Performance of A New Transmitted Reference Pulse Cluster System for UWB Communications Xiaodai Dong∗ , Li Jin∗ , Philip Orlik† and Rongrong Zhang∗ ∗ Department
of Electrical and Computer Engineering University of Victoria, Victoria, BC V8W 3P6, Canada Email: {xdong,jinli,rongrong}@ece.uvic.ca † Mitsubishi Electric Research Laboratories, Inc. 201 Broadway, Cambridge, MA 02139, USA Email:
[email protected] Abstract— A new form of transmitted reference technique is proposed in this paper, where compactly spaced or even multiple contiguous reference and data pulses are used for transmission. This structure enables a simple, robust and practical autocorrelation detector to be implemented in the receiver. It is also compatible with the signal format proposed within IEEE 802.15.4a Working Group for coherent and non-coherent systems. The performance of the proposed receiver and a simple noncoherent energy detector are analyzed and compared. Simulation results show that this new transmitted reference system outperforms the non-coherent system by about 1.3-1.9 dB for 802.15.4a channel model 1 and 1.3-2.3 dB for channel model 8, while offering similar implementation complexity compared to that of the non-coherent system.
I. I NTRODUCTION The transmitted reference (TR) technique for ultrawideband (UWB) communications has attracted substantial interests from the research and industry communities due to its simple implementation and robust performance. The term transmitted reference and the technique itself were invented in as early as 1940’s [1], but its application to UWB communications was introduced fairly recently by [2]. TR is especially suitable for UWB as its auto-correlation receiver does not need to estimate the dense multipath UWB channel. A TR receiver also collects channel energy in a much easier way than in a coherent rake receiver. Moreover, frequency dependent effects of a UWB channel are straightforwardly taken into account by the TR scheme. The TR technique is a subject of extensive study in the literature [2]–[13] (and references therein). Conventional TR schemes use pulse doublet consisting of a reference pulse and a data pulse separated by a large interval to represent information data. The large interval is required to avoid the interference between the received data and reference pulses. Only when the two pulses are spaced further than the channel impulse response length, there will be no interpulse interference (IPI). However, a major hurdle to practical implementation of a TR system is the requirement of accurate long and wideband delay lines. Implementing a delay line longer than 10 ns for UWB signals is not acceptable for a practical system [8], [14]. In [2], a delay hopped TR system was first proposed. Variations to this original TR scheme were
presented in [4]- [7]. Performance analysis of TR systems were carried out in [6]- [12]. In [13], a frequency multiplexed TR was proposed where the data and reference waveforms were multiplexed in disjoint frequency bands. In [15], a dual pulse (DP) scheme that uses two contiguous pulses to transmit data was proposed. The delay between the reference and data pulses is then only a pulse width. Due to the low power spectrum requirement imposed by FCC regulation, a bit is transmitted using multiple “frames” which repeat the bit waveform over a symbol duration. This technique is widely used to increase the received signal-to-noise ratio (SNR) and obtain reasonable error performance. Three receivers of the DP scheme were analyzed in [16]. To effectively reduce the effect of IPI and increase the SNR, averaging the received signal again involves frame long delay line. In this paper, we further extend the idea of dual pulse and transmitted reference techniques to arrive at a simple design that allows short delay lines less than 10 ns and achieves better performance