- Email: [email protected]
Suppression of IEEE 802.11a interference using SVD-based algorithm for DS-UWB systems in wireless multipath channels
Int. J. Electron. Commun. (AEÜ) 61 (2007) 700 – 704 www.elsevier.de/aeue
LETTER
Suppression of IEEE 802.11a interference using SVD-based algorithm for DS-UWB systems in wireless multipath channels Shaoyi Xu∗ , Qinghai Yang, Kyung Sup Kwak UWB-ITRC, The Graduate School of Information Technology and Telecommunications, Inha University, 253 Yonghyun-dong, Nam-gu, Incheon, 402-751, Republic of Korea Received 14 June 2006; accepted 15 November 2006
Abstract IEEE 802.11a systems which operate around 5 GHz and overlap the band of UWB signals will interfere with UWB systems significantly. In this letter, a novel narrow-band interference (NBI) suppression technique based on the singular value decomposition (SVD) algorithm is proposed in direct sequence ultra-wideband (DS-UWB) systems in wireless multipath channels. SVD is used to approximate the interference which then is subtracted from the received signals. In contrast to the conventional suppression methods such as the notch filter and the maximal-ratio combining partial RAKE (MRC PRAKE) receiver, our proposed technique is simple and robust, the hardware complexity of the receiver can be reduced greatly. 䉷 2007 Elsevier GmbH. All rights reserved. Keywords: Narrow-band interference (NBI); Singular value decomposition (SVD); Direct sequence ultra-wideband (DS-UWB); Maximal-ratio combining partial RAKE (MRC PRAKE)
1. Introduction The ultra-wideband (UWB) systems transmit data over a very large bandwidth with appropriate restrictions on effective radiated power (−41 dBm/MHz) thus making the UWB signal have little impact on other devices operating in the same frequency band. Nevertheless, the low energy per pulse makes them susceptible to this strong narrow-band interference (NBI) even though UWB systems may enjoy a high spreading gain due to the large bandwidths. Especially, IEEE 802.11a systems operate around 5 GHz which overlap the band of UWB signals regulated by the FCC, leading to the significant interference to UWB systems. By modeling NBI as a single carrier BPSK modulated waveform or a cosinusoidal tone, NBI suppression has been
∗ Corresponding author.
E-mail addresses: [email protected] (S. Xu), [email protected] (Q. Yang), [email protected] (K.S. Kwak). 1434-8411/$ - see front matter 䉷 2007 Elsevier GmbH. All rights reserved. doi:10.1016/j.aeue.2006.11.004
investigated with a minimum mean square error (MMSE) RAKE receiver [1], a notch filter [2] and designing of a special pulse [3]. Although these techniques are effective to suppress single NBI, the NBI suppression technique is still an eminent challenge since the proposed solutions either have high complexity requirements of UWB receivers or behave ineffective against strong NBI. Furthermore, surprisingly, the interference suppression technique on IEEE 802.11a systems received very little attention so far. With the bandwidth as large as several hundred MHz, IEEE 802.11a interference may not be modeled as a BPSK modulated signal or as a cosinusoidal tone. Recently, both analytically and empirically, it has been demonstrated that IEEE 802.11a signals can be modeled as bandlimited additive white Gaussian noise (AWGN) [4,5]. In our work, we provide a novel technique based on the singular value decomposition (SVD) to suppress IEEE 802.11a signals for the direct sequence UWB (DS-UWB) system. The SVD algorithm is used to estimate NBI which then is subtracted from the received signals. This work is
S. Xu et al. / Int. J. Electron. Commun. (AEÜ) 61 (2007) 700 – 704
an extension of our previous work [6] to deal with wireless multipath channels case and also includes the conventional notch filter and the maximal-ratio combining partial RAKE (MRC PRAKE) receiver for comparison. Simulation results confirm that our method can suppress NBI effectively and robustly, the hardware complexity of the receiver can be reduced greatly.
