Blind MC-DS-CDMA parameters estimation in frequency selective channels
C. Nsiala Nzéza, M. Berbineau and G. Moniak
Université Lille Nord de France FR59000, Lille, France
INRETS/LEOST 20 Rue Elisée Reclus 59666, Villeneuve D’Ascq, France
[email protected] http://www.inrets.fr
R. Gautier and G. Burel
Université Européenne de Bretagne, France Université de Brest
CNRS, UMR 3192 Lab-STICC ISSTB 6 Avenue Le Gorgeu CS 93837
29238 Brest Cedex 3, France [email protected]
http://www.lab-sticc.fr
I. Dayoub
Université Lille Nord de France FR59000, Lille, France Université de Valenciennes
et du Hainaut-Cambrésis
IEMN-UMRS CNRS 8520, UVHC-DOAE 59313 Valenciennes Cedex 9, France [email protected]
http://www.univ-valenciennes.fr
Abstract—An apportunistic or cognitive radio system needs accurate knowledge of the radio spectrum it operates. The concept of cognitive radio is also exploited in the railway context in order to satisfy high availability and interoperability of wireless telecommunication systems everywhere as required by operational or safety applications deployed by the railway operator. It allows for example dynamic spectrum allocation versus QoS (Quality of service) or traffic requirements and very often spectrum reuse especially in rural areas. Blind multi-carrier transmission recognition methods based on the discrimination between single-carrier and multi-carrier modulations to estimate their parameters have been addressed in the literature. Some powerful techniques use autocorrelation and cyclic autocorre- lation based features of the transmitted signal. In this paper, we propose a blind parameter estimation based on analysis of fluctuations of autocorrelation estimators which was initially employed in CMDA signals interception. The proposed technique leads to a fast efficient parameters estimation and is insensitive to receiver phase and frequency offsets as it is highlighted in simulation results.
Index Terms—Blind detection, multi-carrier spread spectrum signal, correlation methods.
I. INTRODUCTION
The OFDM (Orthogonal Frequency Division Multiplexing) has received widespread interest for wireless broadband mul- timedia applications over the last decade and more recently in the railway context [1]. The main advantages of this technique are its robustness in the case of frequency selective fading channels, its capability of portable and mobile reception and its flexibility.
Spread Spectrum has been successfully used by the military services for decades and nowadays takes a significant role in cellular and personal communications. Advantages of spread spectrum techniques are widely known: immunity against multi-path distortion and jamming, low transmitted power, no need for complex frequency planning when using Code Division Multiple Access (CDMA) properties [2], [3].
The advantages and success of multi-carrier modulation and spread spectrum technique motivated many researchers to investigate the suitable combination of both techniques,
known as Multi-Carrier Spread Spectrum (MC-SS) which benefits from the main advantages of both schemes [4]. Among all combinations of both techniques, the so called Multi- carrier Direct Spread Spectrum CDMA (MC-DS-CDMA) is considered throughout this paper, for its blind parameters estimation. These parameters include, for example, symbol and OFDM symbol periods, the cyclic prefix or the zero paddind duration and the bandwidth.
Many blind approaches have been designed to either im- prove the performance of a CDMA receiver in a multirate multiuser context or to reduce its complexity. Some prior knowledge of user parameters, e.g. the signature waveform [5], the processing gain, the code of a group of active users [6], the chip rate [7], [8] is always assumed, but its nature depends on the technique employed.
Moreover, several approaches have been addressed in the literature to discriminate between single-carrier and multi- carrier modulations and to estimate their parameters. Unfortu- nately, most of them use a threshold between statistics given by single-carrier and multi-carrier modulation propagating through an ideal channel.
Furthermore, several blind procedures have been proposed using autocorrelation and cyclic autocorrelation based features to extract parameters for OFDM signals using a Cyclic Prefix time guard interval (CP-OFDM) and propagating through a frequency selective channel, and several of them have also been proposed for OFDM signals using a Zero Padding time guard interval (ZP-OFDM) based on power autocorrelation feature. Nevertheless, all of them exhibit an excessive com- putational cost due to an exhaustive optimization problem [9].
In this paper, we consequently extend the fast and efficient blind detection scheme based on the analysis of estimators of autocorrelation fluctuations previously successfully applied to DS-CDMA transmission [10], [11] to the case MC-DS-CDMA systems. We further demonstrate its efficiency in a frequency selective fading channel since it is insensitive to phase and frequency offsets.
