) Optimization of Energy Detetor Reeivers for UWB Systems Mustafa E Şahin, İsmail Güvenç, and Hüseyin Arslan Eletrial Engineering Department, University of South Florida 4202 E Fowler Avenue, ENB-118, Tampa, FL, 33620 E-mail: mesahin, iguven, arslan @engusfedu Abstrat Pratial and low omplexity implementation of reeivers is of vital importane for the suessful penetration of the ultrawideband (UWB) tehnology Energy detetor reeiver is an attrative solution for UWB signal reeption trading off omplexity with performane In this paper, joint estimation of the optimal threshold, synhronization point, and integration interval for energy detetion based ultrawideband signal reeption with on-off keying (OOK) modulation is developed Suboptimal reeption derived from the optimal solution is also given for pratial implementations Gaussian approximation of the reeived signal statistis enables low omplexity solutions at the expense of some performane degradation The performanes of the optimal and suboptimal solutions are evaluated and ompared 1 I INTRODUCTION Ultrawideband (UWB) is a promising tehnology for future short-range, high-data rate wireless ommuniation networks Compared to other ommuniations systems, UWB is unique in that it has the exiting feature of ombining many desired harateristis like the inreased potential of ahieving high data rates, low transmission power requirement, and immunity to multipath effets Coherent reeivers (suh as RAKE and orrelator reeivers) are ommonly used for UWB signal reeption due to their high power effiienies However, implementation of suh reeivers requires estimation of a priori hannel information regarding the timing, fading oeffiient, and the pulse shape for eah individual hannel tap Coherent signal reeption also stipulates high sampling rates and aurate synhronization On the other hand, non-oherent reeivers have less stringent a priori information requirements and an be implemented with lower omplexity For example, in transmitted referene (TR) reeivers, transmission of the referene pulse(s) (whih inludes the hannel information) to orrelate the information bearing pulse(s) eliminates the need for estimating the hannel parameters Energy detetor is another non-oherent approah for ultrawideband (UWB) signal reeption, where low omplexity reeivers an be ahieved at the expense of some performane degradation [1], [2] As opposed to more omplex RAKE reeivers, estimation of individual pulse shapes, path amplitudes, and delays at eah multipath omponent is not neessary for energy detetors Moreover, energy detetors are less sensitive against synhronization errors [3], and are apable of olleting the energy from all the multipath omponents On-off keying (OOK) is one of the most popular non-oherent modulation options that has been onsidered 1 This researh was supported in part by Honeywell, In (Clearwater, FL), and Custom Manufaturing & Engineering (CME), In (St Petersburg, FL for energy detetors OOK based implementation of energy detetors is ahieved by passing the signal through a square law devie (suh as a Shottky diode operating in squareregion) followed by an integrator and a deision mehanism, where the deisions are made by omparing the outputs of the integrator with a threshold Two hallenging issues for the enhanement of energy detetor reeivers are the estimation of the optimal threshold [1], [4], and the determination of synhronization/dump points of the integrator The effet of integration interval on the system performane has been analyzed before for energy detetors [2], and for transmitted referene (TR) based non-oherent reeivers [5]-[7] In this work, a pratial and adaptive reeiver design for UWB signal transmission is developed An energy detetor reeiver that estimates the optimal deision threshold and integration parameters is disussed Suboptimal solutions whih allow pratial and simple implementations with slight performane degradation are also provided II SYSTEM MODEL Let the impulse radio (IR) based UWB signal reeived for bit in a multipath environment be represented as where we have " (1) # $&% + ( %*) -,/10324,65 0378,:9 (2) the number of pulses per symbol is denoted by ;=<, > is the number of multipath omponents arriving at the reeiver, and? are the frame and tap indies, respetively, is the th transmitted bit with OOK modulation, + # is the reeived pulse shape for the? th path, 0 2 is the frame duration ( 0 2A@ 9 @ 0 7 ), % 5 are the time-hopping odes, and ( 9 are the fading oeffiient and the delay of the? th multipath omponent, respetively and 037 is the hip duration The additive white Gaussian noise (AWGN) with double-sided noise spetral density ;CBEDGF is denoted by The reeived signal is passed through a bandpass filter of bandwidth H to apture the signifiant portion of signal spetrum while removing out- J I of-band noise and interferene, resulting in I Now onsider an energy detetor, where the following deision statisti is used to make a symbol detetion by sensing
