A Pseudo Random Postfix OFDM (PRP-OFDM) modulator and inherent channel estimation techniques

Transcription

1 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 Markus.Muck@motorola.com 3 December 2003

2 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 st 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

3 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) [Giannakis97Scaglione99] : Replacing the CP by zeros allows to choose among complexityperformance trade-offs ZP-OFDM guarantees symbol recovery even if channel zeros are located on carriers (at a moderate performance increase) CP-OFDM-like receiver complexityperformance possible based on overlap-add architecture Unresolved sensibility to CIR estimation and time synchronization Markus Muck Marc de Courville Mérouane Debbah Pierre Duhamel 2

4 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 st order statistics) Constant refinement of time synchronization Keep all advantages of ZP-OFDM (including choice among receivers of different complexityperformance 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 36ms 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 560GHz WLAN Make mobility at high carrier frequencies possible where Doppler is an issue Markus Muck Marc de Courville Mérouane Debbah Pierre Duhamel 3

5 0 $ $ % % % % + " + " " + $ " " + & ' ( ) " " + - " - -!. % $ & ' ( ) * & ) * * 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 ig (i) r(i) r(i) s 0 (i) s (i) s N (i) F H N s 0(i) s (i) s 2(i) s N (i) constant postfix c 0 α i c D α i ❷ Channel model : r P (k) = H ISI (P) PS s n DAC sampling rate T s N(k) α(k)c D s(t) H(i) n(t) r(t) ADC + H IBI (P) r n sampling rate T SP r 0(i) r N+D (i) s N(k ) α(k )c D Demodulation & Equalization r 0(i) r N (i) channel size D s P (k) z P s P (k ) H ISI (P) H IBI (P) r P (k) # $ Markus Muck Marc de Courville Mérouane Debbah Pierre Duhamel 4

6 PRP-OFDM channel estimation and tracking PRP-OFDM channel estimation and tracking ❶ Illustration of a received PRP-OFDM symbol r 0 (k) r (k) r 2 (k) r 3 (k) = h D h s 0 (k ) s (k ) s 2 (k ) s 3 (k ) + h 0 h D s 0 (k) s (k) s 2 (k) s 3 (k) = h 0 h D β i α(k ) α(k) = β i s 0 (k) s (k) s 2 (k) s 3 (k) r 4 (k) α(k )c D α(k)c D α(k)c D h D h 0 h D h 0 [ ] sn (k ) H IBI α(k )c D [ ] sn (k) H ISI α(k)c D [ ] sn (k) H βi α(k)c D ❷ Channel estimation based on st order statistics [ E 0 = E r 0 α(k ) ] E 4 = E[ r4 α(k) ] [ ] = E α(k ) s 0 (k) +E[ c D ] = c D }{{} [ =0 ] () = E α(k) s 3 (k) +E[ c D ] = c D }{{} =0 Markus Muck Marc de Courville Mérouane Debbah Pierre Duhamel 5

7 PRP-OFDM channel estimation and tracking ❸ Find channel convolved by postfix E 0 + E = c D + c D = = h 0 h D h D 2 h h h 0 h D h h D h D 2 h D 3 h 0 c 0 c D c D 2 c c c 0 c D c c D c D 2 c D 3 c 0 }{{} CircularDiagonal on Fourier basis c D (2) h D (3) ❹ Extract channel impulse response h D by standard equalization schemes Zero-Forcing (ZF) equalization Minimum-Mean-Square-Error (MMSE) equalization (if noise contributions relevant) Markus Muck Marc de Courville Mérouane Debbah Pierre Duhamel 6

8 Receiver architectures Receiver architectures ❶ Equalization based on transformation of PRP-OFDM ZP-OFDM r PRP = H β i s N(k) α(k)c D ( ) = H ISI + α(k ) α(k) H IBI s N(k) α(k)c D r ZP = H β i s N(k) H β 0 i N α(k)c D α(k)c D (4) Now all existing ZP-based equalization schemes apply : Overlap-Add based equalization (low complexitymedium performance) Pseudo-Inverse based equalization (increased complexityhigh performance) Minimum-Mean-Square-Error (MMSE) based equalization (increased complexityhigh performance) Markus Muck Marc de Courville Mérouane Debbah Pierre Duhamel 7

