Globecom 2016

1. Orthogonal Faster than Nyquist Transmission for
SIMO Wireless Systems
T. E. Bogale+
, L. B. Le+
, X. Wang++
and L. Vandendorpe+++
Institute National de la Recherche Scientifique (INRS), Canada+
University of Western Ontario (UWO), Canada++
University Catholique de Louvain (UCL), Belgium+++
Dec. 07, 2016 (Globecom 2016)

2. Presentation Outline
Presentation Outline
1 Existing OFDM Transmission (Summary)
OFDM SISO
OFDM SIMO
2 Objective and Main Results
3 Proposed OFTN Transmission
4 Numerical Results and Discussions
Eye Diagram
BER and Sum Rate
5 Conclusions and Open Problems
(Globecom 2016) Orthogonal Faster than Nyquist Dec. 07, 2016 (Globecom 2016) 2 / 9

3. Existing OFDM Transmission (Summary) OFDM SISO
OFDM SISO
OFDM SISO
Tx signal
x(t) =
n
s[n]g(Bt − n)
Rx signal
y(t) =h(t) ∗ x(t) + w(t)
=
n
s[n]
P−1
i=0
hig(B(t − i ˜Ts) − n) + w(t)
where g(t): pulse shaping, ˜Ts = 1
B , B bandwidth.
(Globecom 2016) Orthogonal Faster than Nyquist Dec. 07, 2016 (Globecom 2016) 3 / 9

4. Existing OFDM Transmission (Summary) OFDM SISO
OFDM SISO
OFDM SISO (Cont’d)
Rx digital samples
y[m] =
l
˜hls[m − l] + w[m]
where w[m] is the noise sample and
˜hl =
P−1
i=0
hig l −
˜Ts
Ts
i
Append CP and express
˜y = ˜Hcs + w
Circulant Hc: Diagonalizable with Fourier matrix
⇒ ˜Hcs can be transformed to a parallel channel
(Globecom 2016) Orthogonal Faster than Nyquist Dec. 07, 2016 (Globecom 2016) 3 / 9

5. Existing OFDM Transmission (Summary) OFDM SIMO
OFDM SIMO
OFDM SIMO
Can be extended straightforwardly
(i.e., Enable parallel channel for each antenna)
Apply MRC receive beamforming
⇒ ˆs[m] = s[m] +
˜g[m]H ˜˜w[m]
|˜g[m]|2
, m = 1, · · · , Ns
where ˜g[m] (mth symbol/subcarrier channel gain) and ˜˜w[m] (noise).
Note:
Both SISO and SIMO: Only 1 symbol every Ts
Multiple receive antenna helps to improve each symbol SINR only
If N >> P, s[m − l], ∀l can be decoded from y[m]
∴ y[m], m = iL, ∀i contains redundant information (i.e., to improve SINR)
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6. Objective and Main Results
Objective and Main Results
Objective and Main Results
Objective:
Is it possible to exploit the the inefficiently used transmission durations
y[m], m = iL, ∀i to pack more information per ˜Ts. If ’Yes’, to what
extent?
Main Result:
If N ≥ P and hi, ∀i are independent, S ≤ P symbols can be
transmitted in (3P − 2)˜Ts (But OFDM can transmit 3 symbols only).
⇒ Large improvement when P is large
Possible Interpretation:
Independent multipath components contain extra multiplexing gain
⇒ Logical (remembers i.i.d channel in MIMO)
(Globecom 2016) Orthogonal Faster than Nyquist Dec. 07, 2016 (Globecom 2016) 5 / 9

