systems using on-off keying (OOK) and pulse shape modulation. (PSM). For this scheme, a set of orthogonal pulses is used to represent bits in a symbol.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.
Modulation Schemes Based on Orthogonal Pulses for Time Hopping Ultra Wideband Radio Systems Sudhan Majhi, A. S. Madhukumar, A. B. Premkumar, and Francois Chin
∗
Centre for Multimedia and Network Technology, School of Computer Engineering Nanyang Technological University, Singapore 639798 ∗ Institute for Infocomm Research, A*STAR, Singapore 119613
Abstract— This paper describes a combined modulation scheme for time hopping ultra wideband (TH-UWB) radio systems using on-off keying (OOK) and pulse shape modulation (PSM). For this scheme, a set of orthogonal pulses is used to represent bits in a symbol. These orthogonal pulses are transmitted simultaneously in the same time slot resulting in a composite pulse. By assigning different subset of orthogonal pulses for each user, multi-user interference can be reduced considerably. The proposed transmission scheme can achieve higher data rate by using fewer pulses and can use fewer number of receiver correlators than those used in PSM. Due to the presence of OOK, the proposed scheme requires minimum energy and is applicable for energy constrained UWB systems. The bit-error-rate (BER) performance of the proposed transmission scheme is analyzed both mathematically and through computer simulations in additive white Gaussian noise (AWGN) channel and modified IEEE 802.15.3a S-V UWB multipath channel model. The present paper also compares the proposed scheme with existing PSM and its combined modulation schemes.
I. I NTRODUCTION The successful deployment of Ultra Wideband (UWB) radio systems for high-speed indoor communication strongly depends on the nature of pulse waveforms, modulation techniques and low complexity receivers. For time hopping (TH)UWB systems, the message symbols are transmitted using short analog waveforms confined within the range of UWB radios. Various kinds of modulation schemes such as pulse position modulation (PPM), pulse amplitude modulation (PAM), on-off-keying (OOK), and bi-phase shift keying (BPSK) have been proposed for TH-UWB radio systems by using short pulse waveform to achieve high data rate transmission [1]. The major challenge is the selection of appropriate modulation scheme for the system design. Due to the robustness against multiple-access interference (MAI) and inter-symbol interference (ISI), pulse shape modulation (PSM) can be considered to be a suitable choice for UWB radio systems [2]. However, due to speculative autocorrelation property of higher order orthogonal pulses, PSM cannot be used for higher-level modulation schemes. This is because PSM requires more number of correlators in the receiver, and this increases the system complexity. To address these problems, some combined forms of PSM scheme have been proposed, which can transmit the same amount of data by using few number of orthogonal pulses and receiver correlators [3][4][5]. The other objective for combined modulations schemes is that they are able to reduce the number
of spectral spikes in UWB signal, which helps the UWB system to coexist with narrowband systems without significant interference [6][7][8]. Most of PSM and its combined schemes are analyzed in AWGN channel model. The limitation and performance analysis of these schemes are discussed in section VI. In this paper, a new combined modulation scheme based on OOK and PSM for M -ary modulation scheme is proposed to reduce system complexity. Here the information bits or symbols are mapped into orthogonal pulse waveforms by onoff-keying. M -ary modulation scheme requires N number of orthogonal pulse waveforms and receiver correlators where N = log2 M . The paper also discusses the usefulness of orthogonal pulses in a multi-user environment. It is known that orthogonal pulses are more susceptible in multi-path channel. Therefore, BER performance of the proposed scheme is analyzed through computer simulation in modified IEEE 802.15.3a S-V UWB multi-path channel model. To compare it with other schemes, existing PSM and its combined modulation schemes are also analyzed in multipath channel model. The paper is organized as follows: Section II discusses all the modulation schemes based on orthogonal pulses. Section III describes proposed modulation scheme. Section IV discusses transmission and detection procedures in multipath model. Section V shows the performance analysis of the proposed method and section VI discusses the corresponding simulation results in AWGN channel and in multipath channel. II. M ODULATION S CHEMES BASED ON O RTHOGONAL P ULSES Using orthogonal pulses for radio transmission is becoming an interesting research topic in UWB radio technology. Current research in this direction includes PSM modulation schemes and many other combined forms of PSM modulation such as bi-orthogonal, PPM-PSM, and BPSK-PSM schemes [6][3][4]. Details of some of such modulation schemes and used orthogonal pulses are given below: A. Pulse Shape Modulation The PSM scheme represents different symbols using different pulses, which are orthogonal to each other. This modulation scheme is more useful for M -ary communication signaling system [2]. Since the constellation points are in different Euclidean plane, this scheme has higher power efficiency than
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.
