2011 International Conference on Advanced Technologies for Communications (ATC 2011) Application of Compressive Sensing in Time Hopping Multi-user UWB System Nguyen Thuy Dung, Nguyen Van Sinh, Nguyen Tien Hoa, Nguyen Thanh Hieu Faculty of Electronics and Telecomnunications University of Engineering and Technology Vietnam National University, Hanoi Email: hieunt@vnu.edu.vn Abstract-Recently, ultra-wideband (UWB) is one of the most attractive technologies in communications UWB communication systems are designed to intent to low power, low cost, and low complexity devices However, costly high-speed analog-to-digital converters (ADCs) is required to convert RF/IF signals to digital form for subsequent baseband processing in UWB system By authorized UWB operations over the top of the other bands With wide bandwidth as UWB, the signal is sampled with very high speed sampling rate Clearly, this is the wasteful resources sampling while sampling signal in lower rate within suitable bound still is covered with the accepted bit error rate exploiting sparse property of UWB signal, using compressive (BER) Furthermore, high sampling rate requires the high sensing speed ADC If the ADC which has high-speed, it is very (CS) to reduce the sampling rate is a perspective approach In this paper, we propose a UWB communications system using compressive sensing combined with time-hopping (TH) pulse position modulation (PPM) and pulse amplitude expensive while UWB using as a technology with low cost and low power Thus, the question is how to implement for modulation (PAM), called CS-TH-UWB This system is designed low-speed ADC for signal in UWB reducing the sampling aims to reduce the sampling rate of the origin UWB system rate in UWB The Compressive sensing (CS) is a potential CS technique possesses capability to implement under Nyquist sampling rate at transmitter side At the receiver side, the under Nyquist rate samples are reconstructed with an acceptable loss The simulation of this system is carried out to evaluate the BER of CS-TH-UWB The results show that at low compression ratio investigation in reducing the sampling rate of a sparse signal [5], [6] CS is a method, which allows sampling signal under Nyquist rate and able to apply for sparse signal CS is applied in many fields such as: distributed and remote sensing, etc of sampling rate, the different in BER performance is negligible and specially is in signal sampling in UWB [7], [8] and The higher compression ratio is the more degradation of BER applications in image processing such as medical imaging, performance Keywords: seismic imaging [9] In previous researches, using CS in UWB UWB, multi-user, time hopping, compressive sensing is mentioned such as: CS for 60 GHz in UWB [7], CS based on UWB[8], hybrid modulation scheme combined with time hopping pulse position modulation (TH-PPM) and CS [10], I INTRODUCTION etc However, CS in UWB only applied for single - users In recent years, Ultra-wideband (UWB) is popularly ap (point to point) and using CS for multi-users (point to multi plied and developed Ultra-wideband radio is a fast emerging points) is not considered and compared between TH-PPM technology with uniquely attractive in wireless communica and TH-PAM In this paper, we propose the implementation tions such as wireless personal area network (WPAN) IEEE for reducing the sampling rate by compressive sensing in 802.15.3, IEEE 802.15.4, radar, and localization systems [1], multi-user system using time-hopping (TH) with two basis [2], [3] UWB signal possesses some important properties kinds: pulse position modulation (PPM) and pulse amplitude such as: ultra wide spectrum, low power spectral density modulation (PAM) following the IEEE 802.15.4a standard and acceptable interference with other users UWB has wide with the data rate is 1000 Kbps In this paper, multiple-access bandwidth (over 500 MHz) coexists with other systems can in UWB communications is accomplished with traditional support the high data rate in short range (500 Mbps at 10 spread-spectrum TH technique feet) Thus, UWB can be seen as a potential communications system The results show that at low compression ratio of sampling rate, the different in BER performance is negligible The Normally, the frequency mask depends on the environment higher compression ratio is the more degradation of BER in which the device operates For indoor communications, a performance At sparse rate is about 300, the compression power spectral density of -4l.3 dBmIMHz [4] is allowed in ratio can reach higher 30 for TH-PPM and TH-PAM The the frequency band between 3.1 and 10.6 GHz Lower fre BER performance results also point out that TH-PPM is more quencies are admissible