n/(|C1|2a |C2|2b ), for a > 0, b > 0
Symmetric rate with vanishing probability of error scales like log n
AM, MC, AG (EE, Stanford)
Noncoherent massive mimo
November 26, 2013
5 / 7

7. Numerical results: minimum distance
Achievable Fitted Curve
log(minimum distance)
−0.5
Upper Bound −1
n1=4
−1.5 −2
−2.5
0 10
n1=16
20 30 n2
Figure : Minimum distance with |C1| and |C2|. Fit gives dmin ≥
3.7 (|C1 ||C2 |)1.09
AM, MC, AG (EE, Stanford)
Noncoherent massive mimo
November 26, 2013

8. Numerical results: BER−1
nr = 100
nr = 200
nr = 500
nr = 1000
nr = 2000
nr = 5000 −2
log(BER) −3 −4 −5 6
− 2 3
4 5 6
Number of Constellation points per user 7 8
Figure : BER performance with |C1| and |C2|.
AM, MC, AG (EE, Stanford)
Noncoherent massive mimo
November 26, 2013