than non-coherent systems. The proposed structure is compatible with IEEE 802.15.4a proposals such as [17]. The performance of the proposed system and a non-coherent energy detection system are analyzed, computed and simulated. II. S YSTEM M ODEL AND P ERFORMANCE A NALYSIS In a TR or DP [15], [16] system, information is carried by a pulse pair in a frame: a reference pulse and a data pulse separated by Td seconds. To increase the signal-to-noise ratio (SNR) of the system, the same pulse pair is re-transmitted over Nf frames. Using binary pulse amplitude modulation, a TR or DP signal can be represented by s Nf −1 ∞ Eb X X s˜(t) = [g(t − mTs − iTf ) 2Nf m=−∞ i=0
=
+bm g(t − mTs − iTf − Td ) s ∞ Eb X sm (t − mTs ) 2Nf m=−∞
(1)
PNf −1 PNf −1 where sm (t) = i=0 g(t−iTf )+bm i=0 g(t−iTf −Td ), bm ∈ {+1, −1} is the m-th bipolar information bit, g(t) is the composite pulse with duration Tp resulting from the
convolution of the transmitter pulse gtr (t) and the receiver filter which is matched to gtr (t), Ts is the symbol duration determined by the bit rate, Tf is the frame interval, Nf is the number of repeated frames for one bit, and Eb is the average energy per bit. In the existing TR literature, the pulse delay Td was proposed to be long enough to avoid interpulse interference (IPI) as well as inter-frame interference (IFI), and the frame duration Tf (> Td ) is often related to the symbol duration by Ts = Nf Tf . To improve signal-tonoise ratio, a TR receiver may perform analog averaging of the received pulses for a number of frames. However, this again requires a delay line whose duration is as long as Tf . Large Td and Tf lead to large delay lines which pose serious implementation challenges in practical UWB systems. The DP scheme proposed in [15] and [16] can be represented by (1) with Td = Tp . Hence, the DP structure only requires short delay lines, but at the same time, suffers from IPI due to the compactly spaced pulses. For the multiple frames scenario where Nf > 1, IPI can be alleviated by averaging multiple received signal frames or using the iDP scheme in [15] and [16]. Either way, it requires frame long delay line to perform analog averaging or iDP processing. Moreover, in both TR and DP methods, inter-symbol interference (ISI) and interframe interference (IFI) are likely to occur when Ts and Tf are small relative to the channel delay spread. Although there was some analysis in the literature applicable to the IFI case, it was unknown how to address the adverse effect of IFI. The objectives of this paper are to design, 1) for a given data rate (1/Ts ) and Nf , the pulse structures that require practically short delay lines (i.e., small Td ) and result in minimal ISI; 2) a simple, robust detection scheme that achieves reasonable performance even in the presence of IPI and/or IFI. The UWB channel described by IEEE 802.15.4a channel models can be generalized as [18] h(t) =
K−1 X
αk δ(t − τk )
(2)
k=0
where αk and τk are the complex amplitude and delay of the k-th multipath. The convolution of the transmitter filter gtr (t) with the random complex UWB channel is assumed to have unit average energy. This energy normalization follows the common practice of participating companies in the IEEE 802.15.4a Working Group. The received signal after the lowpass matched filter gtr (t) can then be written as r(t) =
K−1 X
αk s˜(t − τk ) + n(t)
k=0
s = s =
K−1 ∞ X Eb X sm (t − τk − mTs ) + n(t) αk 2Nf m=−∞
Eb 2Nf
k=0 ∞ X
correlation function of n(t) is given byRRn (τ ) = E[n∗ (t)n(t+ ∞ τ )] = N0 Rtr (τ ), where Rtr (τ ) = −∞ gtr (t)gtr (t + τ )dt and N0 is the power spectral density of the complex white Gaussian noise. The receiver performs auto-correlation on the received signal and its Td delayed version. The decision variable (DV) for the m-th bit is given by Z mTs +T2 r(t)r∗ (t − Td )dt D = mTs +T1
=
D1 + D2 + D3 + D4 .