2. System model Consider the single-user DS-UWB system model with NBI which takes the form s(t) =
(i+1)N ss −1 s −1 N j =iN s
di Cn wtr (t − j T f − nT c ),
(1)
n=0
where wtr is the transmitted pulse with the duration of Tp ; Tf and Tc are the frame period and the chip period, respectively, such that the spread spectrum processing gain Nss = Tf /Tc ; Ns is the number of pulses required to transmit a single information bit and Tb = Ns Tf denotes the bit duration; di ∈ ±1 represents the ith transmitted information bit and Cn ∈ ±1 are the spreading chips. Let h(t) = L−1 l=0 l (t − l ) denote the multipath channel with L paths, the received signal can be expressed as r(t) =
L−1 ss −1 (i+1)N s −1 N l=0
j =iN s
l di Cn wrx (t − j T f − nT c
n=0
− l ) + i(t) + n(t),
(2)
where wrx is the received pulse at the output of the antenna; i(t) represents the NBI signal and n(t) is the AWGN with two-sided power spectral density (PSD) N0 /2; l and l are the channel attenuation and the channel delay associated with the lth path which are assumed to be known at the receiver. Defining = [1 , 2 , . . . , L ]T and = [1 , 2, . . . , L ]T as the channel attenuation vector and the channel delay vector, respectively (Superscripts T and H denote transpose and complex transpose of a matrix). To reduce the receiver complexity, we use a PRAKE which adopts first Lp paths out of L available diversity paths and combines them according to MRC. A MRC RAKE receiver employs the weighs vector = and maximizes the signal to noise ratio (SNR) when no interference exists in the system. The template waveform of the kth frame for the lth correlator with the time delay l is given by l (t) =
N ss −1
Cn wrx (t − kT f − nT c − l )
(3)
n=0
producing the output rl (t) =
N s −1 j =0
jT f
(j −1)Tf
r(t)l (t) dt
(4)
701
which can be denoted by a vector as r = [r1 , r2 , . . . , rL ]T . So the RAKE output can be expressed as y(t) = T r = Lp −1 l=0 l rl (t). As a most likely co-exist technology with UWB in the future, IEEE 802.11a systems employ the orthogonal frequency division multiplexing (OFDM) based transmission and possess three 100 MHz wide frequency bands. Both analytically and empirically, it has been demonstrated [4,5] that when the number of subcarriers is large enough a complex baseband OFDM signal can be modeled as a bandlimited AWGN process. With 52 subcarriers, IEEE 802.11a signals satisfy the condition and can be modeled as bandlimited AWGN. In this letter, the worst situation which means IEEE 802.11a signals occupy the full 300 MHz bandwidth is considered. This might not happen in the real situation but gives the worst performance in UWB systems.
3. NBI suppression technique For a time series r(k) with k = 1, 2, . . . , N (N is the sampling number of points), we can construct a Hankel matrix with M = N − L + 1 rows and L columns illustrated as follows: ⎡ ⎤ r(1) r(2) ... r(L) r(2) r(3) . . . r(L + 1) ⎥ ⎢ ⎥. R=⎢ .. .. .. ⎣ ⎦ . . . r(N − L + 1) r(N − L + 2) . . .
r(N ) (5)
Using the SVD, R can be factorized as R = U V H where U (M × M) and V (L × L) are unitary matries. = diag(1 , 2 , . . . , m ) is a diagonal matrix with diagonal entries called the singular values of R which are arranged in the decreasing order and are square roots of the eigenvalues of RH R or RRH . With the characteristic of white noise, the UWB signal has similar singular values which are all close to zero in the absence of high-energy NBI. After NBI are introduced to the UWB system, there will exist several dominant singular values to represent such interference. In this case, the data matrix R is the superposition of the UWB signal space and the noise space and can be partitioned into two subspaces as follows: R 0 R = [UR US ] [VR VS ]H 0 S H = U R R V R + US S VSH = RR + R S ,
(6)
where R =diag(1 , 2 , . . . , k ) and S =diag(k+1 , k+2 , . . . , m ) with 1 > 2 > · · · ?k+1 > k+2 > · · · > m corresponds to the singular values in the interference subspace RR and the data subspace RS , respectively. By subtracting
702
S. Xu et al. / Int. J. Electron. Commun. (AEÜ) 61 (2007) 700 – 704
RR from R, we can get the estimated data matrix with suppressed NBI. In summary, the SVD-based suppressing NBI consists of the following main steps: (1) Pick a number L so that k < L < N − k [7], (k is the number of dominant singular values) and arrange the received signal vector to form a Hankel data matrix R. (2) Compute the SVD of R to obtain the estimated interference subspace RR and subtract it from R to get the ˜ = R − RR . estimated data matrix as R ˜ into the vector and (3) Rearrange the estimated matrix R do performance detection.
4. Effect of NBI algorithm Substituting (2) and (3) into (4) gives rl (t)=zl (t)+il (t)+ nl (t) where zl (t) = Ns di
l
jT f
Lp −1
(j −1)Tf l=0
N ss −1
×
Cn wrx (t − j T f − nT c − l )
Cm wrx (t − j T f − mT c − l ) dt,
(7)
m=0 N s −1 j T f
il (t) =
j =0
(j −1)Tf
i(t)
N ss −1
Cm wrx (t − j T f
m=0
− mT c − l ) dt, nl (t) =
N s −1 j T f j =0
(j −1)Tf
n(t)
(8) N ss −1
Cm wrx (t − j T f
m=0
− mT c − l ) dt.
(9)
Here, zl (t), il (t) and nl (t) correspond to the distribution of the UWB signal, NBI and the noise component at the output of the lth correlator. Among them, nl (t) is a Gaussian random variable with the mean
j T f zero 2and the variance is Ew N0 Ns Nss /2 where Ew = (j −1)T wrx (t) dt. f Thus we can obtain the output of the MRC PRAKE receiver with Lp fingers as Lp −1
y(t) =
l (zl (t) + il (t) + nl (t)) = T (z + i + n), (10)
l=0
where z = [z1 , z2 , . . . , zLp ]T , i = [i1 , i2 , . . . , iLp ]T and n = [n1 , n2 , . . . , nLp ]T . So the signal to interference and noise ratio (SINR) can be represented as SINRout =
˜ 2 = trace[(RS − R)(R ˜ ˜ H] 2SVD = RS − R S − R) ˜U ˜ ˜H = trace[US 2S USH − US S VSH V ˜V ˜ 2U ˜ H ]. ˜ ˜ H VS S USH + U ˜ −U
(12)
˜ and VS ≈ V, ˜ the MSE Under the assumption that US ≈ U of SVD can be approximated by 2SVD ≈ ki=1 2i < k2max , where i is the singular value of the signal matrix RS when no NBI is added into the system and max is the maximum singular values among them. With the small max (close to zero), we can observe that the 2SVD is trivial so that good suppression effectiveness can be obtained.
