The suggested technique is referred to as the wavelet space time coding scheme (WSTC). In WSTC four symbols are transmitted on the same UWB transmission.
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A New Wavelet Space Time Coding Technique Designed for UWB MISO Systems Said E. El-Khamy1 , Ehab Farouk Badran2 , and Amira Ibrahim Zaki2 1
Department of Electrical Engineering, Faculty of Engineering Alexandria University, Alexandria, Egypt 2 Department of Electronics and Communication Engineering Arab Academy for Science and Technology, Alexandria, Egypt
Abstract— A new MISO-STC scheme designed specifically for Ultra-Wideband (UWB) systems is introduced in this paper. The proposed scheme is based on multiplexing multiple symbols in the wavelet domain of the UWB pulses in addition to the spatial multiplexing offered by using multiple transmitting antennas. Rake receivers are used to collect the energy in the dense multipath channel components. The suggested technique is referred to as the wavelet space time coding scheme (WSTC). In WSTC four symbols are transmitted on the same UWB transmission pulse with the same bandwidth, symbol duration, and number of transmitting antennas of the conventional MISO-STC scheme. The used mother wavelet (MW) is selected to be highly correlated with transmitted pulse shape and such that the multiplexed signal has almost the same spectral characteristics as those of the original UWB pulse. The simulation results show that the proposed WSTC scheme has better performance than the conventional scheme in addition to increasing the data rate to four times that of the conventional STC scheme. 1. INTRODUCTION
UWB is a developing short range technique that provides a high data rate. The UWB transmission allows it to be used with systems and fields like in WLAN (Wireless Local Area Network), biomedical and military fields [1–3]. UWB transmission consists of a train of very short pulses. The UWB transmitted pulse is of −10 dB bandwidth ≥ 500 MHz or of fractional bandwidth > 20%. According to the Federal Communication Committee (FCC) regulations, the UWB systems are allowed to transmit over the frequency band between 3.1 and 10.6 GHz with very low power. These strict regulations on UWB systems in addition to the channel effect which is extremely frequency selective, limit the achievable data rates, and transmission range [1, 2]. The UWB channel is characterized by its dense multipath channel. The UWB channel is enriched with resolvable multipath components due to transmission using ultra-short pulses in nanosecond. The Rake receiver can be used to enhance the performance of the UWB system by capturing most of the energy of the multipath components using number of fingers (i.e., performing multipath diversity) [1–5]. To overcome the FCC power limitations, the UWB systems are implemented and studied with MIMO systems. UWB MIMO systems are presented in [6, 7] to obtain multi data stream (MS) transmission. It is also presented with space–time coding (STC) based on Alamouti’s scheme [8, 9] using MRC (maximum ratio combiner) Rake receiver in [10] and [11], to make use of multipath diversity in addition to spatial diversity and thus increase channel performance and/or capacity [12] and [13]. The wavelet transform has been extensively used in the wireless communication field especially in UWB communications [14]. Wavelet transform (WT) was introduced in [15] as a new modulation scheme WSK (Wavelet Shift Keying) which is considered as a generalization of “Wavelet based OFDM (Orthogonal Frequency Division Multiplexing)”. Also the OFDM scheme characteristics are enhanced by using OWDM (Orthogonal Wavelet Division Multiplexing) in a Rayleigh fading channel as illustrated in [16]. On the other hand the OFDM system is studied with DWT (Discrete Wavelet Transform) and DMWT (Discrete Multi-Wavelet Transform) to reduce the level of interference and increase spectral efficiency in [17]. It is shown in [17] that DMWT-OFDM proposes much lower bit error rate (BER), increases the signal to noise ratio (SNR), and thus can be used as an alternative to the conventional OFDM. The WT is also used recently in the UWB communication field. The WT is used in analysing the UWB signal to detect it in the presence of background noise in [18]. The WT is used in [19] and [20] as an UWB pulse shaper to satisfy the FCC limits in addition to enhancing the spectral efficiency, and to cancel narrowband and wideband interferences in [21] and [22].