The choice of the integration interval [T1 , T2 ] is critical to the success of the detection scheme. In order to ensure that we capture all the energy in the received pulse cluster, we select T1 = Td + Tl , T2 = Td + (Nf − 1)Tf + Th , where Tl and Th are the beginning and end of the UWB channel for integration, respectively. Usually Tl is close to time arrival of the first significant path of the channel, especially in a line-of-sight (LOS) environment, and the interval [Tl , Th ] should include sufficient channel energy for detection. Such choices of T1 and T2 guarantee that auto-correlation covers the significant channel portion plus a duration of (Nf − 1)Tf related to the pulse cluster width. Since the subsequent analysis involves only one symbol, the subscript m is omitted for convenience. Assuming there is no ISI, we have Z T2 K−1 X K−1 X Eb D1 = αl αk∗ s(t − τl )s∗ (t − τk − Td )dt 2Nf T1 l=0 k=0 Z T2 Eb = q(t)q ∗ (t − Td )dt, 2Nf T1 s Z T2 Eb D2 = q(t)n∗ (t + mTs − Td )dt 2Nf T1 s Z T2 Eb D3 = q ∗ (t − Td )n(t + mTs )dt 2Nf T1 Z T2 D4 = n(t + mTs )n∗ (t + mTs − Td )dt (5) T1
where D1 is the signal-signal component, D2 and D3 are the random variables (RVs) representing the signal-and-noise product, and D4 is an RV accounting for the noise-noise product. Define the auto-correlation function of s(t), Rss (τ ), in (6) R∞ where Rgg (τ ) = −∞ g(t)g(t + τ )dt only has non-zero values for |τ | < Tp . Assuming Tl = τ0 and Th = τK−1 , the signalsignal P component D1 can then be further written as (7), where K−1 Eh = k=0 |αk |2 is the channel energy. From (6), it can be shown that Rss (Td ) = bm Nf [Rgg (0) + Rgg (2Td − Tf )],
qm (t − mTs ) + n(t)
(3)
m=−∞
PK−1 where qm (t) = k=0 αk sm (t − τk ), and n(t) is the additive complex white Gaussian noise filtered by gtr (t). The auto-
(4)
(8)
given Tf ≥ 2Td ≥ 2Tp . The first term of (7) on the right-handside is proportional to the information data, while the second term represents IPI and IFI that sometimes add constructively to the decision variable and sometimes add destructively to
Z
Nf −1 Nf −1
∞
Rss (τ ) =
s(t)s(t + τ )dt = −∞
D1
=
X
X
i=0
j=0
2Rgg (τ + (i − j)Tf ) + bm [Rgg (τ + (i − j)Tf − Td ) + Rgg (τ + (i − j)Tf + Td )]
(6)
Z T2 K−1 K−1 K−1 K−1 X K−1 X Eb X Eb X X αl α∗k s(t − τl )s(t − τk − Td )dt = [ |αk |2 Rss (Td ) + αl α∗k Rss (|Td − τl + τk |)] 2Nf l=0 k=0 2Nf k=0 T1 l=0 k=0 k6=l
=
Eb [Rss (Td )Eh + 2Nf
K−1 X K−1 X
αl α∗k Rss (|Td − τl + τk |)]
(7)
l=0 k=0 k6=l
the decision variable and its value depends on the particular channel realization and the data bm . Maximizing (8) will maximize the data-bearing component (the first term in (7)) for detection, resulting in low bit error rate of the system. It can be seen from (6) and (8) that when Tf = 2Td , (8) achieves the extremum value of (2Nf − 1)bm Rgg (0). Therefore, Tf should be chosen to be twice the delay Td . Intuitively, this allows the data pulse of one frame in r(t − Td ) to line up with the reference pulse of the succeeding frame in r(t), and hence results in additional auto-correlation of the desired components containing information data. Such design even outperforms the conventional TR receiver operation that performs autocorrelation within one frame and then averages over multiple frames. It is fundamentally different from the delay hopped TR system in [2] or time hopping TR systems in the literature. Considering the advantage of the DP pulse structure and the analysis above, we propose to use multiple contiguous DP pulses or multiple closely and