5. Simulation results and discussion
n=0 N ss −1
where Ri = E{iiH } and Rn = E{nnH } are the correlation matrix of NBI and AWGN, respectively. Let RS =US S VSH be the SVD of the received data matrix ˜ =U ˜ ˜ V ˜ H be the SVD of the received without NBI and R data matrix with NBI suppressed by using our method. So the mean-squared error (MSE) is approximated as
|T z|2 T Ri + T Rn
,
(11)
The performance of our method is evaluated in both CM1 channel model (LOS) and CM3 channel model (NLOS) according to Ref. [8]. At the transmitter, the second-derivative Gaussian pulse is used as the transmitted UWB monocycle. We define the UWB signal to NBI ratio at the input of the correlator (SIRin ) as SIRin = PUWB /PR and the UWB signal to AWGN ratio (SNRin ) as SNRin = PUWB /22 , where PUWB and PR are the power of UWB signal and NBI, respectively; 2 is the variance of AWGN. In the CM1 channel model, without the specific explanation, the receiver is 1finger MRC RAKE whose time delay is adopted according to the main path. The simulation results in the CM1 channel model are shown in Figs. 1–5. In Fig. 1, we plot the NBI suppression result of IEEE 802.11a signals by using the SVD algorithm corresponding to SIRin = −30, −20 and −10 dB, respectively. Satisfying k < L < N − k, we pick the number of columns L as L = N/4, N is the number of sampling points. We can observe that NBI is mitigated greatly by using our technique. To study the robustness of our algorithm, we first compare the results under different sampling rate with L = N/4. Using our technique, the sampling rate in the receiver can be taken just according to the UWB signal, regardless of the NBI. Fig. 2 presents the result in the scenario of different sampling rate at 5.988 GHz [8] and 11.67 GHz, respectively. The UWB signals are oversampled at these two sampling rate but the IEEE 802.11a signal is undersampled with the sampling rate at 5.988 GHz. Fig. 2 proves the robustness of our technique when SIRin = −30 dB, for example, at BER of 10−2 , the performance with undersampling rate can still achieve over 4 dB improvement than without interference suppression when SIRin = −10 dB. In addition, satisfying
100
100
10-1
10-1
10-2
10-2
10-3
10-3
BER
BER
S. Xu et al. / Int. J. Electron. Commun. (AEÜ) 61 (2007) 700 – 704
10-4 10-5
10-4 10-5
SIR = -10dB without NBI suppression
SIR = -10dB without NBI suppression With L = 0.75N with SIR=-30dB
SIR=-30dB with NBI suppression SIR=-20dB with NBI suppression SIR = -10dB with NBI suppression
10-6
With L = 0.5N with SIR=-30dB With L = 0.25N with SIR=-30dB
10-6
AWGN Only
10-7
-4
-2
0
AWGN Only
2
6 4 SNR in dB
8
10
-4
100
100
10-1
10-1
10-2
10-2
10-3
10-3
10-4 10-5
10-5
0
6 4 SNR in dB
8
10
12
SIR = -30dB with notch filter SIR=-30dB with SVD SIR = -10dB with SVD
10-6
AWGN Only
-2
2
SIR=-10dB with notch filter
With undersampling rate with SIR=-30dB With oversampling rate with SIR=-30dB
-4
0
10-4
SIR = -10dB without NBI suppression
10-7
-2
Fig. 3. IEEE 802.11a interference suppression by using SVD algorithm with different L.
BER
BER
10-7
12
Fig. 1. IEEE 802.11a interference suppression by using SVD algorithm.
10-6
703
AWGN Only
2
6 4 SNR in dB
8
10
12
10-7
-4
-2
0
2
6 4 SNR in dB
8
10
12
Fig. 2. IEEE 802.11a interference suppression by using SVD algorithm with different sampling rate.
Fig. 4. IEEE 802.11a interference suppression comparison between SVD method and notch filter.