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In this paper WSTC scheme (WSTC) is proposed to increases the data rate and enhance the performance of conventional STC in [10, 11] without increasing the bandwidth. The paper is organized as follows: In Section 2, the channel model used in simulation is introduced. Section 3 discusses the system model for a single transmitting and receiving antenna (SISO), and the conventional STC UWB systems in [10, 11]. Section 4 presents the proposed WSTC scheme. Section 5 introduces the simulations and results. Finally, the conclusions are shown in Section 6. 2. CHANNEL MODEL
The channel models used is the modified Saleh-Valenzuela (SV) model [23]. It has an impulse response mathematical model given by: M −1 X
h(t) =
α(m)δ(t − τ (m))
(1)
m=0
where, M is the number of multipath components, while, α(m) and τ (m) are the gain and the delay of the mth path respectively. The gain of the channel due to measurements as states in [23] follows the log-normal distribution, while the arrival times of the clusters and the rays included follow the Poisson one. 3. SYSTEM MODEL
This section, presents the system model used in this paper for an UWB SISO and MISO systems for pear-to-pear communication. In the UWB communications binary symbols s = ±1 are transmitted over a train of ultra-short pulses. The system has Nt transmit and Nr receive antennas. The binary symbol is pulse shaped by monocycle pulse. Then the symbols are modulated by PAM (Pulse amplitude modulation) modulation and transmitted repeatedly over Nf frames each of time duration Tf (Ts = Nf Tf , where Ts is the symbol duration). The pulse waveform w(t) has typical duration Tw between 0.2–2 ns, resulting in transmission over an ultra-wide bandwidth. Assuming that the CIR is known at the receiver and the channel is constant for a block of symbols 3.1. SISO Scheme
If a single transmit and receive antennas are assumed (SISO), and PAM modulation, the transmitted waveform for the binary symbol s is given by: s Nf −1 E X w(t − nf Tf ) (2) S(t) = s Nf nf =0
where, E is the symbol energy, and pulse shape w(t) is of unit energy. The multipath channel can be expressed in terms of multipath delays and gains as in (1). Note that, τ (m) > τ (m − 1), and Tm = τ (M − 1) is the maximum delay spread of the dense multipath channel. To avoid the ISI simply choose Tf ≥ Tm + Tw . The modelled multipath fading channel is assumed to be quasi-static (i.e., constant during a block of symbols). A Rake receiver is used at the receiver to collect multipath diversity. It uses L finger (matched filters), where L ≤ M , and uses w(t) as the correlator reference template with an autocorrelation function Rw (τ ) [10]. 3.2. Analog STC MIMO Scheme
For a MISO the output of the first transmit antenna during each symbol Ts = Nf Tf is given by [11]: s S0 (t) = s
Nf −1 E X (−1)nf w(t − nf Tf ) 2Nf
(3)
nf =0
and of the second transmit antenna is: s S1 (t) = s
Nf −1 E X w(t − nf Tf ) 2Nf nf =0
(4)
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4. PROPOSED WAVELET SPACE TIME CODING TECHNIQUE
This section illustrates the proposed wavelet space timecoding (WSTC). The WSTC combines four symbols using the IDWT and multiple transmitting antennas (multiplexing in frequency and space) and send them on the same bandwidth and same symbol duration of the conventional STC presented in Section 3. It is like sending half of the symbols on half of the bandwidth of the transmitted pulse on different transmitting antennas. The WSTC code word is shown in Figure 1 while the transmitter and receiver are shown in Figure 2 and Figure 3 respectively. For a MISO WSTC (Nt = 2 and Nr = 1), the output of the first transmit antenna during each symbol Ts = Nf Tf is given by s Nf −1 2E X S0 (t) = w0 (t − nf Tf ) (5) Nf nf =0
and for the second antenna is given by s S1 (t) =
Nf −1 2E X (−1)nf w1 (t − nf Tf ) Nf
(6)
nf =0
where w0 (t) and w1 (t) are the transmitted pulse w(t) embeddedqwith s1 , s2 and s3 , s4 respectively.
w0 (t) is the IDWT of the approximation waveform x1 (t) = s1 NEf wa (t) and the detail waveform q q q x2 (t) = s2 NEf wd (t) while w1 (t) is that of x3 (t) = s3 NEf wa (t) and x4 (t) = s4 NEf wd (t) respec√ tively. The 2 factor in Equation (7) and Equation (8) is eliminated as the symbol energy is not
Figure 1: WSTC codeword per symbol for Nf = 2.