the conventional modulation schemes. It is robust against ISI when compared with PPM scheme. The typical M -ary PSM signal of the k th user for the ith symbol can be written as (k) (k) (k) si (t) = Etx wi (t − jTf − cj Tc ) (1) j=0
where wi (t) is the orthogonal pulses, Tf is the pulse repetition (k) interval, cj is the pseudo-random code for k th user in j th (k) pulse repetition interval, Tc is the chip duration, Etx is the th transmitted power of the k user. B. Bi-orthogonal and BPSK-PSM Modulation Schemes Two bi-orthogonal modulation schemes have been proposed for M -ary signaling based on orthogonal pulses and their negative ones [4][3]. These requires fewer numbers of pulses and receiver correlators compared to PSM scheme. These schemes transmit the same amount of data by using fewer numbers of pulses, which improve the spectral efficiency in UWB signal [7]. By modifying (1), bi-orthogonal scheme can be represented as a signal of M -ary bi-orthogonal modulation scheme with M/2 different orthogonal pulses, where i = 0, 1, . . . M/2 − 1, and the negative ones are defined by wi+M/2 (t) = −wi (t). The number of correlators or match filters of the receiver drops to half of the PSM scheme. On the other hand, BPSK-PSM scheme transmit several orthogonal pulses in the same time slot. C. 2PPM-PSM Modulation Scheme The combined 2PPM and PSM scheme transmits data by using a composite pulse of orthogonal pulses. To transmit one symbol, one or more numbers of orthogonal pulses is used in two different shift positions [6]. This modulation uses fewer number of pulses and receiver correlators compared with the above modulation schemes. This scheme offers high average power efficiency due to the presence of PPM scheme. The typical M -ary PPM-PSM signal of the k th user for the ith symbol can be expressed as (k) (k) (k) si (t) = Etx xi bN (t − jTf − cj Tc ) (2) j=0
th
where xi is the i row of constellation matrix, which contains vectors of the multipliers for the different pulses in the different positions. Transmitted pulses can be expressed as an N -dimensional vector bN (t) = [w1 (t) · · · wk (t) w1 (t − δ) · · · wk (t − δ)]
(3)
where N = 2k and k is the number of orthogonal pulses. D. Orthogonal Pulses To achieve the above modulation schemes, various types of orthogonal pulses have been proposed such as modified Hermite pulses, Prolate spheroidal wave function (PSWF), orthogonal pulses based on Battle-Lemarie, and pulses based on Harr wavelet [9][3][10]. Most of the modulation schemes are analyzed in AWGN channel model while only BPSK-PSM
TABLE I T RANSMITTED PULSES FOR 2- BIT AND 3- BIT SYMBOLS Schemes
2-bit
3-bit
00 01 10 11 000 001 010 011 100 101 110 111
w0 (t) Off Off Off Off Off Off Off Off On On On On
Tf w1 (t) Off Off On On Off Off On On Off Off On On
w2 (t) Off On Off On Off On Off On Off On Off On
Combined form of transmitted pulses None w2 (t) w1 (t) w1 (t) + w2 (t) None w2 (t) w1 (t) w1 (t) + w2 (t) w0 (t) w0 (t) + w2 (t) w0 (t) + w1 (t) w1 (t) + w2 (t) + w2 (t)
scheme is analyzed in multi-path channel by employing PSWF pulses. In this paper, all modulation schemes are analyzed in AWGN and multi-path channel model and compared with proposed scheme. Due to simplicity and higher power efficiency, Hermite and PSWF pulses have been considered in this paper for discussion and simulation results [2][3]. For ease of understanding, it has been assumed that orthogonality of the pulses is maintained despite the differentiating effect of the transmitter and receiver antennas. III. P ROPOSED C OMBINED M ODULATION S CHEME The proposed method maps a set of message bits or symbol into