for wall imaging systems and ground sensitive to CS than TH-PAM penetrating radar Other countries have similar regulations, The rest of this paper is organized as follows: section II though they might foresee additional protection for frequency describes the TH-PPM and TH-PAM with CS in UWB system bands below GHz, either by completely prohibiting trans model Section III describes CS with some parameters and mission, or requiring "detect and avoid" Since 2002, the FCC their properties Section IV shows the simulation results of 978-1-4577-1207-4/11/$26.00 ©2011 IEEE 248 system with standard specified parameters Finally, section V comes with conclusion B TH-PAM Transmitter Also in [12], TH-PAM model is proposed for UWB commu nication The same as TH-PPM, in TH-PAM, the bit interval [I SYSTEM DESCR[PT[ON Tb is divided into Ns frames with frame duration of Ts [t means that Tb = NsTs Continuously, it is splitting of frame into Nc chips with equal duration of Te Pseudo random TH code Cj takes value such that :::; Cj :::; Ne - Here the transmitted TH-PAM signal can be modeled as: S(t) += = L ajp(t j=-= Where aj - jTs - CjTc) are binary data takes values in the UWB pulse Figure (2) + {-I, \} , p(t) is shows the signal is modulated by TH-PAM Fig l The block diagram of CS-TH-UWB system [n UWB system, method for multi-user access is based on Time Hopping (TH) technique [1I], [[2] This technique combines with two kind of modulation PPM or PAM So, TH UWB signal is known as TH-PPM UWB signal or TH-PAM UWB signal [11] Figure shows the block diagram of the UWB system with TH-PPM/TH-PAM and CS The detail of system is described below A TH-PPM Transmitter Bits data is modulated by transmission encoder in which TH-PPM UWB transmitted signal is represented as S(t) += = L j=-= Where p(t) p(t - jTs - jTc - caj) aj caj corre In TH-PPM UWB, the single bit duration is presented by formula n = NsTs, where Ns is the number of frames with frame duration of Ts There are Nc chips in each frame Period of chip is Tc such that NcTc :::; Ts The user is assigned with a pseudo random TH code takes value such that :::; Cj :::; Ne - Figure Fig (1) c is the UWB pulse, the time shift is sponding to binary data of [12]: Cj that shows the signal is modulated by TH-PPM TH-PAM signal C AWGN Channel TH UWB signal is transmitted over AWGN channel The AWGN channel block adds white Gaussian noise to the input signal [n this system, we have n(t) is the White Gaussian noise The additive noise is a zero-mean, variance Gaussian process n(t) (J and white with two-side power spectral density (PSD) (J No =- lH-I'Pt·1 trlll,mited 5�nal D Receiver We have signal after go through the AWGN channel is expressed by r(t) = s(t) + n(t) (3) Receiver for multi-pulse signals like TH-PPM or TH-PAM can be based on soft decision or hard decision based [\3] Hard decision decoding of TH-PPM and TH-PPM signal is mentioned in this paper In [12] the optimal receiver for the AWGN channel consists of two systems: the correlator and the S Time [s] Fig 10 11 x10 detector The correlator converts -6 r(t) into N decision variable Zk calculated by: TH-PPM signal Zk 249 = +T r(t)1/Jk(t T)dt T IT = aSmk + nk (4) where Q T, 'ljJk orthogonal basis is channel gain, delay sm(t� and Smk J;+I/Jk(t)dt, nk k 0,1,2, , N - of the = function 0" relates to the width of the pulse Simulation parameters for J;+TI/Jk(t - T)dt = where TH-PPM and shown on Table-I and Table-II TH-PAM are The parameters specified in = The detector decide which signal waveform was transmitted based on the set observation of {Z} The optimum detector decides on the C(r(t), sm) C(r(t), sm) [12] N-1 = L SmkZk- Em k=O III = {Zo, Zl, , ZN -I} sm(t) which maximizes 1000 Kbps 5e-7 sec 0.25e-9 sec 0.5e-9 sec 8.3e-s sec Number of chips(Nc) Pulse shape factor( 0" ) Pulse duration(Tm T T + r(t)s (t ) t Em m -T d - T COMPRESSIVE SENSING FOR Values Data rate( Rb ) Frame duration(Ts) = I TH-PPM Parameters dppm ) Sampling rate Gsamps Time hope code [I 02] (5) TABLE T TH-PPM TH-UW B PARAMETERS CS is an effective data compressive method developed and used in communications and network applications for the recent year [5], [8], [14] For data compression, the sparsity of TH-PPM Parameters Values Data rate( Rb ) 1000 Kbps 5e-7 sec 0.25e-9 sec 0.5e-9 sec signal is the essential condition [15] Literatures [16] and [17] Frame duration(Ts) show that xo can be reconstructed from b by solving a convex program, Xo E R N is a sparse vector, a linear measurements Number of chips(Nc) b b = = Pulse shape factor(O") Pulse duration(Tm Axo E RK, K < < N (if there is measurement noise, Axo + Sampling rate e) ) Gsamps [2 2] Time hope code Let S(t) be N sample signal or N point discrete time having TABLE IT