the inequality k < L < N − k, Fig. 3 plots the simulation results with L = 3N/4, L = N/2 and L = N/4, respectively. From the figure, we can observe that although we take different L, our algorithm can still mitigate the NBI effectively with slight difference. As shown in [7], when the number L satisfies the inequality k < L < N − k, the correct or approximately correct estimation can be obtained and L is recommended approximately to L = N/3 for best performance. Actually, satisfying k < L < N − k, the value of L decides the number of larger singular values representing the interference and running efficiency of suppression technique and has no significant impact on system performance. To show the effectiveness of our method, we compare the performance of our method with the conventional notch filter and the MRC PRAKE receiver with 6 fingers. Fig. 4
depicts the simulation results when L=N/4 and SIRin =−30 and −10 dB, respectively. The notch filter is a Chebyshev II IIR bandstop filter with the passband ripple 1dB and the stopband attenuation 40 dB. It is shown that our proposed method outperforms the notch filter. Unlike our method, the center frequency of the NBI need to be estimated and the center frequency of the notch filter need to be adjustable to meet the specific NBI. Furthermore, such in-band notches may impair the performance of UWB signals simultaneously [9]. Hence, as the NBI bandwidth increased, our method can achieve better performance than the notch filter. In contrast to the 6-fingers MRC PRAKE receiver, we plot the simulation results in Fig. 5. We can observe that when SIRin = −20 and −30 dB, the system is almost jammed even a 6-fingers MRC PRAKE is used. As expected, our scheme outperforms
704
S. Xu et al. / Int. J. Electron. Commun. (AEÜ) 61 (2007) 700 – 704
shown in Fig. 6, we can obtain better performance by using our method than by using conventional techniques. Furthermore, by using our method, only a 3-fingers MRC PRAKE receiver is enough to suppress such NBI whereas even a 10-fingers MRC PRAKE receiver is ineffective in such case.
100 10-1
BER
10-2 10-3 10-4
6. Conclusions
SIR = -30dB with 6-fingers MRC PRAKE receiver SIR = -20dB with 6-fingers MRC PRAKE receiver
10-5
SIR=-10dB with 6-fingers MRC PRAKE receiver SIR=-30dB with SVD SIR=-20dB with SVD
10-6 10-7
SIR = -10dB with SVD AWGN Only
-4
-2
0
2
6 4 SNR in dB
8
10
12
Fig. 5. IEEE 802.11a interference suppression comparison between SVD method and 6-fingers MRC PRAKE receiver.
In this letter, a novel algorithm based on SVD is proposed to suppress IEEE 802.11a signals for DS-UWB systems. SVD is useful to acquire the dominant singular values corresponding to the NBI and to obtain the estimated data matrix. In contrast to traditional methods, we can conclude that our algorithm is very effective and robust and the hardware complexity of the receiver can be reduced greatly.
Acknowledgements 100
This research was supported by University IT Research Center Project of Inha UWB-ITRC, Republic of Korea.
10-1 10-2
BER
References 10-3 10-4
SIR = -30dB with 10-fingers MRC PRAKE without SVD SIR = -20dB with 10-fingers MRC PRAKE without SVD
10-5
SIR = -30dB with 3-fingers MRC PRAKE using notch filter SIR = -20dB with 3-fingers MRC PRAKE using notch filter SIR = -30dB with 3-fingers MRC PRAKE using SVD
10-6 10-7
SIR = -20dB with 3-fingers MRC PRAKE using SVD AWGN Only
-4
-2
0
2
6 4 SNR in dB
8
10
12
Fig. 6. IEEE 802.11a interference suppression comparison between SVD method, notch filter and 10-fingers MRC PRAKE receiver in the CM3 channel model.
the 6-fingers MRC PRAKE receiver greatly when SIRin = −20 and −30 dB. As SIRin = −10 dB, a slight improvement (at a target BER of 10−5 , SNR improves less than 1dB) is obtained by using a 6-fingers MRC PRAKE receiver than the SVD-based method but at the cost of greater receiver complexity. Since the hardware complexity of the RAKE receiver depends on its finger number, using our method, the hardware complexity of the receiver can be decreased dramatically. Fig. 6 presents the performance in the CM3 channel model when we compare our method with the notch filter and the 10-fingers MRC PRAKE receiver. The notch filter is the same one as in Fig. 5 and the receiver is a 3-fingers MRC-PRAKE for our algorithm and the notch filter. As
[1] Boubaker N, Letaief KB. A low complexity MMSE-RAKE receiver in a realistic uwb channel and in the presence of NBI, IEEE WCNC 2003;233–7. [2] Li L, Milstein L. Rejection of narrow-band interference in PN spread spectrum systems using transversal filters. IEEE Trans Commun 1984;9:925–8. [3] Taha A, Chugg K. A theoretical study on the effects of interference on UWB multiple-access impulse radio, Asilomar conference on signals, systems, and computers, 2002, pp. 728–732. [4] Li Q, Rusch LA. Multiuser detection for DS-CDMA UWB in the home environment. IEEE J Select Area Commun 2002;9:1701–11. [5] Firoozbakhsh B, Pratt TG, Jayant N. Analysis of IEEE 802.11a interference on UWB systems. IEEE conference on ultra wideband systems and technologies, 2003. p. 473–7. [6] Xu SY, Bai ZQ, Yang QH, Kwak KS. Singular value decomposition-based algorithm for IEEE 802.11a interference suppression in DS-UWB systems. IEICE Trans Fundam 2006;7:1913–8. [7] Tufts DW, Kumaresan R, Kirsteins I. Singular value decomposition and improved frequency estimation using linear prediction. IEEE Trans Signal Process 1982;30(4): 671–5. [8] IEEE p802.15 working group for WPAN, channel modeling sub-committee report final. IEEE P802.15-02/368rSG3a, 2002. [9] Chu X, Murch RD. The effect of NBI on UWB time-hopping systems. IEEE Trans Wireless Commun 2004;3:1431–6.
