Sidelobe Reduction in Non-contiguous Ofdm-based Cognitive Radio Systems Using a Generalized Sidelobe Canceller

In orthogonal frequency division multiplexing (OFDM), sidelobes of the modulated subcarriers cause high out-of-band (OOB) radiation, resulting in interference to licensed and unlicensed users in a cognitive radio system environment. In this work, we present a novel technique based on a generalized sidelobe canceller (GSC) for the reduction of sidelobes. The upper branch of the GSC consists of a weight vector designed by multiple constraints to preserve the desired portion of the input signal. The lower branch has a blocking matrix that blocks the desired portion and preserves the undesired portion (the sidelobes) of the input signal, followed by an adaptive weight vector. The adaptive weight vector adjusts the amplitudes of the undesired portion (the sidelobes) so that when the signal from the lower branch is subtracted from the signal from the upper branch, it results in cancellation of the sidelobes of the input signal. The effectiveness and strength of the proposed technique are verified through extensive simulations. The proposed technique produces competitive results in terms of sidelobe reduction as compared to existing techniques.


Introduction
The rapid growth in wireless communication methods and devices is a major reason for spectrum scarcity.Cognitive radio (CR) is an encouraging solution to tackle such a problem and has received special attention in the research community.CR has the ability to dynamically permit secondary users (SU) to operate in those spectral domains that are not being used by the primary users (PU) at certain times and localities (interweave mode) [1][2][3].Efficient techniques are needed at the transmitter side to control the shapes of the transmitted signal so that both SU and PU can share the same spectrum resources with minimum interference.
Orthogonal frequency division multiplexing (OFDM) is the best candidate for the CR [4][5][6], with the ability to divide the available wideband channel into multiple narrow band orthogonal channels/subcarriers and to transmit those subcarriers in parallel.Some attributes of OFDM include spectral efficiency, multipath delay spread, robustness to channel fading, etc.On the other hand, due to the large sidelobes of the OFDM subcarriers, CR based on OFDM experiences high out-of-band (OOB) radiation that may result in considerable interference with the adjacent bands used by either PU or SU.To tackle the OOB radiation problem, various techniques are proposed in the literature that can be categorized into two groups: time domain techniques and frequency domain techniques.Time domain techniques include filtering [7], which suffers from high complexity and lack of guard interval, and windowing [8,9], which expands the signal in time domain and results in intersymbol interference (ISI).Frequency domain techniques include adaptive symbol transition (AST) [10], which expands the signal by injecting additional samples within a specified power threshold between two transmission blocks to reduce the interference of these two blocks at definite frequencies, active interference cancellation (AIC) [11][12][13], where a few subcarriers lying at the border of the licensed user band are reserved for reducing the interference.These subcarriers, called cancellation subcarriers, are not used for data transmission, but to cancel the interference in a specific frequency range.In Cancellation carriers (CC) [14][15][16] method the authors propose the same technique as in AIC, but consider limiting the power to cancellation subcarriers.In both cases, finding the optimal complex values for cancellation carriers is a least squares (LS) optimization problem.In [17] the weights of cancellation carriers are calculated using Genetic Algorithm (GA) and Differential Evolution (DE).In [18] Selim, A., et al. propose a heuristic algorithm for calculating the weighting factors for the CCs with few computations.Active and null cancellation carriers (ANCC) [19] technique combine active and null cancellation carriers in the guard band.Subcarrier weighting (SW) [20] technique suppresses the sidelobes by weighting all the subcarriers with an optimal set of real-valued coefficients, advance subcarrier weightings (ASW) [21], in which Selim, A. and Doyle, L. propose a heuristic approach for sidelobe suppression for OFDM systems using subcarrier weighting, multiple choice sequence (MCS) [22], where the sequence of symbols carried by subcarriers is mapped to an optimal sequence that yields lower sidelobe interference, Constellation expansion (CE) [23][24][25] transmits symbols from a higher order constellation set and chooses the sequence that results in the lowest possible sidelobe power level, Insertion of guard bands [26,27] where the interference is alleviated by adaptively deactivating the nearby subcarriers, providing flexible guard bands between licensed and un-licensed users and spectral precoding schemes [28][29][30][31][32] to reduce the interference by designing special precoder matrices, etc.
In this paper, we propose a novel technique for the reduction of OOB radiation in OFDM-based CR by using a generalized sidelobe canceller (GSC) at the transmitter of OFDM.It has been observed that so far in OFDM-based CR system, a GSC has not been used to tackle the OOB radiation problem.In the proposed technique, the signal is passed through two branches of a GSC.The upper branch consists of the weight vector designed by multiple constraints to preserve the desired portion of the signal, while the lower branch consists of a blocking matrix followed by a weight vector.The blocking matrix blocks the desired portion and preserves the undesired portions (sidelobes).The weight vector adjusts the undesired portion (sidelobes) in such a way that when subtracted from the signal of the upper branch, it results in significant cancellation of the sidelobes of the OFDM signal.We have compared the performance of the proposed technique with already existing techniques via simulations.The proposed technique achieves better suppression of the sidelobes as compared to the existing methods.
The remaining paper is arranged as follows: Section 2 contains the data model and Section 3 gives the proposed methodology.In Section 4, simulation results are carried out, while Section 5 concludes and gives future work recommendations.

