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1
Channel Estimation and Multiple Access
in Massive MIMO Systems
Junjie Ma, Chongbin Xu and Li Ping
City University of Hong Kong, Hong Kong
2
Li Ping, Lihai Liu, Keying Wu, and W. K. Leung, "Interleave Division
Multiple-Access," IEEE Trans. Wireless Commun., vol. 5, no. 4, pp. 938-947, Apr. 2006.
Peng Wang, Jun Xiao, and Li Ping, "Comparison of Orthogonal and Non-Orthogonal Approaches to Future Wireless Cellular Systems," IEEE Vehicular Technology Magazine, vol. 1, no. 3, pp. 4-11, Sept. 2006.
Junjie Ma and Li Ping, “Data-aided channel estimation in large antenna systems”, IEEE Trans Signal Processing, June 2014.
Chongbin Xu, Peng Wang, Zhonghao Zhang, and Li Ping, "Transmitter design for uplink MIMO systems with antenna correlation," IEEE Trans. Wireless Commun., vol. 14, no. 4, pp. 1772-1784, Apr. 2015.
Main references
3
Contents
Introduction
Channel estimation at the BS
Channel estimation at MTs
Multiple access: OFDMA, SDMA, IDMA and NOMA
Conclusions
4
Contents
Introduction
Channel estimation at the BS
Channel estimation at MTs
Multiple access: OFDMA, SDMA, IDMA and NOMA
Conclusions
5
H. Andoh, M. Sawahashi and F. Adachi, “Channel estimation filter using time-
multiplexed pilot channel for coherent RAKE combining in DS-CDMA mobile
radio”, IEICE Transactions on Communications 81 (7), 1517-1526, 1998.
D. Ishihara, J. Takeda, and F. Adachi, “Iterative channel estimation for
frequency-domain equalization of DSSS signals,” IEICE Trans. Commun., vol.
E90-B, no. 5, pp. 1171–1180, May 2007.
G. Gui, W. Peng and F. Adachi, “Improved adaptive sparse channel estimation
based on the least mean square , ‘IEEE, Wireless Communications and
Networking Conference (WCNC), 2013.
Inspiration from Professor Adachi
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CDMA systems
Professor Adachi is a pioneer in CDMA systems. He made tremendous
contributions in the development of 3G CDMA systems in Japan. In principle,
there is interference among different users in CDMA. Therefore, CDMA can
be also seen as a non-orthogonal multiple access system.
F Adachi, M Sawahashi and H Suda ”Wideband DS-CDMA for next-generation mobile
communications systems”, IEEE Communications Magazine, 1998.
interference among users
7
Iterative channel estimation
Professor Adachi is also a pioneer in iterative channel estimation. He has made
inflation contributions using the frequency domain equalization approach. The
complexity of his approach is surprisingly low, which provides an attractive
option for practice.
D. Ishihara, J. Takeda, and F. Adachi, “Iterative channel estimation for frequency-domain equalization
of DSSS signals,” IEICE Trans. Commun., vol. E90-B, no. 5, pp. 1171–1180, May 2007.
8
SDMA and multi-user gain
The current OFDMA system is orthogonal. How about the future evolution path?
Orthogonal or non-orthogonal? How to optimize multiple access techniques in
massive MIMO environments?
The following is from information theory the capacity for a SDMA system:
sum-rate ~ min(NBS, K × NMT) ∙ log(1+SNR),
where K is the number of users. This gain can be achieved using multi-user
transmission.
Peng Wang, and Li Ping, "On maximum eigenmode beamforming and multi-user gain," IEEE Trans.
Inform. Theory, vol. 57, no. 7, pp. 4170-4186, Jul. 2011.
10
Assumptions: CSIT for the downlink
For the downlink, decoding is done individually. Accurate CSIT is crucial
so as to avoid interference. The system should be orthogonal.
BS
correlation
channel
MT 1
correlation
MT K
correlation
MT k
correlation
individual detection
joint beamforming
11
Assumptions: CSIT for the uplink
For the uplink, accurate CSIT is not crucial. Interference can be suppressed
at the BS via joint detection. The system can be non-orthogonal.
BS
correlation
channel
MT 1
correlation
MT K
correlation
MT k
correlation
joint detection
individual beamforming
12
Difference between down-link and up-link
Assume TDD.
Accurate CSIT is possible for the down-link. Therefore down-link can be orthogonal.