The paper is organized as follows: section II presents the
D E M U X
M U X
Spreading Block IFFT Block
or Padding
Zero
Cyclic Prefix
Channel Multipath a(q)T
y(t) η(t) c= [c0,· · ·, cL−1]T
e(2jπf0t) e(2jπf1t) e(2jπf2t)
e(2jπfM−1t)
Figure 1. MC-DS-CDMA modulator scheme.
MC-DS-CDMA signal model and assumptions made. Section III deals with the proposed approach while numerical results are given in section IV. Finally, section V summarizes the results and set up the conclusions.
II. SIGNAL MODELING AND ASSUMPTIONS
The MC-DS-CDMA system considered in this paper is shown in Fig.1.M is the total number of subcarriers andTsthe symbol period before demultiplexing. Theqthcomplex symbol am(q)transmitted over themthsubcarrier,m= 0,· · · , M−1 (i.e., the symbol at the moment qTs of the transmitted sig- nal s(t)) is highlighted by the subscript m. The vector c stands for the spreading sequence of length L, defined by c= [c(0),· · · , c(L−1)]wherec(ℓ)stands for theℓthsequence chip.
In this system, each am(q)is first multiplied by the whole spreading code c, and the result is then multiplied by each corresponding, as illustrated on Fig.1.
In this configuration, complex symbols am(q) belong to the vectorsaT(q) = [a0(q),· · ·, aM−1(q)]. Therefore, vectors a belong to the matrix A which M rows contain symbols transmitted over each subcarrier at each moment q, i.e., A = [aT(0),· · ·,aT(q),· · ·]. Thus, the required bandwidth (main lobe) is equal to W = (MM T+1)L
s = M+1M T
c, Tc = TLs standing for the chip duration. This allows to guaranty the orthogonality between subcarriers.
We also assume that the multipath channel over each subcarrier is an i.i.d Rayleigh flat fading channel, which fading amplitudes βp have an unitary second-order moment. Then, the complex channel-corrupted received signal over the mth subcarrier set to as ym(t), is then
ym(t) =ψ(t) +ηm(t) ψ(t) =
+∞X
q=−∞
P−1X
p=0
βpa(q)h(t−qTs−Tp)ej2πfmt+ǫm (1) where fm = f0 + M TmL
s = f0 + M Tm
c, Tp represents the pth path transmission delay,ǫm stands for the receiver phase offset, ηm(t)stands for the additive Gaussian noise (AWGN) over the mth subcarrier, and assumed to be independent and uncorrelated with the signal. Accordingly:
• aT(q)are the baseband symbols of varianceσa2assumed to be independent.
• g(t) =PP−1
p=0 βpPL−1
ℓ=0 c(ℓ)h(t−ℓTc−qTs−Tp)stands for the global filter and represents the convolution prod- uct between transmitter, spreading sequence waveform, multipath channel and receiver filters.
• P represents the number of path, and Ts ≥ max(Tp) and to remain constant during the observation.
• η(t) = [η0,· · ·, ηM−1]T is a centered additive white Gaussian noise (AWGN) which components are of equal varianceσ2ηm.
• s(t)is assumed to be independent, centered, noise-free and received with powerσ2s, and the signal-to-noise ratio (SNR) in dB at the detector input is negative (signal hidden in the noise).
Furthermore, let us set to as Tcp the cyclic prefix (CP) duration:Tcp= ∆TsTs, i.e., the CP is a fraction of the symbol period such that0≤∆Ts<1. In order to avoid Inter Symbols Interferences (ISI),Tcpshould satisfyTcp< Ts, and especially must be greater than the longest channel delay.
In this case, the global filter g(t), is composed of the initial filter h(t) samples followed by its first Tcp ones, and is therefore defined during Tu = Ts+Tcp = (1 + ∆Ts)Ts. From this discussion, and over themthsubcarrier, (1) can be rewritten by taking into account the CP duration as follows.
ym(t) =ψcp(t) +ηm(t) ψcp(t)=
+∞X
q=−∞
P−1X
p=0
βpa(q)g(t−qTu−Tp)ej2πfmt+ǫm (2) The CP/MC-DS-CDMA case will be considered through the remainder of the paper. Whenever the particular case of a transmission without the CP will be studied or that of ZP (i.e, zero padding time guard interval), that will explicitly be mentioned. At last, the case of MC-CDMA or that of both CP-OFDM and ZP-OFDM can be easily derived from (1) and (2). Taking into account all subcarriers, the channel-corrupted received signal which will be study in the sequel is given by
y(t) =
MX−1 m=0
ym(t) +η(t) (3) III. PROPOSED APPROACH
As recalled in the introduction, some previous methods exploit autocorrelation or cyclic autocorrelation properties to recover CP-OFDM signals parameters [12], [13]. Some
others define the power autocorrelation feature to estimate ZP- OFDM parameters. Indeed, ZP-OFDM signals differ from CP- OFDM in the fact that zeros are appended at the end of each OFDM symbol (instead of a CP for the next symbol). Thus, ZP-OFDM signals exhibit neither autocorrelation nor cyclic autocorrelation properties [9].