Data Model
A general illustration of the non-contiguous orthogonal frequency division multiplexing (NCOFDM) transmitter that utilizes the proposed method is shown in Figure 1. .These modulated symbols are then divided into N parallel streams using serial to parallel (S/P) converter.An NCOFDM system has the ability to activate only those subcarriers that are located in vacant spectral bands detected by spectrum sensing techniques.These active subcarriers go through the inverse Fourier transform block following parallel to serial (P/S) converter.The cyclic prefix of length Np is added to mitigate the impact of inter-symbol interference (ISI).The discrete time baseband transmitted NCOFDM signal that is to be transmitted in the time domain can be represented as [33][34][35]: The spectral shape of the individual subcarrier is obtained by Fourier transform of the time domain rectangular window, which is equal to the sinc function.The spectrum u (f) of the k th subcarrier is a sinc pulse modulated with data symbol sk and is shifted to the respected subcarrier frequency fk [6].
where f denotes the frequency, fk is the center frequency of the k th subcarrier, To is the NCOFDM symbol duration, and (f -fk) denotes the normalized center frequency of the k th subcarrier.The spectrum of the transmitted NCOFDM signal is then the summation of the spectrum of all the active subcarriers, given by The signal given in Equation ( 3) has large sidelobes, which results in high OOB radiation, as shown in Figure 2 [14].
The main focus of this paper is to preserve the portion of NCOFDM signal from frequencies f1 to fN and to suppress the sidelobe, i.e., the remaining portion of the NCOFDM signal.

Proposed Methodology
In this section, we propose a novel technique by using GSC at the transmitter of NCOFDM.GSC is the simplest version of linearly constrained minimum variance (LCMV), where the constrained optimization problem is converted into an unconstrained problem [36][37][38].The block diagram of GSC is shown in Figure 3, having two branches, the upper branch and the lower branch.The upper branch is the main channel of the GSC, usually called a Fixed Beamformer (FBF).It consists of quiescent weight vector wq, which preserves the signal coming from SU, i.e., the NCOFDM signal, and provides the necessary gain to the desired portion, i.e., the region from f1 to fN satisfying the constraint, as shown in Figure 2. The lower branch consists of the blocking matrix B followed by an adaptive weight vector wa.The blocking matrix B blocks the desired portion of the signal and preserves the sidelobes of NCOFDM signal, as shown by region f < f1 and f > fN in Figure 2. The adaptive weight vector wa adjusts the amplitudes of the sidelobes.The sidelobes that are preserved and adjusted in the lower branch are then subtracted from the signal of the upper branch, resulting in the signal of NCOFDM having suppressed or zero sidelobes.LCMV determines the optimal weight vector H w that minimizes the output power having multiple linear constraints.The optimization problem for LCMV is given by: On solving Equation ( 5), we obtain: where σ is the variance, while C is the constraint matrix with dimension M × N, having N steering vectors given by Equation ( 7): where N represents the total number of frequencies in the desired portion of the signal, as shown in Figure 2; ] where o P can also be written as = − P I P (12) where I is an identity matrix with dimension M × M.
The first component of Equation ( 9) represents the upper portion of GSC, which on solving becomes ] where H q w is the quiescent weight vector having dimension 1 × M.
The second component of Equation ( 9) represents the lower portion of the GSC.On substituting the values for H o w and o P , Equation ( 9) becomes As Equation ( 15) is not particularly useful for implementation, it is divided into two parts.The first part consists of blocking matrix B, and the second part consists of an adaptive weight vector H a w with dimension 1 × (M − N).
The blocking matrix B can be constructed by first finding the Po as given in Equation ( 12), then orthonormalizing Po and choosing the first (M − N) columns of the orthonormalized matrix that will be the resulting blocking matrix B, having the property given by The output of the GSC as shown in Figure 3 after replacing H o w with ( ) H q a − w Bw will become: the output power of which is given by: ( ) ( ) Solving Equation ( 18), we get the adaptive weight vector ( ) a opt w , given by the following equation: ( )

Simulations and Results
In this section both the accuracy and the reliability of the proposed technique are discussed for the reduction of sidelobe suppression of the OFDM signal.The performance comparison of the proposed technique has been done in terms of normalized power spectral density (PSD) with already existing techniques in this area.Several cases have been discussed on the basis of spectral white spaces and its bandwidth between spectral white spaces.Throughout the simulations, the number of samples M is taken as 501, while the number of frequencies N in Case I is taken as 16, in Cases II and IV as 32, while in Case III and Case V, it is taken as 16, 32, 64, and 128, respectively.