Figure 2: WSTC transmitter.
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Integ Wa(t-τ (L-1)) r
α0a(L-1)
Decisi Z 1
Integ w (t) r0
X (t) 1
Wa(t-τ (0)) r
Integ Wd(t-τ (L-1)) r
D X (t) 2 W T
re(t) ro(t)
D W T w (t) r1
α0a(0)
X (t) 3
α0d(L-1)
Decisi
Z 2
Integ Wd(t-τ (0)) r
α0d(0)
Integ α1a(L-1)
Wa(t-τ (L-1)) r
X (t) 4
Z 3 Decisi
Parallel to Series converter
Received Signal
Integ Wa(t-τ (0)) rr
α1a(0)
Integ Wd(t -τ (L-1)) r
Z 4
α1d(L-1)
Decisi Integ
Wd(t-τ (0)) r
α1d(0)
Figure 3: WSTC receiver.
divided amongst the two transmitting antennas. The received noisy signal per even frame for M multipath components is as follows re (t) = S0 (t) ∗ h00 (t) + S1 (t) ∗ h10 (t) + +ηe (t) s M −1 2E X = (α00 (m)w0 (t − τ00 (m))) + α10 (m)w1 (t − τ10 (m))) + ηe (t) Nf
(7)
m=0
And for odd frames ro (t) = S0 (t) ∗ h00 (t) − S1 (t) ∗ h10 (t) + ηo (t) s M −1 2E X (α00 (m)w0 (t − τ00 (m)) − α10 (m)w1 (t − τ10 (m))) + ηo (t) = Nf
(8)
m=0
where ηe (t) and ηo (t) are the additive white Gaussian noise (AWGN) with zero mean and σ 2 variance of the even and off frames respectively. The even and odd frames are combined using a combiner to generate wave forms wr0 (t) and wr1 (t), which are the estimated waveforms of the transmitted ones w0 (t) and w1 (t) respectively. The estimated waveforms are s M −1 2E X wr0 (t) = re (t) + ro (t) = 2 α00 (m)w0 (t − τ00 (m)) + ηe (t) + ηo (t) (9) Nf m=0 s M −1 2E X wr1 (t) = re (t) − ro (t) = 2 α01 (m)w1 (t − τ01 (m)) + ηe (t) − ηo (t) (10) Nf m=0
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By applying the DWT to the estimated waveform, their approximation and detail components (carrying the symbols) X1 (t) and X2 (t) respectively for wro (t) and X3 (t) and X4 (t) for wr1 (t) are obtained as s M −1 E X X1 (t) = 2s1 α00 (m)wa (t − τ00 (m)) + ε1 (t) (11) Nf m=0 s M −1 E X X2 (t) = 2s2 α00 (m)wd (t − τ00 (m)) + ε2 (t) (12) Nf m=0 s M −1 E X X3 (t) = 2s3 α10 (m)wa (t − τ10 (m)) + ε3 (t) (13) Nf m=0 s M −1 E X X4 (t) = 2s4 (14) α10 (m)wd (t − τ10 (m)) + ε4 (t) Nf m=0
where ε1 (t) and ε3 (t) are the approximation components of ηe (t)+ηo (t) and ηe (t)−ηo (t) successively while ε2 (t) and ε4 (t) are their detail components. The approximation and detail components are passed by a Rake receiver. The output per Rake finger for each component is s ZTf E 2 x1 (l) = 2s1 αr0a (l) + ε1 (t)wa (t − τr (l))dt αr0a (l) (15) Nf
s
E 2 α (l) + Nf r0d
x2 (l) = 2s2
0
ZTf
s
E 2 α (l) + Nf r1a
x3 (l) = 2s3
s
E 2 α (l) + Nf r1d
x4 (l) = 2s4
ε2 (t)wd (t − τr (l))dt αr0d (l)
0
ZTf
ε3 (t)wa (t − τr (l))dt αr1a (l)
0
ZTf
(16)
(17)
ε3 (t)wd (t − τr (l))dt αr1d (l)
(18)
0
where Rwa (t) and Rwd (t) are the autocorrelation of wa (t) and wd (t) respectively, and for p = 0, 1. αrpa (l) =
M −1 X