Accurate CSIT is difficult for the up-link. Therefore up-link should be non-orthogonal.
interference down-link up-link
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Contents
Introduction
Channel estimation at the BS
Channel estimation at MTs
Multiple access: OFDMA, SDMA, IDMA and NOMA
Conclusions
14
Accurate channel estimation is crucial at the
BS
Accurate CSIT is required for the downlink.
With TDD, downlink can be estimated at the BS.
Pilot contamination is a serious problem for channel estimation in massive MIMO.
Data aided channel estimation provides an efficient solution to the pilot contamination problem.
15
Pilot contamination
In a multi-cell system, the pilot symbols from neighboring cells may
interference each other, which reduces the accuracy of channel estimation. This
effect is refereed to as pilot contamination.
pilot data
user 1
user 2
user 3
user 4
interference
16
Pilot contamination and capacity
The received power is seriously affected by pilot contamination.
number of BS antennas
received power with
antenna contamination
number of BS antennas
received SNR with
accurate CSIT
17
Impact of pilot length
Pilot contamination is caused by the correlation among pilots. Its effect reduces
with pilot length as:
In principle, pilot contamination can be mitigated by increasing the pilot
sequence length Jp. In practice, this is not desirable, because increasing Jp will
reduce the effective data rate.
Can we reduce pilot contamination without affecting data rate?
2H
1 2
2H
1 1
E 1
E pJ
p p
p p
Jp pilot symbols Jd data symbols
frame length < channel coherent time
18
Data aided channel estimation
The key of the pilot contamination problem is the correlation among pilots.
The data signals have much lower interference (since their length is longer). More
accurate results can be obtained by using data for channel estimation.
pilot data
user 1
user 2
user 3
user 4
19
Iterative data aided channel estimation
decoder
data
detector
channel
estimator
1
dy
1 1,py p
1d
1d
1h
pilot symbol data symbols
However, data symbols are not known initially. We can use partially detected
data for channel estimation based an iterative procedure.
Junjie Ma and Li Ping, “Data-aided channel estimation in large antenna systems”, IEEE Trans
Signal Processing, June 2014.
20
Data-aided channel estimation
Channel estimation phase:
Data detection phase:
H H
1 1 1 1 1 2 2ˆ + noise h d d h d d h
HH H1 1 11 1 1 2
1 1 2H H H
1 1 1 1 1 1
ˆ ˆˆ ˆnoise
ˆ ˆ ˆ ˆ ˆ ˆ
jd j d j d j
h h hh y h h
h h h h h h
self contamination cross contamination
21
Cross-contamination
Cross contamination is now caused by the correlation among data rather
than pilot.
The cross-contamination effect is inversely proportional
• to data length Jd , and
• also to the a priori reliability (1-vd. ).
H
1 2
H HH1
H H
1 1 11 1
1 2 2 2ˆ other terms
0 when .ˆ ˆ other terms
N
d d hh h
d d h hh h
h
2H
1 2
2H
1 1
E 1.
1E d dJ v
d d
d d
22
Self-contamination
When d1 is not perfectly known, and are NOT independent.
Such dependency can be modelled as
where z is independent of and is a random variable. Then
Hence self-interference does not vanish when N. We call this effect
“self-contamination”
For the pilot based scheme, =1 and no such effect exists.
1 1ˆh h1h
1 1 1ˆ ˆ1 z h h h
H H H1 1 1 1 1 1
H H
1 1 1 1
ˆ ˆ ˆ ˆ ˆ11 ,when
ˆ ˆ ˆ ˆN
z
h h h h h h
h h h h
1h
23
Impact of correlation among pilots
Cross contamination:
Self-contamination: (unique to a data-aided scheme)
• Both are inversely proportional to Jd
• When vd = 0, self-contamination vanishes while cross contamination
converges to a positive constant.
2H
21 2
2
2 2H
11 1
ˆE 1
ˆ ˆ 1E d dJ v
h h
h h
β1: large scale factor of h1;
β2: large scale factor of h2
2H
1 1 1
2H
1 1
ˆ ˆE
ˆ ˆ 1E
d
d d
v
J v
h h h
h h
Junjie Ma and Li Ping, “Data-aided channel estimation in large antenna systems”, IEEE Trans
Signal Processing, June 2014.