Unfortunately, these methods can exhibit a prohibitive computational cost since they are based on an optimization problem with an exhaustive search. Thus, we derive the improved blind scheme [10], [11] to the case of MC-DS- CDMA transmission through a frequency selective channel which leads to a low computational cost, as shwon in Table I. Furthermore, combined with the blind source separation approach described in [14], the proposed scheme can be easily extended to the case of MIMO-MC-CDMA transmissions.
Successive investigations of the contributions of noise and channel-corrupted signal through the analysis of the second- order moment of the autocorrelation estimator allowed its description, as hereinafter shortly reported. The received channel-corrupted signal y(t)is first divided intoK temporal windows, each of them of duration TF. Then, within each window k, an estimation of its autocorrelation, set as Rbk is computed as
Rbk(τ) = 1 TF
Z TF
0
yk(t)(yk)∗(t−τ)dt (4) whereyk(t)stands for signal samples over thekthwindow.
Equation (4) is the starting point of the proposed scheme.
Indeed, it is computed from three independent IFFT by win- dows; therefore, no specific condition is need on windows duration choice. Then, according to available computation power, it allows to implement a low complexity algorithm withO(K·(3·NF F T·log2(NF F T)))operations, whereNF F T
stands for the FFT length. Hence, the second-order moment of the estimated autocorrelation R(τb )using K windows can be expressed as
Φ(τ) =Ebn
|R(τb )|2o
= 1 K
K−1X
k=0
|Rbk(τ)|2 (5) whereE(·)b is the estimated expectation of(·). Hence,Φ(τ) is a measure of the fluctuations of R(τ). It is composed ofb fluctuationsΦs(τ)andΦη(τ)due to channel-corrupted noise- free signals and the noise, respectively. Indeed, applying (4) to (2) with the assumption of independent and centered symbols, leads to
R(τ) =b Rbss(τ) +Rbηη(τ) (6) where Rbss(τ) and Rbηη(τ) are respectively, the estimate of the global noise-free channel-corrupted signal and the noise autocorrelation fluctuations. Since fluctuations are computed from many randomly-selected windows, they do not depend on delays Tp. Multipath channel coefficients are taken into account in the received signal power, as it will be shown in the sequel. Equation (5) shows that fluctuations dot not depend on subcarriers frequencies either, since it is the modulus square
of the autocorrelation function which is computed. Moreover, the variance of (4) is given by
varn
|R(τ)|b o
= Φ(τ)− Ebn
|R(τ)|b o2
(7) Using assumptions made in section II about symbols and additive noise, we get
Ebn
|Rbss(τ)|o
=Ebn
|Rbηη(τ)|o
= 0 (8)
Then, from (6), (7) and (8) we have Ebn
|R(τb )|o2
≤ Ebn
|Rbss(τ)|o2
| {z }
=0
+ Ebn
|Rbηη(τ)|o2
| {z }
=0 (9)
Since Ebn
|R(τb )|o2
≥ 0 ⇒ Ebn
|R(τb )|o2
= 0, and consequently (7) becomes
varn
|R(τ)|b o
= Φ(τ) (10)
which proves that Φ(τ) is a measure of fluctuations of the intercepted signal. In the sequel, we successively investigate both channel-corrupted signal and noise contributions through the analysis of the second-order moment of the autocorrelation estimatorΦ(τ). One of the interests features of our proposed scheme is its insensitivity to phase and frequency offsets. This is a direct consequence of (5) where only the square of the estimate of the correlation matrix is calculated.
A. Analysis of the noise contribution to fluctuationsΦ(τ) Only fluctuations due to the noise are uniformly distributed over all values ofτ[10], [11]. Assuming a receiver filter with a flat frequency response in[−BW/2, +BW/2](BW > W in practice) and zero outside. Since the global fluctuations are computed from many randomly-selected windows, noise fluctuations can be characterized by their mean MΦη and standard deviationσΦη as described hereinafter.
Without loss of generality, assuming σ2ηm = σ2η, ∀m = 0,· · ·, M −1, leads to the global standard deviation taking into account all subcarriers, referred to as ση2=σ2eη =M σ2eη. Therefore, we get
MΦη= (σ
2 η)2 W TF =M
2σ4η
W TF (a)
σΦη=q
2
KMΦη=q
2 K
M2ση4 W TF (b)
(11)
Expression (11) shows that the noise contribution to the global fluctuations is amplified by the number of subcarriers.