LETTER
Suppression of IEEE 802.11a interference using SVD-based algorithm for DS-UWB systems in wireless multipath channels Shaoyi Xu∗ , Qinghai Yang, Kyung Sup Kwak UWB-ITRC, The Graduate School of Information Technology and Telecommunications, Inha University, 253 Yonghyun-dong, Nam-gu, Incheon, 402-751, Republic of Korea Received 14 June 2006; accepted 15 November 2006
Abstract IEEE 802.11a systems which operate around 5 GHz and overlap the band of UWB signals will interfere with UWB systems significantly. In this letter, a novel narrow-band interference (NBI) suppression technique based on the singular value decomposition (SVD) algorithm is proposed in direct sequence ultra-wideband (DS-UWB) systems in wireless multipath channels. SVD is used to approximate the interference which then is subtracted from the received signals. In contrast to the conventional suppression methods such as the notch filter and the maximal-ratio combining partial RAKE (MRC PRAKE) receiver, our proposed technique is simple and robust, the hardware complexity of the receiver can be reduced greatly. 䉷 2007 Elsevier GmbH. All rights reserved. Keywords: Narrow-band interference (NBI); Singular value decomposition (SVD); Direct sequence ultra-wideband (DS-UWB); Maximal-ratio combining partial RAKE (MRC PRAKE)
1. Introduction The ultra-wideband (UWB) systems transmit data over a very large bandwidth with appropriate restrictions on effective radiated power (−41 dBm/MHz) thus making the UWB signal have little impact on other devices operating in the same frequency band. Nevertheless, the low energy per pulse makes them susceptible to this strong narrow-band interference (NBI) even though UWB systems may enjoy a high spreading gain due to the large bandwidths. Especially, IEEE 802.11a systems operate around 5 GHz which overlap the band of UWB signals regulated by the FCC, leading to the significant interference to UWB systems. By modeling NBI as a single carrier BPSK modulated waveform or a cosinusoidal tone, NBI suppression has been
∗ Corresponding author.
E-mail addresses: [email protected] (S. Xu), [email protected] (Q. Yang), [email protected] (K.S. Kwak). 1434-8411/$ - see front matter 䉷 2007 Elsevier GmbH. All rights reserved. doi:10.1016/j.aeue.2006.11.004
investigated with a minimum mean square error (MMSE) RAKE receiver [1], a notch filter [2] and designing of a special pulse [3]. Although these techniques are effective to suppress single NBI, the NBI suppression technique is still an eminent challenge since the proposed solutions either have high complexity requirements of UWB receivers or behave ineffective against strong NBI. Furthermore, surprisingly, the interference suppression technique on IEEE 802.11a systems received very little attention so far. With the bandwidth as large as several hundred MHz, IEEE 802.11a interference may not be modeled as a BPSK modulated signal or as a cosinusoidal tone. Recently, both analytically and empirically, it has been demonstrated that IEEE 802.11a signals can be modeled as bandlimited additive white Gaussian noise (AWGN) [4,5]. In our work, we provide a novel technique based on the singular value decomposition (SVD) to suppress IEEE 802.11a signals for the direct sequence UWB (DS-UWB) system. The SVD algorithm is used to estimate NBI which then is subtracted from the received signals. This work is
S. Xu et al. / Int. J. Electron. Commun. (AEÜ) 61 (2007) 700 – 704
an extension of our previous work [6] to deal with wireless multipath channels case and also includes the conventional notch filter and the maximal-ratio combining partial RAKE (MRC PRAKE) receiver for comparison. Simulation results confirm that our method can suppress NBI effectively and robustly, the hardware complexity of the receiver can be reduced greatly.
2. System model Consider the single-user DS-UWB system model with NBI which takes the form s(t) =
(i+1)N ss −1 s −1 N j =iN s
di Cn wtr (t − j T f − nT c ),
(1)
n=0
where wtr is the transmitted pulse with the duration of Tp ; Tf and Tc are the frame period and the chip period, respectively, such that the spread spectrum processing gain Nss = Tf /Tc ; Ns is the number of pulses required to transmit a single information bit and Tb = Ns Tf denotes the bit duration; di ∈ ±1 represents the ith transmitted information bit and Cn ∈ ±1 are the spreading chips. Let h(t) = L−1 l=0 l (t − l ) denote the multipath channel with L paths, the received signal can be expressed as r(t) =
L−1 ss −1 (i+1)N s −1 N l=0
j =iN s
l di Cn wrx (t − j T f − nT c
n=0
− l ) + i(t) + n(t),
(2)
where wrx is the received pulse at the output of the antenna; i(t) represents the NBI signal and n(t) is the AWGN with two-sided power spectral density (PSD) N0 /2; l and l are the channel attenuation and the channel delay associated with the lth path which are assumed to be known at the receiver. Defining = [1 , 2 , . . . , L ]T and = [1 , 2, . . . , L ]T as the channel attenuation vector and the channel delay vector, respectively (Superscripts T and H denote transpose and complex transpose of a matrix). To reduce the receiver complexity, we use a PRAKE which adopts first Lp paths out of L available diversity paths and combines them according to MRC. A MRC RAKE receiver employs the weighs vector = and maximizes the signal to noise ratio (SNR) when no interference exists in the system. The template waveform of the kth frame for the lth correlator with the time delay l is given by l (t) =
N ss −1
Cn wrx (t − kT f − nT c − l )
(3)
n=0
producing the output rl (t) =
N s −1 j =0
jT f
(j −1)Tf
r(t)l (t) dt
(4)
701
which can be denoted by a vector as r = [r1 , r2 , . . . , rL ]T . So the RAKE output can be expressed as y(t) = T r = Lp −1 l=0 l rl (t). As a most likely co-exist technology with UWB in the future, IEEE 802.11a systems employ the orthogonal frequency division multiplexing (OFDM) based transmission and possess three 100 MHz wide frequency bands. Both analytically and empirically, it has been demonstrated [4,5] that when the number of subcarriers is large enough a complex baseband OFDM signal can be modeled as a bandlimited AWGN process. With 52 subcarriers, IEEE 802.11a signals satisfy the condition and can be modeled as bandlimited AWGN. In this letter, the worst situation which means IEEE 802.11a signals occupy the full 300 MHz bandwidth is considered. This might not happen in the real situation but gives the worst performance in UWB systems.
