Presentation Globecom 2003
A Pseudo Random Postfix OFDM (PRP-OFDM) modulator and inherent channel estimation techniques Markus Muck, Marc de Courville, Mérouane Debbah, Pierre Duhamel Motorola Labs, Eurecom, Supelec
[email protected] 3 December 2003
Overview
Overview
❶ Background and evolution of Orthogonal Frequency Division Multiplexing ❷ Target of Pseudo Random Postfix OFDM (PRP-OFDM) and inherent advantages ❸ The PRP-OFDM modulator and a channel model ❹ Channel estimation and tracking based on 1st order statistics in the receiver ❺ Receiver architectures ➀ based on diagonalisation of pseudo circulant matrices ➁ transformation to Zero Padded OFDM ❻ Simulation results ❼ Conclusion
Markus Muck, Marc de Courville, Mérouane Debbah, Pierre Duhamel 1
State of the art and future of OFDM
State of the art and future of OFDM ❶ Existing coherent OFDM with cyclic prefix (CP-OFDM) : A simple way to convert frequency selective FIR channels into flat faded sub-channels ✔ Simple equalization ✔ No noise correlation over sub-carriers and thus simple decoding for COFDM ✘ Sensibility to channel impulse response (CIR) estimation ✘ Sensibility to channel zero locations ✘ Sensibility to time synchronization ❷ Zero Padded OFDM (ZP-OFDM) [Giannakis97,Scaglione99] : Replacing the CP by zeros allows to choose among complexity/performance trade-offs ✔ ZP-OFDM guarantees symbol recovery even if channel zeros are located on carriers (at a moderate performance increase) ✔ CP-OFDM-like receiver complexity/performance possible based on overlap-add architecture ✘ Unresolved sensibility to CIR estimation and time synchronization
Markus Muck, Marc de Courville, Mérouane Debbah, Pierre Duhamel 2
PRP-OFDM : Advantages and targeted applications
PRP-OFDM : Advantages and targeted applications ❶ Pseudo-Random-Postfix OFDM (PRP-OFDM) The CP is replaced by a pseudo-randomly weighted sequence known to TX and RX ✔ Low-complexity channel estimation and tracking (based on 1st order statistics) ✔ Constant refinement of time synchronization ✔ Keep all advantages of ZP-OFDM (including choice among receivers of different complexity/performance tradeoffs) ✘ Very slight receiver complexity increase (some additions) compared to ZP-OFDM ❷ Application targeted by Pseudo-Random-Postfix OFDM (PRP-OFDM) ✔ WLANs with increased mobility : Reach high throughput at 36m/s and more ✔ WLANs of low mobility : Increase system performance through better CIR estimation ✔ Any OFDM system requiring mobility increase ❸ Contribute to PHY of IST BroadWay proposing a hybrid 5/60GHz WLAN ✔ Make mobility at high carrier frequencies possible where Doppler is an issue
Markus Muck, Marc de Courville, Mérouane Debbah, Pierre Duhamel 3
PRP-OFDM modulator and channel model
PRP-OFDM modulator and channel model ❶ A Pseudo-Random-Postfix OFDM (PRP-OFDM) modulator s˜(i)
s(i)
s˜0(i) s˜1(i)
s0 (i)
sig (i)
P/S
s1 (i)
S/P
r0 (i)
Demodulation & Equalization
s2 (i)
r˜ (i)
r(i)
FH N n(t) sn
s(t)
s˜N−1(i)
constant postfix
❷ Channel model : rP (k) = HISI (P)
sN (k)
+ HIBI (P)
α(k)cD
rN+D−1 (i)
sN (k − 1)
α(k − 1)cD
r˜N−1 (i)
, channel size ≤ D *
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Markus Muck, Marc de Courville, Mérouane Debbah, Pierre Duhamel 4
sP (k − 1)
HIBI (P)
z−P
*
rP (k)
HISI (P)
sampling rate T
c 0 · αi cD−1 · αi
sP (k)
ADC
sampling rate T
sN−1 (i)
rn
r(t)
H(i)
DAC
r˜0 (i)
PRP-OFDM channel estimation and tracking
PRP-OFDM channel estimation and tracking ❶ Illustration of a received PRP-OFDM symbol α(k−1) α(k) H1
hD−1 h1 H1
r0(k) r1(k) r2(k)
h0
s0(k − 1)
hD−1
s1(k − 1) =
s2(k − 1)
r3(k)
s3(k − 1)
r4(k)
α(k − 1)cD
h0
s0(k)
H0 H1
s1(k)
H0 H1
+
hD−1
s2(k)
H0 H1
=
βi · H 1
H0 H1
H1
hD−1 h0 sN (k − 1) HIBI · α(k − 1)cD
sN (k) HISI · α(k)cD
s2(k)
H0
s3(k)
H0 H1
α(k)cD
H0
s1(k) H1
s3(k)
H0
s0(k)
H0 H1
α(k)cD
H0
hD−1 h0 sN (k) H · α(k)cD
βi
❷ Channel estimation based on 1st order statistics E0
E4
=
=
h
r0 α(k−1)
E
h
E
r4 α(k)
i
i
1 = E H0 s0 (k) +E [H1 cD ] = α(k − 1) | {z } =0 1 H1 s3 (k) +E [H0 cD ] = E = α(k) | {z }
Markus Muck, Marc de Courville, Mérouane Debbah, Pierre Duhamel 5
=0
H1 cD (1) H0 cD
= β i · H1
PRP-OFDM channel estimation and tracking
❸ Find channel convolved by postfix
E 0 + E 1 = H1 c D + H0 c D
=
= |
h0
hD−1
hD−2
h1 .. .