24
SINR performance
Consider an L-cell System. Each cell contains one user
• Contamination induced distortion 1/Jd
• Conventional cross-cell interference 1/M
4
1
2 2 2H H
1 1 1 1 1 0
1
noiseself-interferencecross-interfernece
2 2
11 0 1
1 1
contamination
ˆESINR
ˆ ˆ ˆ ˆE E E
1
/ 1/ /
1 1
L
i
i
L Ld i
i
i id x d
N
vN
v v J
h
h h h h h h
conventional interference
1
M
=
25
Simulation results: 1 user per cell B
ER
SNR (dB)
conventional pilot-based
SVD blind estimation
data-aided 4 iterations
perfect CSI
-4 -2 0 2 4 6
10-4
10-3
10-2
10-1
100
10-5
r = 1
simulation
prediction
r = 100
r = 1
r = 1
strong interference even
for an extremely high
pilot power
power of pilot symbol
power of data symbolrr =
Settings: 1=1, i=0.2 for i1, N=128, Jp=1, 64-QAM. {i} are large scale
fading factors. The SVD method is from the following reference.
R. R. Muller, et al, “Blind Pilot Decontamination”, IEEE Journal of Selected Topics in Signal
Processing on Signal Processing for Large-Scale MIMO Communications, 2013.
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Contents
Introduction
Channel estimation at the BS
Channel estimation at MTs
Multiple access: OFDMA, SDMA, IDMA and NOMA
Conclusions
27
Accurate channel estimation is not crucial at
MTs
Coarse statistical channel information, such as a covariance matrix, is sufficient in the up-link massive MIMO.
Without accurate CSIT, interference is inevitable. IDMA is an efficient interference cancelation technique, and hence a natural way to realize NOMA.
Chongbin Xu, Peng Wang, Zhonghao Zhang, and Li Ping, "Transmitter design for uplink MIMO systems with antenna correlation," IEEE Trans. Wireless Commun., vol. 14, no. 4, pp. 1772-1784, Apr. 2015.
28
Statistical channel information
Statistical channel information refers to partial knowledge of the channel.
A typical case of statistical channel information is a correlation matrix
containing the power distribution of on different eigen-directions. It does not
contain phase information.
A correlation matrix can be obtained by taking cross-correlation of the received
signals on different antennas. It changes slowly and can be estimated with
much lower cost (compared with full CSIT). The overheads related to CSIT
(such computational cost and pilot usage) can be greatly reduced in this way.
29
Non-orthogonal mode transmission
Statistical channel information, only partial CSIT is available. The system is characterized by the following properties.
Partial CSIT is very useful. It still can provide close to optimal performance.
The channel cannot be fully orthogonalized. There is interference among different users. This leads to the non-orthogonal mode transmission.
Interference cancelation techniques are required to suppress in this case.
initial interference
30
Generalized NOMA
Non-orthogonal scheme are necessary to achieve the ultimate multi-user capacity. The advantage of NOMA becomes noticeable in the high rate regime.
0
1
2
3
4
5
6
7
8
9
-1 1 3 5 7 9 11 13 15 17 19 21
K=1
K=2
K=4 K=8
K=∞
4×4 MIMO
single cell
equal rate for all users
K is the number of
users
sum power (dB)
sum rate
S Tomida and K Higuchi “Non-orthogonal access with SIC in cellular downlink for user fairness enhancement” ISPACS 2011.
Peng Wang, Jun Xiao, and Li Ping, "Comparison of orthogonal and non-orthogonal approaches to future wireless cellular systems," IEEE Vehicular Technology Magazine, Sept. 2006.
31
Mutual information analysis
Chongbin Xu, Peng Wang, Zhonghao Zhang, and Li Ping, "Transmitter design for uplink MIMO systems with antenna correlation," IEEE Trans. Wireless Commun., vol. 14, no. 4, pp. 1772-1784, Apr. 2015.
NBS/NMT = 4
FCSIT = full CSIT
SWF = statistical water filing
NP = no precoding (no-CSIT)
32
CSIT for the uplink
For the uplink, beamforming is individually done, so approximate CSIT is
sufficient to ensure good performance. Decoding can be jointly and
interference can be suppressed.
BS
correlation
channel
MT 1
correlation
MT K
correlation
MT k
correlation
joint detection
individual beamforming
33
Joint detection via IDMA
IDMA is a low-cost technique that facilitates joint detection.
With IDMA, the signals are separated by user-specific interleavers. Channel
estimation, MUD and decoding can be performed jointly and iteratively in an
IDMA receiver.
decoder
MUD
channel
estimator
1
dy
1 1,py p
1d
1d
1h
Li Ping, Lihai Liu, Keying Wu, and W. K. Leung, "Interleave Division Multiple-Access," IEEE
Trans. Wireless Commun., vol. 5, no. 4, pp. 938-947, Apr. 2006.
34
IDMA performance
With a large number of users, conventional MRC detection performs poorly.
Iterative IDMA detection is a low-cost, high performance option.