3. NBI suppression technique For a time series r(k) with k = 1, 2, . . . , N (N is the sampling number of points), we can construct a Hankel matrix with M = N − L + 1 rows and L columns illustrated as follows: ⎡ ⎤ r(1) r(2) ... r(L) r(2) r(3) . . . r(L + 1) ⎥ ⎢ ⎥. R=⎢ .. .. .. ⎣ ⎦ . . . r(N − L + 1) r(N − L + 2) . . .
r(N ) (5)
Using the SVD, R can be factorized as R = U V H where U (M × M) and V (L × L) are unitary matries. = diag(1 , 2 , . . . , m ) is a diagonal matrix with diagonal entries called the singular values of R which are arranged in the decreasing order and are square roots of the eigenvalues of RH R or RRH . With the characteristic of white noise, the UWB signal has similar singular values which are all close to zero in the absence of high-energy NBI. After NBI are introduced to the UWB system, there will exist several dominant singular values to represent such interference. In this case, the data matrix R is the superposition of the UWB signal space and the noise space and can be partitioned into two subspaces as follows: R 0 R = [UR US ] [VR VS ]H 0 S H = U R R V R + US S VSH = RR + R S ,
(6)
where R =diag(1 , 2 , . . . , k ) and S =diag(k+1 , k+2 , . . . , m ) with 1 > 2 > · · · ?k+1 > k+2 > · · · > m corresponds to the singular values in the interference subspace RR and the data subspace RS , respectively. By subtracting
702
S. Xu et al. / Int. J. Electron. Commun. (AEÜ) 61 (2007) 700 – 704
RR from R, we can get the estimated data matrix with suppressed NBI. In summary, the SVD-based suppressing NBI consists of the following main steps: (1) Pick a number L so that k < L < N − k [7], (k is the number of dominant singular values) and arrange the received signal vector to form a Hankel data matrix R. (2) Compute the SVD of R to obtain the estimated interference subspace RR and subtract it from R to get the ˜ = R − RR . estimated data matrix as R ˜ into the vector and (3) Rearrange the estimated matrix R do performance detection.
4. Effect of NBI algorithm Substituting (2) and (3) into (4) gives rl (t)=zl (t)+il (t)+ nl (t) where zl (t) = Ns di
l
jT f
Lp −1
(j −1)Tf l=0
N ss −1
×
Cn wrx (t − j T f − nT c − l )
Cm wrx (t − j T f − mT c − l ) dt,
(7)
m=0 N s −1 j T f
il (t) =
j =0
(j −1)Tf
i(t)
N ss −1
Cm wrx (t − j T f
m=0
− mT c − l ) dt, nl (t) =
N s −1 j T f j =0
(j −1)Tf
n(t)
(8) N ss −1
Cm wrx (t − j T f
m=0
− mT c − l ) dt.
(9)
Here, zl (t), il (t) and nl (t) correspond to the distribution of the UWB signal, NBI and the noise component at the output of the lth correlator. Among them, nl (t) is a Gaussian random variable with the mean
j T f zero 2and the variance is Ew N0 Ns Nss /2 where Ew = (j −1)T wrx (t) dt. f Thus we can obtain the output of the MRC PRAKE receiver with Lp fingers as Lp −1
y(t) =
l (zl (t) + il (t) + nl (t)) = T (z + i + n), (10)
l=0
where z = [z1 , z2 , . . . , zLp ]T , i = [i1 , i2 , . . . , iLp ]T and n = [n1 , n2 , . . . , nLp ]T . So the signal to interference and noise ratio (SINR) can be represented as SINRout =
˜ 2 = trace[(RS − R)(R ˜ ˜ H] 2SVD = RS − R S − R) ˜U ˜ ˜H = trace[US 2S USH − US S VSH V ˜V ˜ 2U ˜ H ]. ˜ ˜ H VS S USH + U ˜ −U
(12)
˜ and VS ≈ V, ˜ the MSE Under the assumption that US ≈ U of SVD can be approximated by 2SVD ≈ ki=1 2i < k2max , where i is the singular value of the signal matrix RS when no NBI is added into the system and max is the maximum singular values among them. With the small max (close to zero), we can observe that the 2SVD is trivial so that good suppression effectiveness can be obtained.