evenly spaced reference and data pulses as shown in Fig. 1 to represent information data. This closely packed TR/DP pulse structure is referred to as TR pulse cluster structure in this paper. Three key points of this structure are: 1) The length of the cluster, Tu , is not equal to the symbol duration. Instead, a cluster only occupies one time slot, shown as S in Fig. 1, with length Tu = Nf Tf ¿ Ts . This compact cluster structure leaves more blank space in each symbol than having 2Nf pulses scattered in the whole symbol duration, and hence leading to low or no ISI; 2) Tf = 2Td . All pulses are evenly spaced in a cluster to achieve good performance. 3) The delay Td should be shorter than 10 ns. In Fig. 1, we use Td = Tp in (a) and Td = 2Tp in (b). Considering a multiple access scenario, we can divide a symbol duration into multiple time slots as shown in Fig. 1, and each user occupies a different time slot where a TR pulse cluster resides. The proposed TR pulse cluster and symbol structure are compatible with the signal structure presented in IEEE 802.15.4a proposals [17]. If time hopping is desired, it can be performed on TR pulse clusters from time slot to time slot instead of hopping within each cluster. Similarly, scrambling, if to be used, should be carried out on a pulse cluster basis as well. Analysis for D2 , D3 and D4 is similar to [16], [8]. These RVs can be closely approximated as Gaussian distributed, especially now that a pulse cluster is longer than a single dual
pulse. The receiver makes a decision on “1” if Re{D} > 0, and “0” if Re{D} < 0. To calculate the bit error rate (BER) of this TR scheme, we need to know the mean and variance of the Gaussian RV Re{D}. It can be easily shown that E[D2 + D3 ] = 0 and E[D4 ] ≈ 0 as Td ≥ Tp . Therefore, the mean of Re{D} is given by mD (bm ) = =
E[Re{D}] ≈ Re{D1 } Z T2 Eb Re{q(t)q ∗ (t − Td )}dt. 2Nf T1
(9)
Since it can be easily shown that Gaussian RVs D2 + D3 and D4 are independent, the variance of Re{D} is the sum of 2 (bm ) = Var[Re{D2 + D3 }] and σ42 . In particular, σ23 σ42
N2 = Var[Re{D4 }] = 0 2
Z
T √i 2
T − √i2
√ √ 2 ( 2y)dy ( 2Ti − 2|y|)Rtr
(10) 2 (bm ) is given by (11). where Ti = T2 − T1 , and σ23 The probability of error for the TR scheme conditioned on the channel realization h is then given by à ! à ! mD (−1) 1 mD (1) 1 + Q p 2 P (e|h) = Q p 2 2 2 σ23 (−1) + σ42 σ23 (1) + σ42 (12) where h = {(αk , τk )|k = 0, ..., K − 1}. III. N ON - COHERENT D ETECTION OF PPM Consider the PPM system that employs the same TR pulse cluster (either “+1” or “−1” pulse cluster) but at two different locations in a bit interval to carry information data. During the m-th bit interval t ∈ [(m − 1)Ts , mTs ], the PPM signal (including the receiver matched filter) using “+1” or “−1” TR pulse cluster is given by s 2Nf −1 Eb X s˜(t) = (1 − d) (−1)n g(t − iTd ) 2Nf i=0 s 2Nf −1 Ts Eb X (−1)n g(t − iTd − ) (13) + d 2Nf i=0 2 where d ∈ {0, 1} is the m-th binary bit, n = 0 for “+1” pulse cluster and n = i for “−1” pulse cluster. The received
2 σ23 (bm )
=
Var[Re{D2 }]
=
Var[Re{D3 }]
=
E[Re{D2 }Re{D3 }]
=
Var[Re{D2 }] + Var[Re{D3 }] + 2E[Re{D2 }Re{D3 }] Z Z Eb N0 T2 T2 Re{q(t)q ∗ (t0 )}Rtr (t0 − t)dtdt0 4Nf T1 T1 Z Z Eb N0 T2 T2 Re{q(t − Td )q ∗ (t0 − Td )}Rtr (t0 − t)dtdt0 4Nf T1 T1 Z Z Eb N0 T2 T2 Re{q(t)q ∗ (t0 − Td )}Rtr (t0 − t + Td )dtdt0 4Nf T1 T1
signal after going through the UWB channel and AWGN is then given by r(t) =
K−1 X
αk s˜(t − τk ) + n(t)
k=0
s
Eb v(t) + n(t). 2Nf
=
(14)
T
T1
Z V1 =
T2 + T2s
T1 + T2s
|r(t)|2 dt.