one or more orthogonal pulses by on-off keying. The number of pulses in each symbol depends on the number of non-zero bits. This method transmits the same number of symbols using fewer pulses and requires fewer correlators than those used in conventional PSM and its combined schemes [2] [6][4]. Table-I shows example of 2-bit and 3-bit symbol transmission and the corresponding transmitted pulses. From the table, it can be seen that in general, to transmit N -bit symbol, M = 2N symbols, N orthogonal pulses are required. These N independent bits can be sent at the same time by assigning different orthogonal pulses. Due to orthogonality, the pulses overlay in both time and frequency domains without any interference. The proposed scheme provides low design complexity due to fewer number of pulses and receiver correlators than those used in PSM. Moreover, it does not require a large number of orthogonal pulses for higher-level modulation scheme. Another advantage is that it can coexist with the overlapping narrowband (NB) systems without giving significant interference due to the presence of fewer number of spectral spikes [6][7]. Each pulse can be recovered from the composite pulses by exploiting their correlation properties. The block diagram for a N -bit symbol transceiver is shown in Fig.1. IV. S YSTEM M ODEL IN THE P RESENCE OF M ULTIPATH In this section, the proposed scheme is analyzed in the presence of multipath channel model proposed by the IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.
802.15 study group 3a [11]. This multipath model can be expressed as of the following discrete time impulse response: h(k) (t) =
LP l=1
(k)
(k)
αl δ(t − τl )
(4)
(k)
where τl is the delay of k th user which takes values in the (k) continuous time-invariant model, αl is the lth path gain of k th user, assuming LP is the total number of paths for all the users. The combined OOK and PSM modulation signal of the k th user and for the ith symbol can be defined as (k)
si (t) =
(k) (k) Etx ai w(k) (t − jTf − cj Tc )
(5)
j=0
where i = 0, 1, . . . , M − 1, index j represents the number of time frame for a symbol and (k)
(k)
(k)
w(k) (t) = [w0 (t) w1 (t) · · · wN −1 (t)]T
(6)
is the N -dimensional column vector, ai is the N -bit binary row data vector for the ith symbol. If there are Nu number of users and each experiences a different channel model (4), then the received signal can be expressed as r(t) =
Lp Nu k=1 l=1
(k) (k) + n(t) αl s(k) t − τl
(7)
where τlk is the time delay of lth path for k th user, and n(t) is the AWGN. The reference signal of the desired user ( say, user 1) q th (= 0, 1, · · · , N − 1) correlator can be expressed as φ(1) q (t)
=
N s −1 j=0
(1)
vq(1) (t − jTf − cj Tc )
(8)
V. P ERFORMANCE IN M ULTI -U SER AND M ULTIPATH E NVIRONMENT For analysis, it is assumed that perfect synchronization exists between transmitter and the reference receiver. Assuming (1) that τl = 0 and the transmitted symbol uses q th order pulse (1) (1) wq (t), the desired signal Sq can be expressed as [12][13] Tf Lp N s −1 (1) (1) (1) (1) (1) Sq = Etr αp αp wq(1) t − cj Tc −
Lp
αp(1) wq(1) (t − τp(1) )
(9)
(1) τp(1) wq(1) t − cj Tc − τp(1) dt Lp (1) 2 (1) = Etr Ns αp p=1
p=1
(11)
The decision statistics of the desired user (say, user 1) in the q th correlator can be written as Zq(1) = =
(j+1)Tf
jTf Sq(1)
(1)
+
r(t)φ(1) q (t)dt
IP Iq(1)
+
0
j=0 p=1
where Ns is the total number of time frame for a symbol and vq(1) (t) =
Fig. 1. (a)A simple Transmitter structure and (b) Receiver structure for combined N -bit OOK-PSM scheme (c) Details of Rake receiver for q th (q = 0, 1, . . . , N − 1) correlator.
