Coherent and Non-Coherent UWB Communications

Transcription

1 Coherent and Non-Coherent UWB Communications José A. López-Salcedo Advisor: Prof. Gregori Vázquez Ph.D. Dissertation Signal Processing for Communications Group Department of Signal Theory and Communications Universitat Politècnica de Catalunya (UPC)

2 INTRODUCTION AND MOTIVATION

3 Fundamentals of UWB Technology Basic features It is the oldest but least explored form of radio communication Main characteristics: Impulsive transmission (i.e. no continuous wave) Very large spectral occupancy Advantages: Low-complexity due to baseband transmission (i.e. no RF) Extremely-short pulses high data-rates multipath immunity precise positioning Low power pulses low probability of interception High penetration capability

4 Fundamentals of UWB Technology Temporal characteristics Frequency-Selective and Direction-Dependent Propagation Typical UWB Received Waveforms (Unknown Aggregated Response) time (ns)

5 Fundamentals of UWB Technology Spectral characteristics FCC Spectral Mask (outdoors) Industry standardization approaches UWB Forum Baseband approach (impulse radio) DS-UWB WiMedia Alliance Carrier-based approach MB-OFDM

6 Motivation and Objectives of this Dissertation Motivation of this dissertation: Evaluate the impact of pulse distortion in UWB communications Design robust signal processing techniques for UWB receivers Evaluate the performance loss with unknown received waveforms Design optimal detectors to cope with the absence of CSI Design optimal non-coherent and non-assisted timing synchronizers Design waveform estimation techniques for low-snr scenarios

7 Roadmap

8 PERFORMANCE LIMITS FOR COHERENT & NON-COHERENT UWB J. A. López-Salcedo, G. Vázquez, Closed-Form Upper Bounds for the Constellation-Constrained Capacity of UWB Communications, Proc. IEEE ICASSP 2007, Hawaii (USA), April 2007.

9 Capacity in the Wideband Regime Impact of Channel State Information Controversial result by Kennedy (1969) and Telatar (2000): no CSI W = CW = P S log N 2 e 0 C AWGN But, does UWB capacity -really- depend on CSI? YES when taking into consideration: the actual effect of finite bandwidth peakiness constraints How to analyze capacity in the wideband regime? Introducing the spectral efficiency ratio ( ) R W SNR R W = E b N 0

10 Capacity in the Wideband Regime The same magnitude, two different perspectives Capacity vs. SNR Capacity vs. E b /N 0 2 Gaussian Capacity (bits/channel use) QPSK BPSK SNR (db) SPECTRAL EFFICIENCY

11 Capacity in the Wideband Regime Analysis of Spectral Efficiency Key parameters for analyzing spectral efficiency [Verdu(2002)]: Local analysis of capacity around SNR = 0 C(SNR) = C (0)SNR C (0)SNR 2 + o ( SNR 2) Minimum required bit energy for reliable communication: ( ) Eb 1 = C (SNR = 0) N 0 min Wideband slope or capacity increase per 3 db of E b /N 0, S 0 = 2 [C (SNR = 0)] 2 C (SNR = 0) (bits/s/hz/3db)

12 Capacity in the Wideband Regime Wideband Optimality

13 Capacity in the Wideband Regime Wideband Optimality Results for AWGN and unknown Rayleigh fading channels Unconstrained peakiness Constrained peakiness (E b /N 0 ) min S 0 AWGN log 2 2 Unknown Rayleigh fading log 2 0 AWGN log 2 2 Unknown Rayleigh fading 0 Concept of wideband optimality 1st Order optimal : ( Eb N 0 )min = ( Eb N 0 ) AWGN min 2nd Order optimal : if 1st order optimal and S0 is achieved

14 Capacity Upper Bounds for UWB Communications Channel Model UWB channel modeling is rather controversial. However, for some working conditions: Gaussian assumption holds easy statistical formulation Histogram for IEEE a CM3 r n,i (10) Histogram for IEEE a CM8 r n,i (10) r n,i (50) r n,i (50) r n,i (150) 1000 r n,i (150) IEEE a CM3 (NLOS) IEEE a CM8 (industrial)