Moreover, it also evidences that its contribution can be lowered by setting the number of analysis windowsKasK≥2M4or by increasing anlysis windows durationTF, which constitutes a compromise to be made according to the computing power available.
B. Analysis of the channel-corrupted signal contribution Focussing only on the signal allows to show that, on average, high amplitudes of the fluctuations Φ(τ) occur for τ multiple of Ts and lower ones occur at multiple of Tcp. Let us also set to as McpΦ their mean value at multiple of Tu. Since symbols are assumed independent and centered,i.e., Ebn
Rbss(Tu)o
= 0. Therefore, we get McpΦ =Ebn
|Rbss(Tu)|2o
= σ2a
TF
2 +∞X
q=−∞
Z TF
0
|g(t−qTu)|2dt
!2 (12)
Then, assuming g(t)a rectangular function, i.e., g(t) = Π
t−12Tu
Tu
=
(1, 0≤t < Tu
0, otherwhise it is obvious to prove that
(RTF
0 g(t)g(t)∗dt= 0 RTF
0 |g(t)|2dt=Tu=Ts+Tcp= (1 + ∆Ts)Ts
(13) Using (12) and (13), and after some simplications, we get
McpΦ = (1 + ∆Ts)Ts
TF
σs4 (14)
whereσ2s=σa2σg2¯, andσ2¯g is given by σ2¯g= 1
Tu
Z Tu
0
|¯g(t)|2dt
=
P−1X
p=0
|βp|2 1 Tu
Z Tu
0
L−1X
ℓ=0
|c(ℓ)g(t−ℓTc)|2
! dt
=
P−1X
p=0
|βp|2Tu
Tc
(15)
From (11), the standard deviationσΦcpof fluctuations due to the noise-free channel-corrupted is deduced as
σΦcp= r2
KMcpΦ = r2
K σ4s TF
(1 + ∆Ts)Ts (16) Equation (16) evidences that any increase in the number K of analysis windows allows to lower fluctuations standard deviation, while (14) shows that the average fluctuations am- plitude is composed of a superposition of fluctuations peaks, which level is tied to the received power at multiple of both symbol period and CP duration.
Expression (14) also proves an increase in the average fluctuations amplitude concomitant with that of the sequence length. It ensues that, at constant transmit power, the lower the transmit data rate is, the higher fluctuations average amplitude is at multiple of the symbol period, while fluctuations average amplitude at multiple of the CP duration remains very low compared to that appearing at multiple of the symbol period.
Thus, the fluctuations curve highlights high equispaced peaks which average spacing corresponds to the estimated
symbol period, and also very low equispaced peaks which average spacing with the high fluctuations peaks at multiple of symbol period in their vicity corresponds to an estimation of the CP duration.
Nervertheless, in practice and according to analysis win- dows duration, i.e., their duration compared to the symbol one, two low fluctuations average amplitude at multiple of the CP duration can appear at the vicinity of high fluctuations average amplitude at multiple of symbol period, each of them at each side.
At last, the ZP-OFDM case can be easily deduced from (14) and (16) by settingg(t)to as
g(t) = Π
t−12Tu
Tu
=
(1, 0≤t < Ts
0, otherwhise
Then, the corresponding fluctuations curve highlights high equispaced amplitude peaks, which average spacing allows the symbol period determination.
C. Bandwidth and subcarriers number estimation
At this point, estimates of both Ts and Tcp are available.
Then, we compute the normalized PSD (i.e., with zero fre- quency at center of the bandwidth) of the intercepted signal, referred hereinafter to as Y, from which we get the set of frequencies, notedF. Then, we compute the PSD cumulative sum, set to as: Ye of size NF F T. Therefore, successive steps described below allow parameters estimation.
First, the central frequency f0, defined asf0=F(nopt) is obtained by solving the following optimization problem:
nopt= argmin
1≤n≤NF F T
n eY−Ye(NF F T)/2o
(17) Second, we compute the signal energy set to as EYe = e
Y+(Nw, nopt)−Ye−(−Nw, nopt), whereNw=min(NF F T− nopt + 1, nopt) is the set of frequencies containing 95%
of signal energy, vector Ye+(Nw, nopt) and Ye−(−Nw, nopt) contain values ofYe from indicesnopt tonopt+Nw+ 1 and from indices nopt−Nw+ 1 tonopt, respectively. Then, the bandwidth defined asW =F(nopt+n′opt)−F(nopt−n′opt) is estimated by solving the following optimization problem:
n′opt= argmin
1≤n′≤NF F T
{EYe>0.95·Y(Ne F F T)} (18) Hence, the number of subcarriers used can be approximated as:M =⌊W·Tu⌋, where⌊∗⌋stands for the immediately lower integer operator. At last, the total computational cost of our proposed algorithm is very low compared to one adressed in [9] as illustrated in Table I.