M P Iq(1)
(10) +
M AIq(1)
+
(1) IP Iq
The ISI is occurred due to IPI and MPI. The of user 1 in the q th correlator can be expressed as Tf Lp Lp N s −1 (1) (1) (1) (1) αp αl wq(1) t− IP Iq = Etr j=0 p=1 l=1 l=p
Nq(1)
(1)
(1)
where Sq is the desired signal, IP Iq is the inter-pulse(1) interference (IPI), M P Iq is the multi-pulse-interference (1) (MPI), M AIq is the multiple-access interference (MAI) due (1) to the presence of multi-user and Nq is the noise term.
=
(1)
cj Tc − τl (1)
Etr Ns
0
Lp Lp p=1 l=1 l=p
(1) wq(1) t − cj Tc − τp(1) dt (1)
(1,1) αp(1) αl Rqq (∆)
(12)
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T (k) (k,k) (k) where Rqq (∆) = 0 f wq (t)wq (t − ∆)dt, q ∈ (1) (1) (1) {0, 1, · · · , N − 1}, and ∆ = (τl − τp ). M P Iq of user one in the q th correlator can be written as Lp Lp N (1) (1) (1,1) (1) M P Iq = Etr Ns αp(1) αl Rqm (∆) (13) p=1 l=1 m=1 l=p m=q
(1)
M AIq is the MAI from the Nu − 1 users, and can be expressed as Lp Lp N N u −1 s −1 (k) (k) (1,k) M AIq(1) = αl αp(1) Rqq (∆ ) Etr j=0 p=1 l=1
k=2
(14) (1)
(k)
(1)
(k)
(1)
where ∆ = (cj −cj )Tc −(τp −τl ). Nq is the AWGN generated by q th correlator, and can be expressed as Tf Lp N s −1 Nq(1) = αp(1) n(t) (15) 0 j=0 p=1 (1) × wq(1) t − cj Tc − τp(1) dt (1) IP Iq ,
The variance of 2 2 2 σIP I , σM P I , σM AI , and pressed as 2 σIP I
=
(1) Etr Ns Tf−1
(1) (1) (1) M P Iq , M AIq and Nq 2 σN , respectively, and can be
Lp Lp Lp Lp p=1 l=1 p =1 l =1 p =p l =l
are ex-
(1) (1) (1) αp(1) αl αp αl Q (∆ )
(16) (1) (1) (1) (1) where ∆ = τl − τp − τl + τp and Q (.) is the correlation function of Rqq (.). The noise due to other multi pulses is 2 σM PI
=
(1) Etr Ns Tf−1
Lp Lp Lp Lp N N p=1 l=1
m=1 p =p l =l m=q m =q p =1 l =1
m =1
(1)
αp(1) αl
(1) (1)
αp αl Q (∆ ) (17) where Q (.) is the correlation between Rqm (.) and Rq m (.). The noise due to other users is −1 2 σM AI = Ns Tf
Nu k=2
(k)
Etr
Lp Lp Lp Lp p=1 l=1
p =1 l =1
(k) (1) (k)
αp(1) αl αp αl
Q (∆ ) (18) (1) (k) (1) (k) where ∆ = τl − τp − τl + τp , and Q (.) is the sum of Q (.) and Q (.), and the white noise component is Lp (1) 2 N0 Ns p=1 αp 2 (19) σN = 2 Due to the different autocorrelation values for the different pulses, each correlator gives different probability of error. It can easily be proved that that the noise/interference terms as
zero-mean gaussian variables, then the corresponding probability of error of the lth correlator in the presence of ISI and MAI can be written as [1]
(1) 2 Sq (20) Pl = Q 2 2 2 2 2(σIP I + σM P I + σM AI + σN ) Since each decision is independent, the average probability of bit error is defined as P rb =