] B % v e { { v e Š { u v(1) LNA BPF ( ) 2 u(1) v(2) u(2) v(n) Signal Proessing Threshold Estimation Symbol Detetion u(n) Synhronization Fig 1 Adaptive parameter estimation for energy detetor reeivers if there is energy or not within the symbol interval K LNMEOQP R+ - ( %3) -,/10324,65 0378,:9 S I UTGVXW1 4 where 0 is the integration window defined by synhronization and dump points #YZN In other words, the above approah for the energy detetor integrates the square of the reeived signal for eah pulse position over the maximum exess delay of the hannel, and sums these statistis over K ;[< pulses The symbol deision is performed by omparing with a threshold \, K \ Observing (3), it is seen that optimal (joint) estimation of Y-Z^ \ is of ritial importane for the performane of energy detetors, as will be disussed throughout the rest of this paper III PROPOSED RECEIVER Sine the radio hannel harateristis hange in time, an adaptive energy detetor reeiver design that optimizes the performane depending on the variation of the hannel is needed The proposed adaptive reeiver, whih is designed in suh a way to fulfill this requirement, is shown in Fig 1 In this reeiver, the reeived signal is amplified, band pass filtered, squared, and passed through a bank of parallel integrators The reason for employing multiple parallel integrators, eah with a different time onstant, is to selet the integration interval that minimizes the bit error rate ( Using the training bits, that are periodially inserted in between data symbols, a synhronization point (the starting point of the multipath energy) is estimated over eah branh, and an optimum shortterm threshold is evaluated Synhronization and optimum threshold determination are ahieved by estimating the signal and noise statistis (like signal and noise power) during the training period These statistis are then used for relating the expeted performane of eah branh Note that inreasing the number of the parallel integrator branhes, in effet, inreases the integration time resolution of the reeiver and enhanes the likelihood of obtaining a lower However, this omes at the expense of omputational and hardware omplexity Note that as an alternative to employing multiple parallel integrator branhes, optimal reeiver parameters an also be (3) evaluated by using a single integrator and larger number of training bits (to test multiple hypothesis), and storing the statistis for eah hypothesis in a buffer for post proessing A Pratial Estimation of Optimum Threshold The optimal threshold in an energy detetor reeiver depends on the noise variane, multipath delay profile, reeived signal energy, integration interval, synhronization point, and the bandwidth of the bandpass filter From the training samples, the exat optimal threshold \N_a`b an be alulated using the entralized and non-entralized Chi-square distributions, orresponding to bits d and e, respetively, and where f denotes the integrator number However, this requires a searh over possible threshold values in order to find the one that minimizes the [4], or, high signal to noise ratio (SNR) assumption in order to use asymptoti approximation of the Bessel funtion (whih still yields a threshold estimate based on tabulated data) [1] It was shown in [8], [4] that by approximating the Chi-square distributions with Gaussian distributions, whih beomes more valid for large degree of freedom (DOF) defined by FGg FGH 0h - e, the threshold estimates \ _aib an be obtained (as an approximation to \ _a`b Even though these estimates are not very aurate [4], they an be obtained easily, without requiring any searh over possible threshold values Let the means and varianes of the Chi-square distributions for bits d and e be given by j B f kql B V f Jmj f k and l V f, respetively [4], [9], where j B f n go; B (4) l B V f n go; B V (5) j f n go;cb FGprq (6) l V f n go; BV ts p q ; B"u (7) The threshold estimate using the Gaussian approximation is loated at the intersetion of the two Gaussian distributions, whih an be evaluated from ƒ G k Fxw l B V f xy1zm{} {~N ˆ a } F w l V XŠ f GyGzQ{ { {}~N (8)
