Partial Channel State Information and Intersymbol Interference in

Partial Channel State Information and Intersymbol Interference in Low Complexity UWB PPM Detection+ T. Zasowski, F. Troesch, A. Wittneben 12. MCM of COST 289 October 30 -31, 2006 + has been published in part at ICUWB, September 2006, Waltham/Boston, USA Communication Technology Laboratory Wireless Communication Group

Outline • Introduction – Motivation – Intersymbol Interference aware ML symbol detection with partial channel state information • Performance without Intersymbol Interference – MLfull, MLIDPD, MLAPDP • Performance with Intersymbol Interference – MLfull, ISI, MLIDPD, ISI, MLAPDP, ISI – Energy detector with MLSE • Conclusions Communication Technology Laboratory Wireless Communication Group 2

Wireless Body Area Network • ultra low power consumption: – low duty cycle, i. e. high peak data rate (50 Mbps): ISI – low complexity modulation and detection • robustness to synchronization errors • sufficient link margin (>25 d. B) within FCC constraints • reasonable excess path delay (<20 ns) • low data rate: throughput < 1 Mbps • • 2 -PPM impulse radio single pulse per bit symbol-wise (energy) detector Goal: get intuition on the impact of partial CSI in the presence of ISI Communication Technology Laboratory Wireless Communication Group 3

Partial Channel State Information • full CSI – (discrete) channel impulse response known at the receiver • instantaneous power delay profile (IPDP) – only magnitude of the real channel taps known at RX – measured after squaring device of energy detector receiver • average power delay profile (APDP) – average power of each channel tap known at RX • no CSI – average energy of channel impulse response known at RX Communication Technology Laboratory Wireless Communication Group 4

Discrete System Model observation window f 2 -PPM channel S Communication Technology Laboratory Wireless Communication Group P Detector 5

Intersymbol Interference Aware Symbol-Wise ML Detection with Partial Channel State Info • observation vector : one PPM frame • statistically independent normal channel taps – diagonal correlation matrices • maximum length of discrete channel impulse response: T • symbolwise -ML decision variable with partial CSI C PPM frame 1 Communication Technology Laboratory Wireless Communication Group 6

Outline • Introduction – Motivation – Intersymbol Interference aware ML symbol detection with partial channel state information • Performance without Intersymbol Interference – MLfull, MLIDPD, MLAPDP • Performance with Intersymbol Interference – MLfull, ISI, MLIDPD, ISI, MLAPDP, ISI – Energy detector with MLSE • Conclusions Communication Technology Laboratory Wireless Communication Group 7

Special Case: Decision Metrics without ISI • full CSI: • instantaneous power delay profile: • average power delay profile: • ISI metrics in paper – for Communication Technology Laboratory Wireless Communication Group : energy detector 8

ED: Energy Detector • uses the decision variable – with • a unitary transformation H has no impact on the error performance • we choose H such, that • after the unitary transformation H we obtain the statistically equivalent decision variable – performance independent of "shape" of impulse response • excess noise due to excess dimensions • without ISI we have for s 1=-1 same as N/2=1 statistically independent zero mean noise from excess dimensions Communication Technology Laboratory Wireless Communication Group 9

MLIPDP: Instantaneous Power Delay Profile • in the high SNR regime we obtain the approximation • without ISI we obtain for IPDP • for MLfull • compare to MLfull • as L(s 1=1)<0 causes a decision error => loss for IPDP Communication Technology Laboratory Wireless Communication Group 10

Performance Results without ISI • based on physical system (continuous time) – PPM frame duration T=20 ns – 10 d. B-bandwidth B 10=3 GHz • uniform power delay profile – max. delay: 10 ns • • equivalent discrete model has N/2=60 i. i. d. normal channel taps energy of each channel realization normalized to 1 – MLfull performance same as AWGN – emphasizes impact of PDP • • minor improvement with IPDP ED performance sufficient Communication Technology Laboratory Wireless Communication Group 11

Outline • Introduction – Motivation – Intersymbol Interference aware ML symbol detection with partial channel state information • Performance without Intersymbol Interference – MLfull, MLIDPD, MLAPDP • Performance with Intersymbol Interference – MLfull, ISI, MLIDPD, ISI, MLAPDP, ISI – Energy detector with MLSE • Conclusions Communication Technology Laboratory Wireless Communication Group 12

MLfull, ISI-Symbol-Wise Detector: Considers ISI • energy per bit: • impulse crosscorrelation: • decision regions adapted to ISI • requires three correlators • free Euclidean distance: Communication Technology Laboratory Wireless Communication Group 13

MLfull-Symbol-Wise Detector: ignores ISI • decision variable – mismatched to ISI – requires only one correlator • free Euclidean distance: • optimal without ISI ( ) • for a=0 and Eh=Eg: 1. 8 d. B loss in comparison to MLfull, ISI • for a=0 we obtain for the loss w. r. t the ISI aware metric Communication Technology Laboratory Wireless Communication Group 14

High SNR performance of MLAPDP (ignores ISI) PPM frame 1 • decision metric for uniform PDP (energy detector) • without additive noise we obtain e. g. for s 1= -1 => ISI causes error floor Communication Technology Laboratory Wireless Communication Group 15

MLSE : Maximum Likelihood Sequence Estimator • uses two decision variables per PPM frame • very limited instantaneous CSI required: – energy detector: L=L 2 -L 1 • simple two-state trellis: • simplified branch metrics – the noise is modelled as normally distributed with nonzero mean • potentially removes error floor of ED with ISI • note: operates with bit clock (as opposed to sample rate) Communication Technology Laboratory Wireless Communication Group 16

Performance Results: Weak ISI • based on physical system (continuous time) – PPM frame duration T=20 ns – 10 d. B-bandwidth B 10=3 GHz • uniform power delay profile – max. delay: 14 ns • • energy of each channel realization normalized to 1 ISI aware metrics substantially improve performance MLAPDP, ISI essentially blanks ISI segment of PPM frame MLSE close to MLAPDP, ISI even though max. delay is not known – no error floor Communication Technology Laboratory Wireless Communication Group 17

Performance Results: Strong ISI • based on physical system (continuous time) – PPM frame duration T=20 ns – 10 d. B-bandwidth B 10=3 GHz • uniform power delay profile – max. delay: 17 ns • • energy of each channel realization normalized to 1 ED not applicable due to 10% error floor – MLSE removes error floor • MLIPDP, ISI almost as robust to ISI as MLfull, ISI – ISI aware metric very efficient • MLSE and MLAPDP, ISI again have similar performance Communication Technology Laboratory Wireless Communication Group 18

Summary and Conclusions • we derived the intersymbol interference aware MLsymbol decision metrics for partial CSI – full CSI (MLfull, ISI) – instantaneous power delay profile (MLIPDP, ISI) – average power delay profile (MLAPDP, ISI) • • MLAPDP, ISI removes the ISI induced error floor of the ED MLfull and MLIPDP are suprisingly robust to ISI MLSE performs similar to MLAPDP, ISI overall the MLSE seem the most attractive compromise between complexity and performance in our application Communication Technology Laboratory Wireless Communication Group 19