Cyclic Autocorrelation based Blind OFDM Detection and ...

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IV to show the feasibility and advantages of the proposed method. Finally, we conclude the paper in Section V. II. CYCLOSTATIONARITY OF OFDM SIGNAL Cyclostationary random process has been studied since the 1980s. It is well known that the signal in wireless communications can be modeled as a cyclostationary random process instead of stationary one. It gives us another view to analyze the unique characteristics embedded in signals. The basic concept of cyclostationary random process is reviewed in this section and the characteristics in the CAF of OFDM signal is exploited and discussed as the preliminary of the proposed detection and identification method. A. Definition of CAF A process, for instance x(t), is said to be cyclostationary in the wide sense if its mean and autocorrelation are periodic with some period, say T [7]: ( ) ( ) m t+ T = m T (1) x x τ τ τ τ Rxt+ T + , t+ T − = Rxt+ , t− 2 2 2 2 where R ( t τ 2, t τ 2) x + − , the function of two independent variables t and , is periodic in t with period T for each value of ( τ 2, τ 2) Rxt+ t− is polyperiodic in t for each . The associated Fourier series for this function is τ τ R t t R e ( τ ) (2) α i2παt x + , − = x 2 2 { α} (3) for which { Rx } α are the Fourier coefficients, T 2 α 1 −i2παt x ( τ) x( , τ) T −T 2 R = R t e dt (4) and the sum over includes all integer multiples of the reciprocal of the fundamental period T. is the cycle frequency, which could be used to separate different signals. B. CAF of OFDM signal The CAF of baseband OFDM signal can be calculated as follows [6]: ( πN∆fτ) ( π∆τ) α A sin n Rx= e T sin f s ∞ πα ( ) τ −i2n−f N −1 i2π∆f τ 2 ( ) ( α ) ⋅ e G f G − f df −∞ Where G(f) is the Fourier transform of the rectangular pulse shape g(t). A is the variance of the symbol sequence. Ts = Tu + Tg is the symbol duration, where Tu = 1/f is the useful n (5) 978-1-4244-2108-4/08/$25.00 © 2008 IEEE symbol duration, Tg is the duration of the guard interval and f is the subcarrier spacing. The typical CAF magnitude of OFDM signal is shown in Fig. 2, in which is normalized to 1/Ts and is normalized to useful symbol duration. The signal exhibits discrete cyclic autocorrelation surfaces for the cycle 1 frequencies n = n/Ts, which peak at τ =± =± T where u ∆f sin ( πN∆fτ) the factor takes its maximum value. It is sin ( π∆fτ) clear that is selected as the integer number of 1/Ts, and when τ =± T , the CAF values exhibit peak properties. As the u value increases the peak decreases. If the value of Ts and Tu is known in the detector, we are able to design the detection process to catch the peaks exhibited in the CAF functions. However, in blind detection and identification, the parameters of received signal is unknown by the detector of cognitive radio. It means the values of at which CAF exhibit peaks are unable to obtain a priori. Figure 1. CAF with step between equals integer number of 1/Ts Figure 2. CAF with step between equals fraction number (1/20) of 1/Ts
In order to detect all possible OFDM signals, a step size of that is smaller than subcarrier spacing should be selected to calculate the CAF of received signal as shown in Fig. 3. Thus, we can observe the changes in the CAF of OFDM signal in details, as illustrated at u T τ =± , the pattern of which is better for us to understand the characteristic of CAF of OFDM signal. It is clear that the peak values decrease when takes the integer number of 1/Tu. However, there are other smaller peaks between them. Since the information of Tu is unknown, the detector has to check the CAF with a step size that is smaller than the subcarrier spacing. Figure 3. CAF when =Tu with step size between equals fraction number (1/20) of 1/Ts III. BLIND DETECTION AND IDENTIFICATION OF OFDM SIGNAL OFDM has been selected for most of the future wireless communication standards. For various operation environments and applications, different values of parameters are selected to implement the system with the purpose of achieving optimum capacity. These parameters include number of subcarriers, subcarrier spacing, the length of guard interval, etc. Even in the same standard, there are several operation options in which the parameters are setup differently to achieve various transmission data rates. Thus, when detecting the incoming signal, it is impossible to select the detection criteria based on the known OFDM parameters as in [6]. Therefore, in order to fit into the practical application, the parameters of OFDM signal should be treated as unknown factors at the detector. In this paper, we propose a blind detection and identification method for cognitive radio, which consists of two steps: the simple but reliable peak detection method that calculates the subcarrier spacing in the first step and a peak searching method employed to determine the length of guard interval in the second step. We assume that the observation time is longer than one OFDM symbol and the step size between each is selected as the fractional value of subcarrier spacing such as 1/20, 1/10. A. OFDM Signal Detection The blind detection of OFDM signal could be considered as a binary hypotheses test: 1 () = () () = () + () H 0 : r t w t signal absent H : r t s t w t signal present where r(t) is the received signal, s(t) and w(t) represent the OFDM signal and noise respectively. As described previously, the peaks in the CAF of OFDM signal are mainly due to the cyclic prefix in OFDM symbol. This feature is employed as the main criterion to separate OFDM signal from noise. In the first step of the proposed scheme, we employ the simple peak detection method that detects the symmetric peaks when = 0, as demonstrated in Fig. 4. Based on the characteristic of OFDM symbol with cyclic prefix, we consider that the time period between the major peaks should be equal to Tu, the effective symbol duration. Figure 4. CAF when =0 as a function of In order to catch these symmetric peaks, we formulate the amplitude of CAF with equal to 0 as the test statistic, which is expressed as follows: Z = R 1 0 r ( τ ) 2 ( πN∆fτ) ( π∆τ) A sin = ⋅ − T sin f s ( ) sin ( N∆f ) T sin ( π∆fτ) 978-1-4244-2108-4/08/$25.00 © 2008 IEEE N −1 i2π∆f τ 2 e ∞ i2π fτ e G( f ) G( −∞ f ) df δ τ π τ = A + N0 s From the theoretical analysis, Z1 takes the largest peak when = 0 and two other peaks when u T τ =± , which agrees with our expectation. Since the subcarrier spacing is determined, it could be used for signal identification. 2 2 (6)
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