V F à z Å Taking the natural logarithm of both sides and rearranging the terms, one obtains \N_aib V V \N_aib where the oeffiients are given by Œ d (9) l V f,6l B V f Ž (10) SŒ o, F j B f l V f,:j f l B V f (11) l V f j B V f -,:l B V f Uj V f, F l B V f l V f U l f l B f x (12) 10 0 10 1 10 4 10 5 10 6 10 7 10 8 with (9) being a seond order polynomial equation that an be easily solved for \N_aib (only one of the roots is appropriate The Gaussian approximation approah above is different from the one presented in [4], beause here the noise variane is pratially obtained from the training symbols instead of being taken as a given parameter As an alternative to using frequent training symbols, the threshold an be updated (traked) in a deision-direted manner one it is initially estimated B Adaptation of Integration Interval and Calulation of When implementing an energy detetor, speifying an integration interval that sarifies the insignifiant multipath omponents in order to derease the olleted noise energy will improve the performane [6], [2] For a better performane it is also signifiant that the reeiver synhronizes with the starting point of the multipath energy Therefore, the optimal interval, whih minimizes the, an ideally be ahieved by a joint and adaptive determination of the starting point and duration of integration The starting points and integration durations an be estimated by a synhronization algorithm that tests multiple integration intervals along with various starting points and jointly hooses both so that the is minimized However, this method onsiderably inreases the omputational omplexity of the reeiver A sub-optimal solution, where the initial point of the reeived signal is taken as the ommon starting point for all possible integration durations, yields very lose performane to the optimal ase when the power delay profile (PDP) of the hannel realization is exponentially deaying For example, the hannel model CM1 in [10] reflets suh a minimum phase senario where single synhronization point performs as well For dispersive hannels (suh as CM4) however, there will be some performane degradation Using the training bits, multiple hypothesis for the integration interval an be tested (using multiple integrators) and the one that minimizes the an be seleted Let Y- f and Z^ f denote the starting and dump points of the f th integrator, respetively Then, based on the energy and noise statistis for a partiular integrator, either exat or Gaussian approximation (whih is less omplex but suboptimal) approahes an be used to evaluate the thresholds \ _a`b and \ _aib In order to derease the omputational omplexity, the serial searh for \N_ `b an be performed in the range go; B d u š prq go; B prq, as the normalized threshold in most ases falls in between d u F š and d u š The observed after eah integrator for the two ases are then given by œ-q f \N_a`b and œq f \N_aib, respetively [1], 10 9 with Exat Threshold with Gaussian threshold 10 10 5 10 15 20 25 E /N (db) b 0 Fig ˆªk ˆ«J ˆ k r N 2 Bit error rate vs ž Ÿ8 for different integration intervals ( and $ ± t² k ³ µ ) and for both Gaussian approximated and exat threshold estimates where œ q f \ $ œ E¹ º d^»}e 3 œ ¹ º e» d (13) œ ¹ º d¼»e $ d u š, s d u š¼½ ¾ -À prq ; B À Fx\ (14) ; B8Á  œ ¹ º e» d $ y ¾[Ä z \ Dk; B ¾ Å - Æ g,:y= e (15) the average energy reeived for bits d and e is denoted by p q, Æ ½ ¾ is the generalized Marum- ½ funtion of order g, and Ç* is the Gamma funtion whih equals ÇÈ, e JÉ for Ç integer The optimum integrator is the one that minimizes the, ie ÊGËÌ1ÍÈÎ œq f \ IV SIMULATION RESULTS Computer simulations are done to analyze the performanes of the proposed approahes In these simulations the hannel models in [10] are used and the reeived signal s bandwidth is taken as 2 GHz For eah different integration interval, an exat threshold \N_a`b as well as a Gaussian approximated threshold \N_aib is alulated The s alulated for the two different ases, in whih the exat and Gaussian thresholds are employed, respetively, are ompared to eah other It is observed that the loseness of the two s depends on the bandwidth of the reeived signal For large bandwidths, they obviously differ from eah other, whereas for a relatively small bandwidth like 500 MHz, the values obtained making use of the Gaussian threshold mostly math with the exat s, as shown in Fig 2 Therefore, one an take the advantage of omputational easiness of the Gaussian approximation when setting the threshold if the reeived signal s bandwidth is small It is also found that the effet of determining the synhronization point adaptively is more ritial for shorter integration intervals For longer ones, this approah yields slight gains