15 Capacity Upper Bounds for UWB Communications Coherent receivers - Available CSI Statistics for coherent PPM: f (y x i, g) N (h i, C w ) Closed-form upper bound for the constellation-constrained capacity: ( C c coh log 2 P log 2 (1 + (P 1) exp ρ )) 2

16 Capacity Upper Bounds for UWB Communications Non-coherent receivers - Not available CSI Statistics for non-coherent PPM: f (y x i ) N (0, C w + C hi ) Closed-form upper bound for the constellation-constrained capacity: ( ) Cc US no coh log 2 P 1 P 1 P 1 log P 2 exp 1 N ss 1 γ i (k) γ j (k) 2 σw 2 + γ j (k) i=0 j=0 k=0

17 Capacity Upper Bounds for UWB Communications Coherent vs. Non-coherent receivers Coherent receivers Non-coherent receivers (US) 6 5 IEEE a CM1 (line of sight) IEEE a CM2 (non line of sight) IEEE CM8 (industrial non line of sight) Orthogonal signaling (closed form upper bound) Orthogonal signaling (numerical) from Ref. [10] 6 5 IEEE CM8 IEEE CM8 (closed form upper bound) P= P=16 bits/channel use 3 bits/channel use 3 P= P= ρ (db) ρ (db)

18 Capacity Upper Bounds for UWB Communications Coherent vs. Non-coherent receivers Coherent receivers Non-coherent receivers (US) 6 5 IEEE a CM1 IEEE a CM2 IEEE a CM8 Orthogonal signaling (closed form upper bound) Orthogonal signaling (numerical) from [Dol00] P= P=64 4 P=16 4 P=16 bits/s/hz 3 P=8 bits/s/hz 3 P= P=2 1 P= E b /N 0 (db) ( ) Eb N = ρ 0 min 2C(ρ) IEEE a CM8 IEEE a CM8 (upper bound) E b /N 0 (db)

19 Capacity Upper Bounds for UWB Communications Some Conclusions... Then, which is the most convenient approach? Coherent? Non-coherent? Channel Available Detection Observations time variation CSI approach slow yes coherent -Excellent performance but, how to obtain perfect CSI? moderate/rapid no non-coherent -Low-complexity but, penalty for no CSI -Efficiency problem when P

20 NON-COHERENT DETECTION OF UWB RANDOM SIGNALS J. A. López-Salcedo, G. Vázquez, Detection of UWB Random Signals, Under second review in IEEE Trans. on Signal Processing, May 2006.

21 Motivation How to detect information symbols from UWB signals? Channel Available Detection Receiver time variation CSI approach implementation slow yes coherent correlator-based moderate no non-coherent transmitted-reference (TR) rapid no non-coherent statistics-based (?)

22 Waveform Signal Model Received waveforms Gaussian distributed with exponential PDP - [Kar04], [Sch05b] Histogram for IEEE a CM8 r n,i (10) r n,i (50) Amplitude Time (samples) 10 Uncorrelated samples r n,i (150) Amplitude Correlated samples IEEE a CM8 (industrial) Time (samples) Uncorrelated and Correlated Scattering

23 Optimal Decision Statistics Decision based on the Generalized Likelihood Ratio Test (GLRT) L(r n C g ). = log f (r n H + ; C g ) f (r n H ; C g ) ŝ n = sign (L(r n C g )) Low-SNR optimal decision statistics (GLRT): L (r n C g ) = T r ( [ ] ) C + C R n }{{} 2nd order correlation template Consistent with traditional but ad-hoc energy detection schemes Extends deterministic correlation receivers to second order statistics Insensitive to narrowband interferences

24 Optimal Decision Statistics Uncorrelated Scattering Assumption Low-SNR US optimal decision statistics: L (r n ) = N sf 1 k=0 w(k) N f 1 i=0 r 2 n,i(k) Optimal statistics become a pure energy detector, but... incoming samples are weighted according to their SNR Allows a simple receiver implementation:

25 Optimal Decision Statistics Correlated Scattering Assumption Low-SNR CS optimal decision statistics: L (r n C g ) = T r ( [ ] ) C + C R n }{{} unknown!! Proposed Conditional log-glrt ) ( ) 1. Estimate C + from incoming data: vec (Ĉ+ = A 1 S vec R CN ) ) 2. Create the correlation template: vec (Ĉ+ Ĉ = A T D (Ĉ+ vec 3. Compress the estimated template into the low-snr GLRT: ( ) (A L (r n ) = vec T ) R T 1 CN S A T D vec R n. } {{ } hypothesis testing template

26 Optimal Decision Statistics Rank-1 Receiver via Jeffrey s Divergence Maximization Rank-1 receiver: Rank-1 filter design criterion: Jeffrey s divergence: u = arg max J(H + H ) u m C+ =u mu T m J (H + H ). = E rn H + [L(r n )] E rn H [L(r n )]

27 Optimal Decision Statistics Rank-1 Receiver via Jeffrey s Divergence Maximization For the problem at hand: J(H + H )= C + C 2 F full rank J divergence Divergence IEEE a CM1 IEEE a CM3 IEEE a CM Time shift (samples) Rank-1 Jeffrey s divergence: J(H + H ) = 2 C+ =umu T N m f λ 2 ( ) m }{{} 1 u T 2 m J N u m }{{} eigenmode energy false detection constraint

28 Simulation Results Simulation parameters: BER N Δ =30 samples BER N Δ =400 samples 2-PPM in CS scenario Gaussian random waveforms Exp-Ds=100 samples, Exp-Cs=200 samples N f = 20, N sf = 2000, L = 500 Channel changes every two frames 10 3 ED detector PDP detector rank 1 detector full rank detector TR signal + TR detector TR signal + full rank detector E s /N 0 (db) E s /N 0 (db) Conclusions: ED and PDP significantly degrade Rank-1 near-optimal performance when increasing N

29 NON-COHERENT TIMING SYNCHRONIZATION J. A. López-Salcedo, G. Vázquez, Waveform Independent Frame-Timing Acquisition for UWB Signals, IEEE Trans. on Signal Processing, Vol. 55, No. 1, January J. A. López-Salcedo, G. Vázquez, Frame-Timing Acquisition for UWB Signals via the Multifamily Likelihood Ratio Test, IEEE SPAWC, Cannes (France), June 2006.

30 Motivation How to synchronize when the received waveform is unknown?

31 Proposed Frame-Timing Acquisition Technique (I) Direct UML Approach Low-SNR Unconditional Maximum Likelihood (UML) criterion: N UML ɛ = arg max 0 m (N f 1) ΠT (m)r 2 (0)Π(m) 2 F Interpretation as an energy detection technique

32 Simulation Results Direct UML Approach BER Perfect timing acq. Without timing acq. Dirty template Proposed method Simulation parameters: 2-PAM IEEE a CM1 T f = 86 ns, N f = 16, L = 200 Uniformly distributed timing error E s /N 0 (db) Conclusion: Much more robust performance compared to existing techniques (DT)

33 Simulation Results Direct UML Approach Prob. Correct Acquisition Dirty template Proposed method L=300 L=200 L=100 L=300 L=200 L= E /N (db) s 0 Simulation parameters: 2-PAM IEEE a CM1 T f = 86 ns, N f = 16, L = 200 Uniformly distributed timing error Conclusion: Probability of correct acquisition can be improved up to a factor of 8 compared to DT

34 Proposed Frame-Timing Acquisition Technique (II) Multifamily Likelihood Ratio Test Approach Complexity can be reduced by reformulating the UML criterion as N ɛ UML = arg max 1(0, 1) 2 F 0 m N f 1 R k (m, l). = E [ r n (m) r T n+k (m + l)] Timing acquisition becomes a model order detection problem

35 Proposed Frame-Timing Acquisition Technique (II) Multifamily Likelihood Ratio Test Approach How to determine the length of an unknown signal? Multifamily Likelihood Ratio Test (MFLRT) [Kay05] Reformulation of the UML cost function: N ɛ MFLRT = arg max T m(r) 0 m (N f 1) T m(r) = L m (R) }{{} log-likelihood ( ( ) ) Lm (R) N u (m) ln + 1 N u (m) }{{} model order penalty ( u ) Lm(R) Nu(m) 1