(16)
If V0 > V1 , a decision on “0” is made; otherwise, a decision on “1” will be made. Suppose “0” is transmitted, the energy detector output V0 can be further written as V0 = D1 + D2 + D3 + D4
(17)
where D1 D2 D3 D4
Z T2 Eb |v(t)|2 dt 2Nf T1 s Z T2 Eb = v(t)n∗ (t)dt 2Nf T1 s Z T2 Eb = v ∗ (t)n(t)dt 2Nf T1 Z T2 = |n(t)|2 dt. =
(18)
T1
The energy detector output V1 is given by Z V1 =
T2 + T2s
T1 + T2s
|n(t)|2 dt.
(19)
The final decision variable is then given by D = V0 − V1 = D1 + D2 + D3 + D4 − V1 .
Again, D can be approximated as a Gaussian RV with mean D1 . Because D2 , D3 , D4 and V1 are independent, the variance of D is given by Z Z Eb N0 T2 T2 2 σD = Re{v(t)v ∗ (t0 )}Rtr (t0 − t)dtdt0 Nf T1 T1 Z √Ti √ √ 2 2 ( 2Ti − 2|y|)Rtr ( 2y)dy. (21) + 2N02 − √i2
The receiver employs two simple energy detectors to demodulate the received signal. The outputs of the two energy detectors are given by Z T2 V0 = |r(t)|2 dt (15) and
(11)
(20)
Therefore, the conditional probability of error for the noncoherent detection of binary PPM is expressed as µ ¶ D1 P (e|h) = P (D < 0) = Q . (22) σD IV. S IMULATION AND N UMERICAL R ESULTS In this section, we present simulation results for the performance of the proposed TR cluster system as illustrated in Fig. 1(a), the non-coherent pulse position modulation (PPM) and a conventional TR system in two representative channels, i.e., IEEE 802.15.4a CM1 and CM8 channels. CM1 models strong line-of-sight channels and CM8 models channels with an extremely large delay spread [18]. The non-coherent PPM system employs either all “+1” or all “-1” pulse cluster placed at different time slots within a symbol and the position of the pulse cluster represents information data. The conventional TR system spreads out Nf reference and data pulse pairs evenly in one symbol duration. We did not include time hopping in the conventional TR but it is expected that the performance will be worse with time hopping. Here is a description of the system parameters. The transmitter pulse shape filter and the receiver filter are the root raised cosine (RRC) pulses with roll-off factor β = 0.25. The zero-to-zero main lobe width of the RRC pulse is Tp = 2.02 ns, and a truncated RRC pulse of duration 8Tp is used in the simulation. The pulse cluster is composed of 8 contiguous pulses, i.e., Nf = 4. The pulse cluster length is then Tu = 16.16 ns. Low bit rates of 2 Mbps for CM1 and 1 Mbps for CM8 are simulated, and hence the system is ISI free. The sampling frequency used in the simulation is 3.952 GHz. The integration interval related parameters Tl and Th are determined as the beginning and end paths of the channel with magnitude larger than a fraction of the channel maximum magnitude. In other words, any multipath components before Tl and after Th are smaller than s · max(|αk |K−1 k=0 ), where s (= 0.3 in the simulation) is the scale factor and αk is the k-th path gain. For each channel model, the final BER is obtained by averaging the BERs of 100 channels.