5. Simulation results and discussion
n=0 N ss −1
where Ri = E{iiH } and Rn = E{nnH } are the correlation matrix of NBI and AWGN, respectively. Let RS =US S VSH be the SVD of the received data matrix ˜ =U ˜ ˜ V ˜ H be the SVD of the received without NBI and R data matrix with NBI suppressed by using our method. So the mean-squared error (MSE) is approximated as
|T z|2 T Ri + T Rn
,
(11)
The performance of our method is evaluated in both CM1 channel model (LOS) and CM3 channel model (NLOS) according to Ref. [8]. At the transmitter, the second-derivative Gaussian pulse is used as the transmitted UWB monocycle. We define the UWB signal to NBI ratio at the input of the correlator (SIRin ) as SIRin = PUWB /PR and the UWB signal to AWGN ratio (SNRin ) as SNRin = PUWB /22 , where PUWB and PR are the power of UWB signal and NBI, respectively; 2 is the variance of AWGN. In the CM1 channel model, without the specific explanation, the receiver is 1finger MRC RAKE whose time delay is adopted according to the main path. The simulation results in the CM1 channel model are shown in Figs. 1–5. In Fig. 1, we plot the NBI suppression result of IEEE 802.11a signals by using the SVD algorithm corresponding to SIRin = −30, −20 and −10 dB, respectively. Satisfying k < L < N − k, we pick the number of columns L as L = N/4, N is the number of sampling points. We can observe that NBI is mitigated greatly by using our technique. To study the robustness of our algorithm, we first compare the results under different sampling rate with L = N/4. Using our technique, the sampling rate in the receiver can be taken just according to the UWB signal, regardless of the NBI. Fig. 2 presents the result in the scenario of different sampling rate at 5.988 GHz [8] and 11.67 GHz, respectively. The UWB signals are oversampled at these two sampling rate but the IEEE 802.11a signal is undersampled with the sampling rate at 5.988 GHz. Fig. 2 proves the robustness of our technique when SIRin = −30 dB, for example, at BER of 10−2 , the performance with undersampling rate can still achieve over 4 dB improvement than without interference suppression when SIRin = −10 dB. In addition, satisfying
100
100
10-1
10-1
10-2
10-2
10-3
10-3
BER
BER
S. Xu et al. / Int. J. Electron. Commun. (AEÜ) 61 (2007) 700 – 704
10-4 10-5
10-4 10-5
SIR = -10dB without NBI suppression
SIR = -10dB without NBI suppression With L = 0.75N with SIR=-30dB
SIR=-30dB with NBI suppression SIR=-20dB with NBI suppression SIR = -10dB with NBI suppression
10-6
With L = 0.5N with SIR=-30dB With L = 0.25N with SIR=-30dB
10-6
AWGN Only
10-7
-4
-2
0
AWGN Only
2
6 4 SNR in dB
8
10
-4
100
100
10-1
10-1
10-2
10-2
10-3
10-3
10-4 10-5
10-5
0
6 4 SNR in dB
8
10
12
SIR = -30dB with notch filter SIR=-30dB with SVD SIR = -10dB with SVD
10-6
AWGN Only
-2
2
SIR=-10dB with notch filter
With undersampling rate with SIR=-30dB With oversampling rate with SIR=-30dB
-4
0
10-4
SIR = -10dB without NBI suppression
10-7
-2
Fig. 3. IEEE 802.11a interference suppression by using SVD algorithm with different L.
BER
BER
10-7
12
Fig. 1. IEEE 802.11a interference suppression by using SVD algorithm.
10-6
703
AWGN Only
2
6 4 SNR in dB
8
10
12
10-7
-4
-2
0
2
6 4 SNR in dB
8
10
12
Fig. 2. IEEE 802.11a interference suppression by using SVD algorithm with different sampling rate.
Fig. 4. IEEE 802.11a interference suppression comparison between SVD method and notch filter.