7. Proposed OFTN Transmission
Proposed OFTN Transmission
Proposed Transmission (SISO)
Split the bandwidth B Hz to P non overlapping bands (i.e., each with BL = B
L Hz).
Represent
xl x(l ˜Ts) =
P
2
n=−P
2
˜g(t − n˜Ts)dl+n
where d0, d1, d2, · · · are transmitted symbols mapped with ˜Ts, ˜g(t) = 1, 0 ≤ t ≤ P ˜Ts
(rectangular pulse shaping).
SISO
After some steps, Rx can be expressed as
yl =hT
Adl + wl = ¯hT
RT
Adl + wl
where wl ZMCSCG noise, dl = [dl, dl−1, · · · , dl−3P+4, dl−3P+3]T , A = A0A1 with
A0 = convmtx(1T
P, 2P − 1) ∈ P×2P−1 and A1 = convmtx(1T
P, 3P − 2) ∈ 2P−1×3P−2.
(Globecom 2016) Orthogonal Faster than Nyquist Dec. 07, 2016 (Globecom 2016) 6 / 9

8. Proposed OFTN Transmission
Proposed OFTN Transmission
Proposed Transmission (SIMO)
SIMO
⇒ yl = ¯HT
RAdl + wl
yl: Same as MIMO I/O structure!!
Decodability of dl depends on rank(RA) ≤ P
∴ dl can be decodable uniquely iff dl has a maximum of P independent symbols.
(i.e., S = P symbols in 3P − 2 sample durations!!!)
dl can be estimated(decoded) using ZF, MRC etc beamforming types
Improved performance
The decoded BER can be reduced further by again exploiting structure of A and R.
e.g., shown that SIC-ZF, SIC-MRC can be applied (better performance)
(Globecom 2016) Orthogonal Faster than Nyquist Dec. 07, 2016 (Globecom 2016) 6 / 9

9. Numerical Results and Discussions Eye Diagram
Eye Diagram
-0.5 0 0.5
Time
-1
-0.5
0
0.5
1
Amplitude
Eye Diagram
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Time
-1
-0.5
0
0.5
1
Amplitude
Eye Diagram
-0.5 0 0.5
Time
-1
-0.5
0
0.5
1
Amplitude
Eye Diagram
-0.5 0 0.5
Time
-1
-0.5
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1
Amplitude
Eye Diagram
Eye diagram of the proposed design when P = 8 and SNR (γ) → ∞:
[Top left]: N = 6, [Top right]: N = 7, [Bottom left]: N = 8 and [Bottom right]: True eye diagram.
(Globecom 2016) Orthogonal Faster than Nyquist Dec. 07, 2016 (Globecom 2016) 7 / 9

10. Numerical Results and Discussions BER and Sum Rate
BER and Sum Rate
0 5 10 15 20 25 30 35
SNR (dB)
10-4
10-3
10-2
10-1
100
BER
N=6
N=7
N=8
3 4 5 6 7 8
Normalized number of antennas (N0
)
0
5
10
15
20
25
30
35
40
Rate(bps/Hz)
Existing OFDM
Proposed (ZF)
Proposed (ZF-SIC)
SNR=15.3dB
SNR=-4.6dB
Performance in terms of BER and transmission rate when P = 8:
[left]: Effect of N when (γ) → ∞, [Right]: Effect of SNR (N = 2N0 ).
Observations
When N < P, dl cannot be decoded with linear receiver
(i.e., Eye diagram is not open and there is a BER floor)
Using SIC-ZF or SIC-MRC helps improve performance
Larger performance gap at higher SNR
If P is large (e.g., urban environment), massive MIMO will boost performance
(Globecom 2016) Orthogonal Faster than Nyquist Dec. 07, 2016 (Globecom 2016) 8 / 9

11. Conclusions and Open Problems
Conclusions and Open Problems
We propose novel OFTN signaling (transmission) approach for
SIMO system exploiting multipath channels
The proposed algorithm achieves significantly better performance
compared to that of existing OFDM
The proposed design is simple to realize
It can be extended to MIMO, multiuser (multicell) MIMO etc
Some remaining research problems:
It is still not clear how to exploit multipath multiplexing gain in MISO
system (i.e., exchanging role of Tx and Rx)[Non trivial!]
Examine performance of OFTN for standard CSI models (with
varied pulse shaping)
How does the system performance varies in system and link levels
for different systems
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