IV. NUMERICAL RESULTS
Simulations have been carried out considering a QPSK- DS-CDMA modulation, and following parameters were set:
L=127(Complex GOLDsequence),Fc=150M Hz, the sam- pling period,Fe=300M Hz, the window durationTF=2µs, and the number of windows,K= 300; then each data stream contains N = TF/Te samples. N can not be defined as
Table I
TOTAL COMPUTATIONAL COST COMPARISON.
Methodes Proposed approach Proposed algorithm in [9]
Computational cost O`4·K·NF F T ·log2(NF F T) +N3+N´ O`
K·NF F T·log2(NF F T) +N3(N−2)!´
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0 5 10 15 20 25 30 35 40 45 50
Times (in µs)
Fuctuations amplitude
Fluctuations Φ(tau) Noise theoretical mean Noise theoretical maximum
Figure 2. Fluctuations of correlation estimators with CP, SNR = -5 dB.
−1000 −80 −60 −40 −20 0 20 40 60 80 100
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Frequency (in MHz)
Normalized and centerred signal estimated PSD
Figure 3. Bandwidth estimation, SNR = -5 dB.
N =TF/Tc, sinceT c is still unknown at this point.M = 64 subcarriers with 16 ones allocated for the CP or ZP, and the signal duration is equal to 436 µs. The channel model used is the COST207RAx6 [15]. The performance in terms of probability of detection was studied for different SNR at the receiver input. From (11)(b) and (14), the SNR is defined as:
SN R=McpΦ σ2Φη and the detection threshold was set to as
ζ=MΦη+ 3·σΦη
Hence, the probability of detectionPd, i.e., the probability for the fluctuations average amplitude to be above the threshold ζ is defined as
Pd=P(McpΦ > ζ) (19)
0 1 2 3 4 5 6 7 8 9
0 10 20 30 40 50 60 70
Times (in µs)
Fluctuations amplitude
Fluctuations Φ(τ) Noise theoretical mean Noise theoretical maximum
Figure 4. Fluctuations of correlation estimators, without CP or with ZP, SNR
= -5 dB.
−250 −20 −15 −10 −5 0 5 10
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
SNR (in dB)
Probability of detection
with K=10 windows with K=300 windows with K=1000 windows
Figure 5. Probability of detection for different SNRs as a function of the number of analysis windows.
Fig. 2 illustrates the detector output, which is in accordance with theoretical developments. Using the average spacing between high amplitude peaks and low amplitude ones re- spectivly, we get Tes = 0.51 µs and Tecp = 0.1275 µs, thus Teu= 0.6375µs.
Fig. 3 shows the centered spectrum bandwith estimated, from which we deduce W=100 M Hz; therefore, M=63, which is very close to the real number of subcarriers.
Fig. 4 highlights the case of transmission without CP or with ZP, obtained using the same parameters as in Fig. 2.
As expected, it shows high amplitude equispaced fluctuations peaks, which average spacing gives the estimate of the symbol periodTes= 0.51µs. As suggested in [9],Tzpcan be estimated
using the following expression Teu=Tes+Tezp= N
nopt
(20) where nopt = 942 is obtained when estimating the corre- spoding spectrum like done in Fig. 3. Then, from (20), we deduce Tezp= 0.1275µs.
Finally, the proposed scheme is able to detect signals even at very low SNR, as illustrated in Fig. 5. Moreover, it also shows that, the probability of detection can be strongly improved by increasing the number of analysis windows. Nevertheless, the computation cost can be very prohibitive. Therefore, a com- promise must be made between both expected performance and computational cost given in Table I.
V. CONCLUSION
We proposed a blind detection method aimed at MC-DS- CDMA transmission parameters estimation. The described scheme leads to an efficient estimation of symbols duration, cyclic prefix or zero padding duration, and it is insensitive to phase and frequency offsets and also to multipath. Simula- tions results given for different scenarios confirm theoretical developments. Moreover, this method can be used in several applications such that spectrum monitoring, dynamic spec- trum management, power control strategies (detect and avoid) through the assessment of transmission parameters.
ACKNOWLEDGMENT
The work was performed within the CISIT project supported by the Region Nord France and FEDER within the ANR- PREDIT MOCAMIMODYN project.
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