αp0 (m)Rwa (τr (l) − τp0 (m))
m=0
and αrpd (l) =
M −1 X
αp0 (m)Rwd (τr (l) − τp0 (m))
m=0
By summing up the Rake finger outputs and the Nf frames, the resulting decision statistics equivalent to symbol s1 , s2 , s3 and s4 are given by Nf Tf −1 Z L−1 L−1 2 X X X p p 2 Z1 = s1 Nf E αr0a (l)+ ε1 (t)wa (t − τr (l))dtαr0a (l) = s1 Nf EEm0a +ψ1 (19) l=0
nf =0 l=0
0
−1 L−1 ZTf L−1 X X X p p 2 Z2 = s2 Nf E αr0d (l)+ ε2 (t)wd (t − τr (l))dtαr0d (l) = s2 Nf EEm0d +ψ2 (20) Nf 2
l=0
nf =0 l=0
0
Nf −1 L−1 ZTf L−1 2 X X X p p 2 Z3 = s3 Nf E αr1a (l)+ ε3 (t)wa (t − τr (l))dtαr1a (l) = s3 Nf EEm1a +ψ3 (21) l=0
nf =0 l=0
0
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Z4 = s4
p
Nf E
L−1 X
Tf Z X X p 2 αr1d (l)+ ε4 (t)wd (t − τr (l))dtαr1d (l) = s4 Nf EEm1d +ψ4 (22) Nf 2
l=0
−1 L−1
nf =0 l=0
0
where Empa and Empd are the energy captured by the Rake receiver, and ψb is the noise component and b = 1, . . . , 4. Note that Rake receiver is composed of number of correlator fingers, where the reference waveform are delayed versions of the approximation and detail waveforms of w(t), where, the delays are equivalent to the delays of the multipath components. The mother wavelet (MW) transform function used is chosen to be with high similarity with the transmitted pulse and poor with the noise. 5. SIMULATION AND RESULTS
In this section the simulation, results and comparison between different systems, conventional STC and WSTC UWB systems are illustrated. In order to compare systems with different bit rates, a figure of merit F [1/(bit/sec/Hz)] for comparison is used, which is given by F =
BER BER · Bandwidth = Bandwidth efficiency Bit rate
(23)
F(1/(bit/sec/Hz))
As stated in section II the channel used is the modified SV-model. The main parameters of the channel are presented in the IEEE802.15.3a proposal for the line-of-sight (LOS) channel CM1 [23]. The used frame duration Tf = 100 nsec, with Nf = 2. The transmission monocycle pulse w(t) used is with pulse width 0.5 ns and unit energy. The transmission monocycle pulse w(t) used was first chosen to be the second derivative of the Gaussian function [1]. It showed a very bad performance 10
3
10
2
10
1
10
0
Conventional STC WSTC-I
-1
10
0
2
4
6
8
10 E/No (dB)
12
14
16
18
20
Figure 4: The conventional STC and WSTC using 2nd derivative Gaussian.
F ( 1 / ( bit/ sec / Hz ) )
10
UWB STC I and WSTC I using different mother wavelets with L=4
3
10
2
10
1
10
0
Conventional STC I Wavelet STC I using sym2 wavelet Wavelet STC I using coif3 wavelet Wavelet STC I using coif5 wavelet
0
2
4
6
8
10 E/No (dB)
12
14
16
18
20
Figure 5: The conventional STC and WSTC using the detail component of the 2nd derivative Gaussian pulse as the transmission pulse with different MW’.