10 1 60 Gaussian Approx Exat Calulation 50 CM4 10 4 10 5 Optimum Interval (ns) 40 30 20 CM3 CM2 10 6 CM 4, 20ns, with synh CM 4, 20ns, without synh CM 4, adaptive interval + synh CM 1, 6ns, with synh CM 1, 6ns, without synh CM 1, adaptive interval + synh 5 10 15 20 25 E b /N 0 (db) Fig 3 vs žÿ8 for randomly seleted fixed integration intervals, adaptive integration interval, and adaptive synhronization point ( Ï ªmÐ8µ CM1 10 0 6 8 10 12 14 16 18 20 E b /N 0 (db) Fig 5 Optimum integration interval vs ž Ÿ8 for different hannel models ( Ñ ªÐ8µ V CONCLUSION 10 1 CM1 Fig 4 ( $ ƒ ªQÐ8µ CM2 CM3 05 1 15 2 25 3 35 4 45 5 55 T i (ns) CM4 10dB 20dB x 10 8 vs Optimum integration interval for different hannel models in CM4 (with almost idential performane for other hannel models In Fig 3, is plotted with respet to prqkdk;cb for CM4 and CM1 for a fixed integration interval (synhronized and non-synhronized), as well as for the optimum integration interval Another observation is that the optimum integration interval hanges substantially for different hannel models, implying the fat that signifiant gains an be obtained for a mobile devie when the integration interval is adaptively determined, as shown in Fig 4 Variation of the optimal integration interval with respet to p q DJ; B is plotted for different hannel models in Fig 5 The line-of-sight (LOS) omponent of CM1 yielding a parallel variation with CM2 is observed, together with CM3 and CM4 having larger optimal integration values (and slopes) due to more spread distribution of their multipath omponents over time In this paper, optimization of adaptive energy detetor reeivers for UWB systems is disussed The need for the joint adaptation of the integration interval, optimal threshold, and the synhronization point (for ertain hannels) is learly demonstrated, whih an be extended to other non-oherent approahes Threshold estimation an benefit from the omputational easiness brought by the Gaussian approximation of reeived signal statistis, whih yields reasonable results for ertain bandwidths There are some other issues related to the energy detetor worth to be disussed before onluding By averaging the noise over many pulses that represent a single bit, performane of energy detetor reeivers may be further enhaned Seondly, onsidering the omputational requirements for adaptive threshold determination, for some appliations one may find it more reasonable to employ a fixed long-term threshold that takes the hannel variations into aount UWB multipath omponents an be modeled with Nakagami-Ò distribution [11], [12], and are known to be omposed of less diffuse (speular) omponents for the initial taps (with larger Ò parameter), and more diffuse omponents for the subsequent taps (with smaller Ò parameter One the signal passes through the square-law devie in an energy detetor, the distribution of the signal omponent (when a bit e is transmitted) will be due to the sum of squares of the fading oeffiients [13] Therefore, taking into aount this new distribution (whih is observable over many bloks in the long term), as well as the effet of noise, a long-term fixed threshold an be alulated REFERENCES [1] S Paquelet, L M Aubert, and B Uguen, An impulse radio asynhronous transeiver for high data rates, in Pro IEEE Ultrawideband Syst Tehnol (UWBST), Kyoto, Japan, May 2004, pp 1 5 [2] M Weisenhorn and W Hirt, Robust nonoherent reeiver exploiting UWB hannel properties, in Pro IEEE Ultrawideband Syst Tehnol (UWBST), Kyoto, Japan, May 2004, pp 156 160
Ó [3] A Rabbahin and I Oppermann, Synhronization analysis for UWB systems with a low-omplexity energy olletion reeiver, in Pro IEEE Ultrawideband Syst Tehnol (UWBST), Kyoto, Japan, May 2004, pp 288 292 [4] P A Humblet and M Azizoglu, On the bit error rate of lightwave systems with optial amplifiers, J of Lightwave Tehnology, vol 9, no 11, pp 1576 1582, Nov 1991 [5] H Akahori, Y Shimazaki, and A Kasamatsu, Examination of the automati integration time length seletion system using PPM in UWB, in Pro IEEE Ultrawideband Syst Tehnol (UWBST), Kyoto, Japan, May 2004, pp 268 272 [6] S Franz and U Mitra, Integration interval optimization and performane analysis for UWB transmitted referene systems, in Pro IEEE Ultrawideband Syst Tehnol (UWBST), Kyoto, Japan, May 2004, pp 26 30 [7] N He and C Tepedelenlioglu, Adaptive synhronization for nonoherent UWB reeivers, in Pro IEEE Aoustis, Speeh, Signal Proessing Conf (ICASSP), Montreal, Canada, May 2004, pp 517 520 [8] J Edell, Wideband, nonoherent, frequeny-hopped waveforms and their hybrids in low-probability of interept ommuniations, Report Naval Researh Laboratory (NRL) 8025, Nov 1976 [9] R Mills and G Presott, A omparison of various radiometer detetion models, IEEE Trans Aerospae Eletron Syst, vol 32, no 1, pp 467 473, Jan 1996 [10] J Foerster, IEEE P80215 working group for wireless personal area networks (WPANs), hannel modeling subommittee report - final, Mar 2003 [Online] Available: http://wwwieee802org/15/pub/2003/mar03/ [11] H Urkowitz, Energy detetion of unknown deterministi signals, in Pro of IEEE, vol 55, no 4, Apr 1967, pp 523 531 [12] V I Kostylev, Energy detetion of a signal with random amplitude, in Pro IEEE Int Conf on Commun (ICC), vol 3, New York, Apr - May 2002, pp 1606 1610 [13] M-S Alouini, A Abdi, and M Kaveh, Sum of gamma variates and performane of wireless ommuniation systems over Nakagami-fading hannels, IEEE Trans Vehi Tehnol, vol 50, no 6, pp 1471 1480, Nov 2001