The simulation results in Fig. 2 show that at BER = 10−3 in CM1 channels, TR pulse cluster outperforms conventional TR and non-coherent with “+1” pulses by about 1.9 dB, and non-coherent with “-1” pulses by about 1.3 dB. The performance gaps are wider at medium SNRs but get narrowed at higher SNRs, especially for conventional TR. The relative performance between non-coherent detection with “+1” pulse cluster and “-1” pulse cluster is channel dependent. Fig. 3 shows that in CM8 channels, TR pulse cluster outperforms non-coherent with “+1” pulses by about 2.3 dB and noncoherent with “-1” pulses by about 1.3 dB at BER = 2×10−3 . The conventional TR scheme significantly lags behind the new TR pulse cluster scheme in performance and the ease of implementation. Even at the data rate as low as 1 Mbps, IFI and ISI are present in the conventional TR scheme and they are strong enough to significantly degrade its performance. Figs. 4 and 5 plot the effect of Td on the performance of TR and non-coherent systems in CM1 and CM8, respectively, numerically computed by using (9)-(12) and (18), (21) and (22). The numerical calculation of the means and variances of decision variables involves single and double integration. Once the numerical integration is completed, obtaining BER for any SNR is very easy and therefore preferred over simulation. For the 100 channels used in Fig. 4, Td = 3Tp in TR yields the best performance, about 0.5 dB (0.9 dB) superior than Td = Tp at BER = 10−3 (BER = 10−4 ). However, Td = 2Tp lags behind Td = Tp at high SNRs (> 19 dB). One possible explanation is that one of the 100 channels is observed to have two major taps separated at about Td = 4.04 ns, causing the reference and data pulses cancelation when bit b = −1 is transmitted. For the non-coherent scheme, Td = 2Tp pulse structure has slightly worse performance than Td = Tp for a wide range of SNR, and Td = 3Tp achieves the best performance. Although not shown here, the “-1” pulse cluster with Td = 2Tp and Td = 3Tp underperforms “+1” pulse cluster in the non-coherent system for this example. Fig. 5 demonstrates that increasing Td from one pulse width to two has smaller impact on the performance. V. C ONCLUSION This paper has proposed a new TR pulse cluster structure that repeatedly sends closely spaced TR/DP pulses. This method allows a simple and robust receiver to be implemented, i.e., analog front end, symbol rate sampling and short delay line requirement, overcoming a major hurdle (long delay lines) of conventional TR receivers. Simulation results have shown superior performance of the proposed scheme over noncoherent and conventional TR systems. ACKNOWLEDGMENT The authors would like to thank Ms. Yue Wang for helping with some initial simulations of this work. R EFERENCES [1] M. K. Simon, J. K. Omura, R. A. Scholtz, and B. K. Levitt, Spread Spectrum Communications Handbook. New York: McGraw-Hill, 1994. [2] R. Hoctor and H. Tomlinson, “Delay-hopped transmitted-reference RF communications,” in IEEE Conf. Ultra Wideband Syst. Techno., May 2002, pp. 265–269.
Fig. 1.
The proposed pulse structure
[3] N. V. Stralen, A. Dentinger, K. W. II, R. Hoctor, and H. Tomlinson, “Delay-hopped transmitted-reference experimental results,” in IEEE Conf. Ultra Wideband Syst. Techno., May 2002, pp. 93–98. [4] H. Zhang and D. L. Goeckel, “Generalized transmitted-reference UWB systems,” in IEEE Conf. Ultra Wideband Syst. Techno., Nov. 2003, pp. 16–19. [5] S. Franz and U. Mitra, “On optimal data detection for UWB transmitted reference systems,” in Globecom, Dec. 2003, pp. 744–748. [6] Y.-L. Chao and R. A. Scholtz, “Optimal and suboptimal receivers for ultra-wideband transmitted reference systems,” in Globecom, Dec. 2003, pp. 759–763. [7] J. D. Choi and W. E. Stark, “Performance of ultra-wideband communications with suboptimal receivers in multipath channels,” IEEE J. Select. Areas Commun., pp. 1754–1766, Dec. 2002. [8] S. Gezici, F. Tufvesson, and A. F. Molisch, “On the performance of transmitted-reference impulse radio,” in Globecom, Nov. 2004, pp. 2874–2879. [9] T. Q. S. Quek and M. Win, “Analysis of UWB transmitted-reference communication systems in dense multipath channels,” IEEE J. Select. Areas Commun., pp. 1863–1874, Sept. 2005. [10] K. Witrisal, G. Leus, M. Pausini, and C. Krall, “Equivalent system model and equalization of differential impulse radio UWB,” IEEE J. Select. Areas Commun., pp. 1851–1862, Sept. 2005. [11] Y.-L. Chao and R. A. Scholtz, “Ultra-wideband transmitted reference systems,” IEEE Trans. Veh. Technol., pp. 1556–1569, Sept. 2005. [12] Z. Xu, B. M. Sadler, and J. Tang, “Data detection for UWB transmitted reference systems with inter-pulse interference,” in ICASSP, vol. III, 2005, pp. 601–604. [13] W. Gifford and M. Win, “On transmitted-reference UWB communications,” in Proc. Asilomar Conf. Signals, Systems and Computers, Nov. 2004, pp. 1526–1531. [14] M. Casu and G. Durisi, “Implementation aspects of a transmittedreference UWB receiver,” Wireless Communications and Mobile Computing, pp. 537–549, May 2005.