64 BS antennas
16 users
total rate = 16
IDMA
MRC
-20 -19 -18 -17 -16 -15 -14 -13 -12
10-4
10-3
10-2
10-1
100
Eb/N0(dB)
BER
35
Contents
Introduction
Channel estimation at the BS
Channel estimation at MTs
Multiple access: OFDMA, SDMA, IDMA and NOMA
Conclusions
36
Overview
OFDMA is suboptimal for MIMO. Orthogonal SDMA can do better but is still
sub-optimal. In general, any orthogonal scheme is suboptimal for MIMO.
Theoretically, NOMA can achieve MIMO capacity but, practically, interference
can still be a problem.
IDMA is a low-cost interference cancelation technique, and hence a natural
way to realize SDMA and NOMA.
37
Balanced and unbalanced MIMO
Ideally, we want a true MIMO system, with large numbers of antennas at both
ends. Such a setting can provide a huge rate gain.
In practice, however, we can only mount a limited number of antennas on a
handset. Such a setting can achieve large power gain but not rate gain.
rate
N
power
N
38
OFDMA
In conventional OFDMA, only one user is allowed to transmit on each subcarrier
at a given time in a cell. OFDMA with massive MIMO achieves good power gain.
However, the related rate gain is less impressive.
Can we do better?
rate
N
39
Space-division multiple access (SDMA)
In massive MIMO, more users can be supported using the SDMA via ZF.
sum-rate ~ min(NBS, K × NMT) ∙ log(1+SNR).
However, ZF requires accurate CSIT.
rate
N
K=1
K=2
K=3
40
IDMA and NOMA
IDMA does not require accurate CSIT in the upper link. It can acquire and refine channel information iteratively.
SDMA-IDMA thus provides a robust implement technique NOMA.
S Tomida and K Higuchi “Non-orthogonal access with SIC in cellular downlink for user fairness enhancement” ISPACS 2011.
Peng Wang, Jun Xiao, and Li Ping, "Comparison of orthogonal and non-orthogonal approaches to future wireless cellular systems," IEEE Vehicular Technology Magazine, Sept. 2006.
Y Chen, J Schaepperle and T Wild, “Comparing IDMA and NOMA with superimposed pilots based channel estimation in uplink” PIMRC 2015.
initial interference
41
Multi-user (non-orthogonal) gain
We can view IDMA-SDMA as a NOMA or a non-ideal SDMA. With iterative
processing, it can potentially provide the similar gain as ideal SDMA.
sum-rate ~ min(NBS, K × NMT) ∙ log(1+SNR).
.
rate
N
K=1
K=2
K=∞
Peng Wang, and Li Ping, "On maximum eigenmode beamforming and multi-user gain," IEEE Trans.
Inform. Theory, vol. 57, no. 7, pp. 4170-4186, Jul. 2011.
initial interference among users
42
Simulation Results: 4 Users per Cell
conventional pilot-based
SVD blind estimation
data-aided: 4th iteration
-10 -8 -6 -4 -2 0 2 410
-4
10-3
10-2
10-1
100
BE
R
SNR (dB)
Settings: 1=1, i=0.2 for i1. Jp=1. 64-QAM. Other parameters are the
same as the previous figure. {i} are large scale fading factors.
43
Contents
Introduction
Channel estimation at the BS
Channel estimation at MTs
Multiple access: OFDMA, SDMA, IDMA and NOMA
Conclusions
44
Conclusions
Down-link requires accurate CSIT.
Pilot contamination is a problem in this case, but it can be mitigated by a
data aided channel estimation technique.
Up-link requires only coarse statistical CSIT, provided that iterative
detection is used at the BS.
OFDMA is suboptimal for massive MIMO. Orthogonal SDMA can do
better but is still sub-optimal. Theoretically, NOMA can achieve MIMO
capacity but, practically, interference can be a problem. IDMA is a low-cost
interference cancelation technique, and hence a natural way to realize
SDMA and NOMA.
45
Pilot overhead
pilot data
An challenge how to design pilots for NOMA? In a massive MIMO system
with many users, it can be very costly to allocate orthogonal positions to all
users.
user 5
user 1
user 2
user 3
user 4
user 6
user 7
user 8
46
Superimposed pilots
pilot and data
This problem can be resolved in SDMA-IDMA using superimposed pilots. This
technique is discussed in the paper below and we are current working on this
issue.
Chulong Liang, Junjie Ma and Li Ping, “Rate maximization for data-aided channel estimation in multi-user large antenna systems”, under preparation.
user 1
user 2
user 3
user 4
user 5
user 6
user 7
user 8