the inequality k < L < N − k, Fig. 3 plots the simulation results with L = 3N/4, L = N/2 and L = N/4, respectively. From the figure, we can observe that although we take different L, our algorithm can still mitigate the NBI effectively with slight difference. As shown in [7], when the number L satisfies the inequality k < L < N − k, the correct or approximately correct estimation can be obtained and L is recommended approximately to L = N/3 for best performance. Actually, satisfying k < L < N − k, the value of L decides the number of larger singular values representing the interference and running efficiency of suppression technique and has no significant impact on system performance. To show the effectiveness of our method, we compare the performance of our method with the conventional notch filter and the MRC PRAKE receiver with 6 fingers. Fig. 4
depicts the simulation results when L=N/4 and SIRin =−30 and −10 dB, respectively. The notch filter is a Chebyshev II IIR bandstop filter with the passband ripple 1dB and the stopband attenuation 40 dB. It is shown that our proposed method outperforms the notch filter. Unlike our method, the center frequency of the NBI need to be estimated and the center frequency of the notch filter need to be adjustable to meet the specific NBI. Furthermore, such in-band notches may impair the performance of UWB signals simultaneously [9]. Hence, as the NBI bandwidth increased, our method can achieve better performance than the notch filter. In contrast to the 6-fingers MRC PRAKE receiver, we plot the simulation results in Fig. 5. We can observe that when SIRin = −20 and −30 dB, the system is almost jammed even a 6-fingers MRC PRAKE is used. As expected, our scheme outperforms
704
S. Xu et al. / Int. J. Electron. Commun. (AEÜ) 61 (2007) 700 – 704
shown in Fig. 6, we can obtain better performance by using our method than by using conventional techniques. Furthermore, by using our method, only a 3-fingers MRC PRAKE receiver is enough to suppress such NBI whereas even a 10-fingers MRC PRAKE receiver is ineffective in such case.
100 10-1
BER
10-2 10-3 10-4
6. Conclusions
SIR = -30dB with 6-fingers MRC PRAKE receiver SIR = -20dB with 6-fingers MRC PRAKE receiver
10-5
SIR=-10dB with 6-fingers MRC PRAKE receiver SIR=-30dB with SVD SIR=-20dB with SVD
10-6 10-7
SIR = -10dB with SVD AWGN Only
-4
-2
0
2
6 4 SNR in dB
8
10
12
Fig. 5. IEEE 802.11a interference suppression comparison between SVD method and 6-fingers MRC PRAKE receiver.
In this letter, a novel algorithm based on SVD is proposed to suppress IEEE 802.11a signals for DS-UWB systems. SVD is useful to acquire the dominant singular values corresponding to the NBI and to obtain the estimated data matrix. In contrast to traditional methods, we can conclude that our algorithm is very effective and robust and the hardware complexity of the receiver can be reduced greatly.
Acknowledgements 100
This research was supported by University IT Research Center Project of Inha UWB-ITRC, Republic of Korea.
10-1 10-2
BER
References 10-3 10-4
SIR = -30dB with 10-fingers MRC PRAKE without SVD SIR = -20dB with 10-fingers MRC PRAKE without SVD
10-5
SIR = -30dB with 3-fingers MRC PRAKE using notch filter SIR = -20dB with 3-fingers MRC PRAKE using notch filter SIR = -30dB with 3-fingers MRC PRAKE using SVD
10-6 10-7
SIR = -20dB with 3-fingers MRC PRAKE using SVD AWGN Only
-4
-2
0
2
6 4 SNR in dB
8
10
12
Fig. 6. IEEE 802.11a interference suppression comparison between SVD method, notch filter and 10-fingers MRC PRAKE receiver in the CM3 channel model.
the 6-fingers MRC PRAKE receiver greatly when SIRin = −20 and −30 dB. As SIRin = −10 dB, a slight improvement (at a target BER of 10−5 , SNR improves less than 1dB) is obtained by using a 6-fingers MRC PRAKE receiver than the SVD-based method but at the cost of greater receiver complexity. Since the hardware complexity of the RAKE receiver depends on its finger number, using our method, the hardware complexity of the receiver can be decreased dramatically. Fig. 6 presents the performance in the CM3 channel model when we compare our method with the notch filter and the 10-fingers MRC PRAKE receiver. The notch filter is the same one as in Fig. 5 and the receiver is a 3-fingers MRC-PRAKE for our algorithm and the notch filter. As
[1] Boubaker N, Letaief KB. A low complexity MMSE-RAKE receiver in a realistic uwb channel and in the presence of NBI, IEEE WCNC 2003;233–7. [2] Li L, Milstein L. Rejection of narrow-band interference in PN spread spectrum systems using transversal filters. IEEE Trans Commun 1984;9:925–8. [3] Taha A, Chugg K. A theoretical study on the effects of interference on UWB multiple-access impulse radio, Asilomar conference on signals, systems, and computers, 2002, pp. 728–732. [4] Li Q, Rusch LA. Multiuser detection for DS-CDMA UWB in the home environment. IEEE J Select Area Commun 2002;9:1701–11. [5] Firoozbakhsh B, Pratt TG, Jayant N. Analysis of IEEE 802.11a interference on UWB systems. IEEE conference on ultra wideband systems and technologies, 2003. p. 473–7. [6] Xu SY, Bai ZQ, Yang QH, Kwak KS. Singular value decomposition-based algorithm for IEEE 802.11a interference suppression in DS-UWB systems. IEICE Trans Fundam 2006;7:1913–8. [7] Tufts DW, Kumaresan R, Kirsteins I. Singular value decomposition and improved frequency estimation using linear prediction. IEEE Trans Signal Process 1982;30(4): 671–5. [8] IEEE p802.15 working group for WPAN, channel modeling sub-committee report final. IEEE P802.15-02/368rSG3a, 2002. [9] Chu X, Murch RD. The effect of NBI on UWB time-hopping systems. IEEE Trans Wireless Commun 2004;3:1431–6.