36 Simulation Results Multifamily Likelihood Ratio Test Approach BER L=128 symbols 10 4 Perfect timing acq. Without timing acq. DT lowsnr UML lowsnr UML via MFLRT E s /N 0 (db) Probability Correct Acquisition L=128 symbols 0.2 DT lowsnr UML lowsnr UML via MFLRT E s /N 0 (db) Simulation parameters: 2-PAM IEEE a CM1 T f = 46 ns, N f = 8, L = 128 Uniformly distributed timing error Conclusion: No performance degradation in terms of BER

37 WAVEFORM ESTIMATION FOR COHERENT RECEIVERS J. A. López-Salcedo, G. Vázquez, NDA Waveform Estimation in the Low-SNR Regime, IEEE Trans. on Signal Processing, accepted for publication. J. A. López-Salcedo, G. Vázquez, NDA Maximum-Likelihood Waveform Identification by Model Order Selection in Digital Modulations, IEEE SPAWC, New York (USA), June 2005.

38 Motivation How to obtain (perfect) channel state information? Problems: Traditional channel estimation techniques require high SNR... but UWB operates in the low-snr regime Estimating the channel response may imply hundreds of delays and amplitudes to be estimated Proposed approach: Unstructured approach for estimating the whole waveform The low-snr Maximum Likelihood criterion is adopted Nondata-aided approach to avoid pilot symbols

39 Signal Model General signal model for PAM, PPM and APPM modulations: r = P 1 p=0 A p (g)x p + w r = P 1 K p=0 n= K x n,p K n,p g + w

40 Maximum Likelihood Estimation Low-SNR Approximation Optimal ML waveform estimate: ĝ ML = arg max Λ (r g; x) g The low-snr approximation leads to a compact log-likelihood cost function ( L (r g) = T r [ M R σwi 2 ] ) 1 Nr + }{{} 2 M 2 F }{{} Correlation Matching 2nd Order Constraint M. = L p 1 p=0 K r n= K r K n,p gg H K H n,p

41 Maximum Likelihood Estimation Subspace Compressed Approach Efficient formulation by using the projection coordinates onto the signal subspace rather than the waveform samples themselves, g = U s α length {α} length {g} < 1 SNR gain The log-likelihood can indeed be formulated as a least-squares problem by using the vec( ) operator, max α v L (r g) = max α v α H v Q H r v + 1 }{{} 2 αh v Q H Qα v }{{} CM 2nd OC = min α v r v Qα v 2

42 Simulation Results MSE Performance L=250 symbols SS d max d MAP d opt L=1000 symbols SS d max d MAP d opt Simulation parameters: 16-QAM modulation Complex-valued Gaussian waveform with N g = 8 Oversampling N ss = 2 NMSE(g) (db) Es/N0 (db) NMSE(g) (db) Es/N0 (db) Conclusions: Significant gain in low-snr regime Same slope as SS optimal performance in low-snr regime Floor effect at high-snr

43 Simulation Results BER Performance L=100 symbols L=250 symbols Simulation parameters: 16-QAM modulation Complex-valued random waveform with N g = 8 Oversampling N ss = 2 BER d MAP SS Perfect CSI E s /N 0 (db) BER d MAP SS Perfect CSI E s /N 0 (db) Conclusions: No significant degradation is observed due to ill-conditioning BER can be reduced up to one order of magnitude

44 CONCLUSIONS

45 Conclusions Performance limits for coherent and non-coherent receivers Closed-form approximations of capacity are derived Tradeoff between using coherent or non-coherent receivers Non-coherent detection of UWB signals Optimal schemes are proposed for rapid time-varying channels Low-complexity implementations are proposed via rank-reduction Non-coherent timing synchronization Optimal acquisition techniques are proposed based on low-snr UML Proposed techniques outperform existing frame-timing synchronizers Waveform estimation for coherent receivers Optimal operation under the low-snr regime is possible The link with correlation matching techniques is established

46 Future Work Capacity analysis for UWB signals Link between waveform distributions and capacity maximization Further insights into the capacity convergence rate of coherent and non-coherent receivers Challenges in specific applications Cognitive radio Self-synchronized ad-hoc networking High-sensibility positioning techniques

47 Thank you for your attention!