N −1 1 Pl N
(21)
l=0
where N is the total number of correlators for N -bit symbols transmission. The correct decision of the lth correlator is 1 − Pl . The received symbol is perfect if all correlators take correct decisions. Since decisions are independent, the correct decision for a symbol can be defined as Pc =
N −1
(1 − Pl )
(22)
l=0
and (1 − Pc ) gives the error probability N bit-symbols. VI. S IMULATION R ESULTS AND D ISCUSSION A. AWGN channel In this section, simulation results of 2-bit symbols for PSM and its combined schemes are presented. The simulation studies are conducted in AWGN and IEEE 802.15.3a S-V UWB multi-path channel model under the assumption of perfect synchronization between transmitter and reference receiver. All simulations assume either modified Hermite or PSWF orthogonal pulses without using any coding or guard interval [2][14] [3]. The performance of 2-bit schemes are given in Fig.2 and Fig.3 by using modified Hermite pulses and PSWF, respectively, it can be seen that all the combined modulation schemes outperform PSM scheme. The proposed scheme provides low design complexity due to fewer number of pulses and receiver correlators than PSM. It does not require large number of orthogonal pulses for higher-level modulation scheme. Another advantage is its coexistence with the overlapping NB systems without giving significant interference due to fewer number of spectral spikes. Compared with bi-orthogonal scheme, the proposed scheme requires fewer number of pulses and receiver correlators. However, for 1-bit modulation, bi-orthogonal modulation scheme shows better performance due to the same number of pulses. For higher-level modulation, OOK-PSM shows nearly the same performance. Due to polarity dependent property of biorthogonal modulation, it is difficult to design antipodal signal for orthogonal pulses, which increases complexity of system design [15]. It can be seen that the proposed scheme gives nearly the same performance as 2PPM-PSM scheme. However, due to the presence of pulse position in 2PPM-PSM scheme, the ISI and MAI issues resurface in 2PPM-PSM modulation scheme,
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.
Pb vs Eb/N0 for 2−bit scheme
0
10
−1
10
BER vs Eb/N0 for 2−bit scheme
0
10
PSM Bi−orthogonal PPM−PSM BPSK−PSM OOK−PSM theory of OOK−PSM
PSM Bi−orthogonal 2PPM−PSM BPSK−PSM OOK−PSM
−1
10
−2
10
−2
BER
BER
10
−3
10
−3
10
−4
10
−4
10
−5
10
0
2
4
6
8 Eb/N0 [dB]
10
12
14
16
Fig. 2. Performance of PSM, bi-orthogonal, PPM-PSM, BPSK-PSM and OOK-PSM for 2-bit symbols transmission scheme for modified Hermite pulses in AWGN .