0
10 0
10
CM8
−1
10 −1
10
−2
10
TR cluster,Td=2.02ns
BER
−2
BER
10
TR cluster,Td=4.04ns −3
10 −3
10
d
Non−coherent,−1 pulses,T =2.02ns d
−4
10
Conventional TR,Td=62.5ns −4
Fig. 2.
d
10
13
14
15
16 Eb/N0 (dB)
17
18
19
The BER of TR and non-coherent systems in CM1.
−1
−2
BER
10
CM8
Conventional TR,T =125ns d
−4
10
Non−coherent,+1 pulses Non−coherent,−1 pulses TR cluster,Td=2.02ns
−5
12
Fig. 3.
13
14
15
16 Eb/N0 (dB)
17
18
19
20
The BER of TR and non-coherent systems in CM8.
0
10
CM1
−1
10
−2
BER
10
−3
10
TR cluster,Td=2.02ns TR cluster,Td=4.04ns TR cluster,Td=4.04ns,simu.
−4
10
TR cluster,T =6.06ns d
Non−coherent,T =2.02ns d
−5
10
Non−coherent,Td=4.04ns Noncoherent,Td=4.04ns,simu. Non−coherent,Td=6.06ns
−6
10
12
13
14
15
16 E /N (dB) b
Fig. 4. Td s.
14
15
16 E /N (dB)
17
18
19
20
0
Fig. 5. Td s.
The BER of TR and non-coherent systems in CM8 with different
[15] X. Dong, A. C. Y. Lee, and L. Xiao, “A new UWB dual pulse transmission and detection technique,” in ICC, May 2005, pp. 2835– 2839. [16] X. Dong, L. Xiao, and A. C. Y. Lee, “Performance analysis of dual pulse transmission in UWB channels,” IEEE Commun. Lett., Aug. 2006. [17] I. Lakkis, “Modulation summary for tg4a,” IEEE P802.15-05-617-01004a, Tech. Rep., Oct. 2005. [18] A. F. Molisch, K. Balakrishnan, C.-C. Chong, S. Emami, A. Fort, J. Karedal, J. Kunisch, H. Schantz, U. Schuster, and K. Siwiak, “Ieee 802.15.4a channel model - final report,” IEEE P802.15-04-0662-00004a, Tech. Rep., Oct. 2004.
10
10
13
20
0
−3
12
Non−coherent,−1 pulses,Td=6.06ns
b
10
10
Non−coherent,−1 pulses,Td=4.04ns
−5
−5
12
Non−coherent,+1 pulses,Td=4.04ns Non−coherent,+1 pulses,T =6.06ns
Non−coherent,+1 pulses Non−coherent,−1 pulses TR cluster,Td=2.02ns
10
10
TR cluster,Td=6.06ns Non−coherent,+1 pulses,T =2.02ns
CM1
17
18
19
20
0
The BER of TR and non-coherent systems in CM1 with different