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when embedded by the symbols using different MW. Figure 5 shows the performance of WSTC verses conventional STC using second derivative Gaussian pulse and Coiflet 3 MW for embedding the symbols with L = 4. The transmitted pulse is re-shaped to enhance the performance and to keep the spectrum limitations of the FCC. The w(t) is then taken to be the wavelet detail component of the 2nd derivative Gaussian pulse using MW’s with high similarity with the 2nd derivative Gaussian pulse. The examined MW’s are the Symlets, and Coiflets [14, 24–26]. Figure 6 shows a comparison of WSTC using different MW’s. It is concluded from Figure 6 that Coiflet 3 presents nearly the same performance as Coiflet 5. But if the MW Coiflet 5 is used, the transmitted pulse will not be able to keep the same bandwidth and spectrum shape after multiplexing the symbols in the wavelet domain (i.e., after the IDWT process in the transmitter) as shown in Figure 7. Thus, the MW Coiflet 3 is preferred due to its good performance, keeping the spectrum characteristics approximately the same when embedded with different symbols and restrict to the FCC spectrum regulations. This can be concluded from Figure 8, which illustrates the spectrum of the transmitted pulse (w0 (t) or w1 (t)) after being embedded with different symbols (s1 , s2 or s3 , s4 ). Notice that the spectrum of the pulse w(t) (i.e., before embedding the symbols) is the same as the case s1 = s2 in Figure 8. The performance of the proposed WSTC using Coiflet 3 MW is compared to the conventional one using L = 1, 4 and 8 in Figure 9. Figure 9 shows that WSTC outperforms the conventional one for L = 1 by about 8 dB, for L = 4 by 3dB and for L = 8 by about 4 dB for low symbol energy to noise power spectral density ratio E/No (required by the FCC regulations). Figure 9 shows also that as L increase, the performance is enhanced (increasing the multipath gain. Figure 9 shows that one of the benefits of the WSTC is that it introduces a better performance with L = 1 than the conventional STC with L = 8 for low E/No . Thus WSTC also decreases the receiver complexity. The performance is examined too with different non-line-of-sight (NLOS) channels CM2, CM3, and CM4 presented in the IEEE802.15.3a proposal [2, 23]. The WSTC also succeeded to enhance 0.35 0.3
s1 equal s2 (1 1 or -1-1) s1 not equal tos2 (-1 1 or 1-1)
Amplitde
0.25 0.2 0.15 0.1 0.05 0 0
2
4
6 8 Frequency (GHz)
10
12
14
Figure 6: The spectrum of the transmitted pulse wo (t) symbols are multiplexed in the wavelet domain (same for w1 (t)) using MW Coiflet 5. 0.35 s1 equal s2 (1 1 or -1-1) s1 not equal tos2 (-1 1 or 1-1)
0.3
Amplitde
0.25 0.2 0.15 0.1 0.05 0 0
2
4
6
8
10 12 Frequency (GHz)
14
16
18
20
Figure 7: The spectrum of the transmitted pulse wo (t) after symbols are multiplexed in the wavelet domain (same for w1 (t)) using MW Coiflet 3.
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F ( 1 / ( bit / sec / Hz) )
103 102 1
10
Conventional STC L=1 Conventional STC L=4 Conventional STC L=8 Wavelet STC I L=1 Wavelet STC I L=4 Wavelet STC I L=8
0
10
-1
10
10-2 0
2
4
6
8
10 E/No
12
14
16
18
20
Figure 8: The performance of conventional STC and WSTC UWB system using Coiflet 3 MW and different L Rake fingers.
F ( 1 / ( bit / sec / Hz) )
10
3
2
10
1
10
0
Conventional STCI CM2 Wavelet STCI CM2 Conventional STCI CM3 Wavelet STCI CM3 Conventional STCI CM4 Wavelet STCI CM4
10
0
2
4
6
8
10 E/No (dB)
12
14
16
18
20
Figure 9: The performance of conventional STC and WSTC UWB system using Coiflet 3 MW and L = 4 Rake receiver for different channel models.
the performance for the non-line of sight (NLOS) channel models CM2, CM3, and CM4. This is estimated from Figure 10 that illustrates the performance of WSTC for different channel models and L = 4. 6. CONCLUSION
The WSTC scheme is proposed to increase the transmission rate to four times that of the conventional STC in addition to enhancing the performance. The WSTC scheme multiplexes different symbols in the wavelet domain of the UWB pulses and transmits different multiplexed symbols on multiple transmitting antennas to offer spatial multiplexing. The simulation results showed that WSTC leads the conventional STC in performance for different channel models CM1, CM2, CM3, and CM4. The WSTC for CM1 also outperforms the conventional STC with less number of fingers, thus reduces the receiver complexity. The enhancement in performance takes place due to the high correlation of the MW used with the transmitted signal. REFERENCES
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