TH-PAM the sparse rate e is a ratio of non-zero number to total number PARAMETERS of sample e Total number of samples = (6) Number of non zero samples where K « N - K (7) For different sparse rate e, there are different maximum compression ratios of p S(t) can A is a K x N measurement matrix be recovered from y with high probability y = AS(t) (8) £1 norm S(t)' BP tion algorithm which finds the vector with smallest [17] After reconstruction, the recovered signal is attempt to find a solution to the following equation: where 11 111 = minIIS(t)111 is the £1 IY 3,9,18,30,45 The results show that subject to AS(t) = BER performance is negligible In Fig 4, at compression ratio p = 3,9,18, the BER performance degrades less than dB In this case, the sampling rate can reduce from Gsamp/s to 333 Msamp/s W hen p = 30, at BER = 10-4, the SNR penalty is about 2.4 dB The higher compression ratio is the In this paper, we focus on using basis pursuit (BP) reconstruc S(t)' = at low compression ratio of sampling rate, the different in N = We have checked the CS signal recovery with different compression ratios p We define the compression ratio p two above table determines the sparse rate e is about 300 y (9) more degradation of BER performance 10 � � � � � �==�==� _ p=45 -p=30 ·_·_·p=18 - - -p=9 p=3 naGS norm SIMUL ATION RESUL TS To verify the quality of our model, several simulations are carried out In this paper, numerical results show the potential of CS for UWB signal in reducing sampling rate capability The performance of the CS- TH-UWB system is considered with correlator-based detectors and AWGN channel model Also the hard decision decoding is applied for this system At 10 -4L - o -"'- -' - � � � ' ' - 10 12 14 � EbNO (dB) here, we consider the second derivative monocycle Gaussian pulse (Scholtz's pulse) as the transmitted pulse waveform Gaussian monocycle is given by [18]: p(t) = _ _ (!)2l -(�)(t/(J")2 _ e [1 0" y'2'if0" (10) 250 Fig BER performance of TH-PAM signal In Fig 5, the BER is investigated to show how degradation if p increases In this simulation, the SNR is fixed at dB The BER increases almost linear with p [2] M.Ghavami,L.B.Michael and R.Kohon, Ultra Wideband signals and systems in communication engineering, Second edition, Wi ley,2007 0.02 [3] C.Duan, G Pekhteryev, JFang, Y-P Nakache, J Zhang, K Tajima, Y Nishioka and H Hirai, " Transmitting multiple HD 0.018 video streams over UWB links" IEEE Consumer Communication & Networking Conference (CCNC), Vol 2,pp 691-695,January 0.016 2006 0.014 0:: w al [4] Andreas F.Molisch, "Ultrawide band Communications - 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'- ' ">-"'-' -' "-' o 14 B 10 [14] Z.Tian, "Compressed wideband sensing in cooperative cognitive EbNO (dB) radio networks", in Proceeding IEEE Global Communications Conference , pp 1-5,New Orleans,Dec.200S Fig [15] J.L.Paredes, G.R.Arce, and Z.Wang, 'Compressed sensing for BER performance of TH-PPM signal ultra-wide band impulse radio", IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2007 [16] S Boyd and L Vandenberghe,Convex Optimization, Cambridge V CONCLUSION University Press,2004 To reduce the sampling rate in UWB use CS with TH-PPM and TH-PAM gets the satisfactory result with suitable sparse (in this paper is 300), we have proposed the combination of CS with multi-user TH-UWB system The simulation is carried [17] Emmanuel Candes and Justin Romberg, ll-magic: "Recovery of Sparse Signals via Convex Programming",Caltech, October 2005 [IS] J.T.Conroy, J.L.LoCicero, and D.R.Ucci, "Communication techniques using monopulse wave-forms", in Proceedings of out to show BER performance for CS-TH-UWB systems with IEEE Military Communications Conference (MJLCOM'99), vol.2, TH-PPM and TH-PAM At the rate is as low as 18, the BER pp.l1S1-l1S5,Atlantic City,NJ,USA,October-November 1999 losses 3dB with TH-PPM and less than I dB with TH-PAM Then, the TH-PPM is more sensitive to CS than TH-PAM REFERENCES [1] Terence W.Barett, "History of Ultra Wideband (UWB) Radar & Communications: Pioneers and Innovators",Progress in Electro magnetics Symposium 2000,Cambridge,MA, July,2000 251 ... bit interval [I SYSTEM DESCR[PT[ON Tb is divided into Ns frames with frame duration of Ts [t means that Tb = NsTs Continuously, it is splitting of frame into Nc chips with equal duration of Te... modulated by TH-PAM Fig l The block diagram of CS-TH -UWB system [n UWB system, method for multi-user access is based on Time Hopping (TH) technique [1I], [[2] This technique combines with two kind... P =45 -p=30 WANG, Hongxin ZHANG," Hybrid Modulation Scheme Combined with TH-PPM, Compressive Sensing and - - - P -18 OFDM", Journal p = of Computational Information Systems 6:S(2010) 2563-2570