h0 .. .
hD−1 .. .
hD−1
hD−2
c0
···
h1
··· .. .
h2 .. .
hD−3
···
h0
cD−1
cD−2
c1
c1 .. .
c0 .. .
cD−1 .. .
···
cD−1
cD−2
cD−3 {z
··· .. .
c2 .. .
···
c0
CircularDiagonal on Fourier basis
❹ Extract channel impulse response hD by standard equalization schemes
cD
hD }
✔ Zero-Forcing (ZF) equalization ✔ Minimum-Mean-Square-Error (MMSE) equalization (if noise contributions relevant)
Markus Muck, Marc de Courville, Mérouane Debbah, Pierre Duhamel 6
(2)
(3)
Receiver architectures
Receiver architectures ❶ Equalization based on transformation of PRP-OFDM ➫ZP-OFDM
rPRP
rZP
=
Hβi
sN (k)
α(k)cD sN (k) α(k−1) = HISI + α(k) HIBI α(k)cD sN (k) 0N − Hβi = Hβi α(k)cD α(k)cD
(4)
Now, all existing ZP-based equalization schemes apply :
✔ Overlap-Add based equalization (low complexity/medium performance) ✔ Pseudo-Inverse based equalization (increased complexity/high performance) ✔ Minimum-Mean-Square-Error (MMSE) based equalization (increased complexity/high performance)
Markus Muck, Marc de Courville, Mérouane Debbah, Pierre Duhamel 7
Receiver architectures
❷ Equalization based on diagonalisation of pseudo-circulant matrices α(k−1) β i ➀ It can be shown that the pseudo-circulant matrix H = HISI + α(k) HIBI is diagonalised as follows : Hβ i Di
= V−1 P (i)Di VP (i), P−1 − P1 − P1 j2π P−1 P ) = diag H(βi ), · · · , H(βi e where H(z) = ∑ z−n · hn
VP (i) =
(5) (6)
n=0
"
P−1
2n 1 P |β | i ∑ P n=0
#− 1 2
1 P
P−1 P
FP diag{1, βi , . . . , βi
(7)
}
➁ The following equalization schemes are derived GPRP ZF GPRP MMSE Q ˆ Q
=
FN [IN 0N,D ] Hβi
−1
=
H
= FN [IN 0N,D ] RsP ,sP Hβi Q−1 = =
H
RnP ,nP + Hβi RsP ,sP Hβi , ˆ s ,s DH Rn ,n + Di R P
P
P P
i
Markus Muck, Marc de Courville, Mérouane Debbah, Pierre Duhamel 8
=
−1 FN [IN 0N,D ] VH P (i)Di VP (i), ˆ −1 VP (i), FN [IN 0N,D ] Rs ,s VH (i)DH Q P P
P
i
(8)
Low complexity receiver architecture
Low complexity receiver architecture r˜ (i)
r(i) r0 (i)
CP-OFDM identical treatment
S/P
rD−1 (i) rD (i)
rn
r(t)
ADC
rN−1 (i)
sampling rate T
rN (i)
r˜0 (i)
r˜N−1 (i)
rN+D−1 (i)
α(i − 1)HIBI (D)cD +HISI sN,0 (i)
α(i)HISI (D)cD +HIBI sN,1 (i) analog to digital converter
serial to parallel conversion
1 α(i−1)
E[·]
α(i − 1)
1 α(i)
E[·]
α(i)
undo pseudo random weighting
expectation calculation
do pseudo random weighting
demodulation and equalization
✔ Slight complexity increase (≈ 6D additions per symbol) compared to ZP-OFDM
Markus Muck, Marc de Courville, Mérouane Debbah, Pierre Duhamel 9
PRP-OFDM simulation results in IEEE802.11a context
PRP-OFDM simulation results in IEEE802.11a context Comparison CP−OFDM vs PRP−OFDM (BPSK, R=1/2, BRAN−A)
0
10
−1
BER
BER
10
−2
10
−3
−4
−2
10
−3
10
PRP, ZF80 (10symb) IEEE802.11a Preamble CIR−est PRP MMSE (20symb) PRP MMSE (40symb) PRP ZF−OLA (40symb) IEEE802.11a CIR known
−4
10
PRP, ZF80 (20symb) PRP ZF−OLA (72 symb) IEEE802.11a Preamble CIR−est PRP MMSE (72symb) IEEE802.11a CIR known
−1
10
10
Comparison CP−OFDM vs PRP−OFDM (QPSK, R=1/2, BRAN−A)
0
10
−4
−3
−2
−1
0
1
C/I (dB)
2
3
4
5
6
7
F IG . 1 – BPSK constellations, static case.