which can severely affect the system performance in multipath environment. Maintaining orthogonality of constellation vector is very important for better system performance. So, it requires some coded modulation to achieve the orthogonality of constellation vector [16]. Since 2PPM-PSM scheme uses 2PPM with PAM, recovery of signals at the receiver is complicated in the presence of multipath. In addition, due to the presence of constellations matrix, map decision vector and distance comparator vector increases the complexity of system design [6]. Due to polarity dependent property of bi-orthogonal modulation and BPSK-PSM, it is difficult to design antipodal signal for orthogonal pulses [15]. On the other hand, OOKPSM is polarity independent modulation scheme and needs minimum power when compared with BPSK-PSM scheme. For higher-level modulation scheme, BPSK-PSM cannot be used for energy constrained UWB system. B. Multipath Channel Since the orthogonal pulses are more sensitive in multipath channel, it is required to analyze the performance of PSM modulation and its combined scheme in the presence of multipath environment. In this paper modified S-V channel model are used for the simulation studies. Channel model corresponding line of sight (0-4m) environment (CM1) is used for this studies. Channel estimation is done by using selective RAKE receiver and maximum ratio combining MRC [11]. The number of significant path is decided by taking path within 10 dB of the strongest paths and 85% energy of the multipath. To collect all these multipaths, RAKE combined method is employed in the proposed system. It is assumed that the transmitted pulse average interval is much longer than the pulse duration. In channel estimation, only distinguishable
−5
10
0
2
4
6
8 Eb/N0 [dB]
10
12
14
16
Fig. 3. Performance of PSM, bi-orthogonal, PPM-PSM, BPSK-PSM and OOK-PSM for 2-bit symbols transmission scheme for PSWF pulses in AWGN.
paths are selected. Fig.4 and Fig.5 show the performance of combined PSM schemes by using modified Hermite and PSWF, respectively, where number of Rake fingers is 17. The PSWF gives better performance than modified Hermite pulses in the presence of multipath. Fig.6 shows the performance for 23 Rake fingers by using modified Hermite pulses. The proposed OOK-PSM shows better performance than PSM scheme, but BPSKPSM gives better performance than all the other modulation schemes. Since zero is represented by pulse off, OOK complexity is nearly half of that in any other modulation scheme. Hence the combined form OOK-PSM has (3/4)th complexity of that of BPSK-PSM. Therefore, M -ary OOK-PSM compensates for lower implementation cost complexity systems. In multipath scenarios, it is assumed that chip duration is greater than the access delays. Although, some others modulation schemes give nearly the same performance, OOK scheme and its combined form with PSM is appropriate choice for system design due to its simplicity and low cost. VII. C ONCLUSION This paper shows a combined modulation scheme for N bit symbol transmission by using fewer number of orthogonal pulses and receiver correlators than conventional PSM scheme. Due to the presence of OOK, it is simpler, easier to operate and is applicable to energy constrained UWB systems. The paper shows the performance of PSM and its combined scheme in multipath channel model. The proposed scheme is downward compatible and hence is useful for adaptive modulation systems to suit different channel conditions. R EFERENCES [1] I. Guvenc and H. Arslan, “On the modulation option for UWB systems,” in IEEE Military Communications Conference, Oct. 2003, pp. 892–897.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2007 proceedings.
BER vs Eb/N0 for 2−bit scheme in multipath −10dB
0
BER vs Eb/N0 for 2−bit scheme in multipath 85%
0
10
10
−1
−1
10
−2
10
10
−2
BER
BER
10
−3
10
−3
10
−5
10
0
5
PSM Bi−orthogonal 2PPM−PSM BPSK−PSM OOK−PSM
−4
10
PSM Bi−orthogonal 2PPM−PSM BPSK−PSM OOK−PSM
−4
10
−5
10
10
15
20
25
0
5
10
15
20
25
Eb/N0 [dB]
Eb/N0 [dB]
Fig. 4. Performance of PSM, bi-orthogonal, PPM-PSM, BPSK-PSM and OOK-PSM for 2-bit symbols transmission scheme in multipath channel model where path taking within 10dB of the strongest path and used pulses are modified Hermite pulses.
Fig. 6. Performance of PSM, bi-orthogonal, PPM-PSM, BPSK-PSM and OOK-PSM for 2-bit symbols transmission scheme in multipath channel model where 85% energy is captured and used pulses are modified Hermite pulses.