9 Receiver architectures ❷ Equalization based on diagonalisation of pseudo-circulant matrices ( ) ➀ It can be shown that the pseudo-circulant matrix H β i = H ISI + α(k ) α(k) H IBI is diagonalised as follows : H βi = V P (i)d iv P (i) (5) { } D i = diag H(β P i ) H(β P P j2π P i e P ) where H(z) = z n h n (6) n=0 V P (i) = [ P ] P 2 β i 2n P P F P diag{β n=0 ➁ The following equalization schemes are derived G PRP i...β P P i } (7) ZF = F N [I N 0 ND ]H β i = F N [I N 0 ND ]V H P (i)d i V P (i) G PRP MMSE = F N [I N 0 ND ]R sp s P H β i H Q = F N [I N 0 ND ]R sp s P V H P (i)dh i ˆQ V P (i) Q = R np n P + H β ir sp s P H β i H ˆQ = R np n P + D i ˆR sp s P D H i (8) Markus Muck Marc de Courville Mérouane Debbah Pierre Duhamel 8

10 Low complexity receiver architecture r(i) Low complexity receiver architecture r(i) r n r(t) ADC sampling rate T SP r 0 (i) r D (i) r D (i) r N (i) r N (i) CP-OFDM identical treatment r 0 (i) r N (i) r N+D (i) α(i )H IBI (D)c D +H ISI s N0 (i) α(i ) E[ ] α(i ) α(i)h ISI (D)c D +H IBI s N (i) α(i) E[ ] α(i) analog to digital converter serial to parallel conversion 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

11 PRP-OFDM simulation results in IEEE802.a context PRP-OFDM simulation results in IEEE802.a context 0 0 Comparison CP OFDM vs PRP OFDM (BPSK R=2 BRAN A) 0 0 Comparison CP OFDM vs PRP OFDM (QPSK R=2 BRAN A) PRP ZF80 (20symb) PRP ZF OLA (72 symb) IEEE802.a Preamble CIR est PRP MMSE (72symb) IEEE802.a CIR known 0 0 BER 0 2 BER PRP ZF80 (0symb) IEEE802.a Preamble CIR est PRP MMSE (20symb) PRP MMSE (40symb) PRP ZF OLA (40symb) IEEE802.a CIR known CI (db) CI (db) FIG. BPSK constellations static case. FIG. 2 QPSK constellations static case. Parameters : N = 64 carriers 20MHz bandwidth in the 5.2GHz band using a 6 sample prefix or postfix. A rate R = 2 constraint length K = 7 Convolutional Code (CC) (o7o33) is used before bit interleaving followed by QPSKBPSK mapping. BPSK static case : > 2dB gain is possible by PRP-OFDM for a BER of 0 3 QPSK static case : A.5dB gain is achieved by PRP-OFDM for a BER of 0 3 As expected poor performances for ZF based equalization due to noise spreading Markus Muck Marc de Courville Mérouane Debbah Pierre Duhamel0

12 PRP-OFDM simulation results in IEEE802.a context (High Mobility) PRP-OFDM simulation results in IEEE802.a context (High Mobility) Comparison CP OFDM vs PRP OFDM (BPSK R=2 BRAN A 432 Bytesframe) HL2 Preamble CIR est speed 20ms HL2 Preamble CIR est speed 0ms HL2 Preamble CIR est speed 0ms PRP Doppler Separated MA MMSE (40symb) speed 72ms PRP Doppler Separated MA MMSE (40symb) speed 36ms HL2 CIR known speed 0ms Comparison CP OFDM vs PRP OFDM (QPSK R=2 BRAN A) PRP ZF80 IEEE802.a Preamble CIR est PRP MMSE 72ms MMSE CIR estimation PRP MMSE 36ms MMSE CIR estimation IEEE802.a CIR known BER 0 2 BER CI (db) FIG. 3 BPSK constellations high mobility CI (db) FIG. 4 QPSK constellations high moblity. BPSK mobility vs static case : db 36ms and 0dB 72ms for a BER of 0 3 QPSK mobility vs static case : 0.8dB 36ms for a BER of 0 3 poor 72ms As expected poor performances for ZF based equalization due to noise spreading Markus Muck Marc de Courville Mérouane Debbah Pierre Duhamel

13 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 st order statistics is possible ❹ Several decoding schemes with different complexityperformance trade-offs are proposed ❺ Slight complexity increase compared to CP-OFDM must be tolerated ❻ Performance increase by approx..5db in typical IEEE802.a 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 Duhamel2