10
−2
0
2
4 C/I (dB)
6
8
10
F IG . 2 – QPSK constellations, static case.
✔ Parameters : N = 64 carriers, 20MHz bandwidth in the 5.2GHz band using a 16 sample prefix or postfix. A rate R = 12 , constraint length K = 7 Convolutional Code (CC) (o171/o133) is used before bit interleaving followed by QPSK/BPSK mapping. ✔ BPSK, static case : > 2dB gain is possible by PRP-OFDM for a BER of 10−3 ✔ QPSK, static case : A 1.5dB gain is achieved by PRP-OFDM for a BER of 10−3 ✘ As expected poor performances for ZF based equalization due to noise spreading
Markus Muck, Marc de Courville, Mérouane Debbah, Pierre Duhamel10
PRP-OFDM simulation results in IEEE802.11a context (High Mobility)
PRP-OFDM simulation results in IEEE802.11a context (High Mobility) 0
10
Comparison CP−OFDM vs PRP−OFDM (BPSK, R=1/2, BRAN−A, 432 Bytes/frame)
−1
BER
BER
10
−2
10
−3
−2
10
−3
10
10
−4
−4
PRP, ZF80 IEEE802.11a Preamble CIR−est PRP MMSE 72m/s, MMSE CIR estimation PRP MMSE 36m/s, MMSE CIR estimation IEEE802.11a CIR known
−1
10
10
Comparison CP−OFDM vs PRP−OFDM (QPSK, R=1/2, BRAN−A)
0
10
HL2 Preamble CIR−est, speed 20m/s HL2 Preamble CIR−est, speed 10m/s HL2 Preamble CIR−est, speed 0m/s PRP Doppler Separated−MA−MMSE (40symb), speed 72m/s PRP Doppler Separated−MA−MMSE (40symb), speed 36m/s HL2 CIR known, speed 0m/s
−4
−3
−2
−1
0
1
C/I (dB)
2
3
4
5
6
7
F IG . 3 – BPSK constellations, high mobility.
10
−2
0
2
4 C/I (dB)
6
8
10
F IG . 4 – QPSK constellations, high moblity.
✔ BPSK mobility vs static case : 1dB gain @ 36m/s and 0dB gain @ 72m/s for a BER of 10−3 ✔ QPSK mobility vs static case : 0.8dB gain @ 36m/s for a BER of 10−3 , poor perf. @ 72m/s ✘ As expected poor performances for ZF based equalization due to noise spreading
Markus Muck, Marc de Courville, Mérouane Debbah, Pierre Duhamel11
Conclusion
Conclusion ❶ A new Pseudo-Random-Postfix OFDM (PRP-OFDM) modulator is proposed ❷ We capitalize on the study results from Zero-Padded OFDM (ZP-OFDM) ❸ Low-complexity channel estimation and tracking based on 1st order statistics is possible ❹ Several decoding schemes with different complexity/performance trade-offs are proposed ❺ Slight complexity increase compared to CP-OFDM must be tolerated ❻ Performance increase by approx. 1.5dB in typical IEEE802.11a scenario due to CIR estimation improvement ❼ Make mobility at high carrier frequencies possible : IST BroadWay ❽ Outlook : Doppler environment, combination of different CIR estimations, unbiased equalizers, etc.
Markus Muck, Marc de Courville, Mérouane Debbah, Pierre Duhamel12