BER vs Eb/N0 for 2−bit scheme in multipath −10dB
0
10
PSM Bi−orthogonal 2PPM−PSM BPSK−PSM OOK−PSM
−1
10
[6]
[7] −2
10 BER
[8] −3
10
[9] [10]
−4
10
[11] −5
10
0
5
10
15
20
25
Eb/N0 [dB]
Fig. 5. Performance of PSM, bi-orthogonal, PPM-PSM, BPSK-PSM and OOK-PSM for 2-bit symbols transmission scheme in multipath channel model where path taking within 10dB of the strongest path and used pulses are PSWF.
[12] [13]
[14] [2] M. Ghavami, L. B. Michael, S. Haruyama, and R. Kohno, “A novel UWB pulse shape modulation system,” Kluwer International Journal on Wireless Personal Communication, vol. 23, Oct. 2002. [3] K. Usuda, H. Zhang, and M. Nakagawa, “M-ary pulse shape modulation for PSWF-based UWB systems in multipath fading environment,” in IEEE Global Telecommunication Conference, Nov. 2004, pp. 3498– 3504. [4] H. Wen and Z. Guoxin, “Orthogonal hermite pulses used for UWB Mary communication,” in Proceedings of the International Conference on Information Technology, April 2005, pp. 97–101. [5] S. Majhi, A. S. Madhukumar, A. B. Premkumar, and F. Chin, “M-ary
[15] [16]
signaling for ultra wideband communication systems based on pulse position and orthogonal pulse shape modulation,” in Accepted in IEEE Wireless Communication & Networking conference, 2007. C. Michell, G. T. F. de Abreu, and R. Kohno, “Combined pulse shape and pulse position modulation for high data rate transmission in ultra-wideband communication,” International Journal of Wireless Information Networks, pp. 167–178, Oct. 2003. A. S. Madhukumar, Z. Ye, and S. Majhi, “Coexisting narrowband and ultra wideband systems: Analysis of power spectral density and inband interference power,” World Scientific and Engineering Academy and Society (WSEAS), vol. 6, pp. 318–324, Feb. 2007. S. Majhi, A. S. Madhukumar, and A. B. Premkumar, “Reduction of uwb interference at NB systems based on a generalized pulse waveform,” IEICE Electronics Express, vol. 3, pp. 361–367, Dec. 2006. Y. Kim, B. Jang, C. Shin, and F. Womack, “Orthogonal pulses for high data rate communication in indoor UWB systems,” IEEE Communication Letters, vol. 9, May 2005. L. Zhang and Z. Zhou, “Research on orthogonal wavelet synthesized UWB waveform signal,” in IEEE International Conference on Communication, Oct. 2005, pp. 803–805. J. Foerster, “UWB channel modeling sub-committee report final,” IEEEP802.15 Working Group for Wireless Personal Area Networks (WPANs), Feb. 2003. T. Jia and D. I. Kim, “Analysis of average signal-to-interference-noise ratio for indoor uwb rake receiving system,” in in proceedings of IEEE 61st Vehicular Technology Conference, June 2005, pp. 1396–1400. L. Jiang, Y. Wang, and J. Guo, “The capacity of m-ary ppm ultrawideband communication over multipath channels,” in IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technology for Wireless Communication Proceedings, Aug. 2005, pp. 1606–1609. C. J. Mitchell and R. Kohno, “Orthogonal coded modulation for combined pulse position and pulse shape modulation,” in International Workshop on Ultra Wideband Systems, Joint with Conference on Ultra Wideband Systems and Technologies, May 2004, pp. 177–181. J. A. N. dey Silva and M. L. R. de Campos, “Performance comparison of binary and quaternary UWB modulation schemes,” in IEEE Global Communication Conference, Oct. 2003, pp. 789–793. K. Usuda, H. Zhang, and M. Nakagawa, “Orthogonality and coded modulation for combined pulse position and pulse shape modulation,” in International Workshop on UWB Systems, Joint with Conference on UWB Systems and Technologies, May 2004, pp. 177–181.