Case I
In this case, we are considering a spectral white space that is not used by the PU and is available for the SU.The total number of OFDM subcarriers used by SU is 16 modulated with BPSK, whose power is normalized to |dn| 2 = 1.The performance of the proposed technique is compared with different existing techniques, including CC [14], CC using GA and DE [17], ACC [18], and ASW [21].In CC techniques, two CCs have been used either side of the data subcarriers, whereas in SW techniques all subcarriers are used for weighting.Figures 4 and 5 show the comparison of the proposed technique with the existing techniques in terms of PSD.It can be observed from Figures 4 and 5 that the existing techniques give a maximum of 36 dB improvement, while the proposed technique gives 92 dB improvement compared with the original OFDM spectrum.The proposed technique gives 58 dB improvement compared with the spectrum of OFDM using existing techniques.The comparison of the proposed technique with the existing ones is also given in Table 1, which shows the effectiveness of the proposed technique.

Case II
In this case, we are considering nine sub-bands mentioned as regions in Figures 6 and 7. We assume that regions I, III, V, VII, and IX are occupied by PUs, while regions II, IV, VI, and VIII are occupied by SUs.Each SU has an equal number of subcarriers, i.e., 32 OFDM subcarriers modulated with BPSK, whose power is normalized to |dn| 2 = 1.The bandwidth allocated to each PU is considered equal in all regions.The comparison of the proposed technique is done with already existing techniques including CC [14], CC using GA and DE [17], ACC [18], and ASW [21].In CC techniques, two CCs have been used on either side of data subcarriers, while in the SW technique all subcarriers are taken into consideration.Figures 6 and 7 show the superiority of the proposed technique in terms of PSD, even in a spectrum-sharing scenario.The proposed technique performs well: it outclasses all these techniques and gets significant suppression in all regions.The comparison of suppression of the sidelobe power level achieved in a spectrum-sharing scenario using the existing technique and our proposed technique are given in Table 2, which also shows the performance of our proposed technique in all regions of PU.

Case III
In this case, we are considering the spectrum-sharing scenario consisting of a total of nine sub-bands mentioned as regions in Figures 8 and 9.We assume that regions I, III, V, VII, and IX are used by PUs, while regions II, IV, VI, and VIII are used by SUs.An equal bandwidth is allocated to each PU, whereas it is unequal in the case of SU.The SU operating in region II has 16 subcarriers, region IV has 32, region VI has 64, and SU, operating in region VIII, has 128 subcarriers, modulated with BPSK, whose power is normalized to |dn| 2 = 1.The performance of the proposed technique is compared with different existing techniques including CC [14], CC using GA and DE [17], ACC [18], and ASW [21].In CC techniques, two CCs have been taken on either side of the data subcarriers, and in SW techniques all subcarriers are used for suppression.Figures 8 and 9 show that the proposed technique outclasses all these techniques and gives a significant suppression in all regions of the spectrum-sharing scenario.The performance comparison of reduction of OOB radiation in all PU regions between the existing and the proposed technique is given in Table 3.It clearly shows that the proposed technique gives significant reduction in sidelobes at all regions of PU and performs better than the rest.

Case IV
In this case, we are considering the spectrum-sharing scenario shown in Figures 10 and 11, consisting of nine sub-bands in total.Out of these nine, four are given to SUs designated by regions II, IV, VI, and VIII, while regions I, III, V, VII, and IX are given to PUs.Consider that the bandwidth allocated to all SUs is equal, while the bandwidths allocated to PUs are unequal.Each SU has 32 OFDM subcarriers.Figures 10 and 11 show the comparison of the proposed technique with already existing sidelobe suppression techniques including CC [14], CC using GA and DE [17], ACC [18], and ASW [21].

Conclusions and Future Work Recommendation
We have proposed a novel wave-shaping technique, GSC, for the reduction of sidelobes of OFDM signal.The proposed technique allows the desired portion of the signal to pass and blocks the undesired portion, i.e., the sidelobes.The performance comparison of the proposed technique in different spectrum-sharing scenarios with already existing sidelobe suppression techniques is done through simulations, which show that the proposed technique achieves more than 90 dB reduction in sidelobes as compared to the existing techniques.
In the future, one can use the proposed approach for direction of arrival estimation of plane waves, as well as spherical waves.Moreover, the proposed scheme can also be tested for independent null steering.
correlation matrix, with dimension M × M, I is the identity matrix with dimension M × M,2

w
= s is an i th steering vector with dimension M × 1 containing M samples of the i th spectrum; and [1,1,...,1] T = g is called the gain vector with dimension N × 1, which contains the desired gain related to each steering vector.The effective implementation of LCMV is the division of a field with dimension M × M into the constraint subfield defined by columns of C, an M × N matrix, and an orthogonal subfield defined by columns of B an M × (M − N) matrix such that is a null matrix with dimension N × (M − N) and B is a blocking matrix that blocks the desired portion of the NCOFDM signal.Now consider the decomposition of H o onto the orthogonal subfield.c P and o P are the projection matrices onto the constraint and orthogonal subfields with dimension M × M given by

Figure 4 .
Figure 4.The PSD comparison between the proposed technique and existing techniques including SW, CC (Brandes), CC (GA), and CC (DE).

Figure 5 .
Figure 5.The PSD comparison between the proposed technique and existing techniques including ASW and ACC.

Figure 6 .
Figure 6.The PSD comparison between the proposed technique and existing techniques including ACC and ASW.

Figure 7 .
Figure 7.The PSD comparison between the proposed technique and existing techniques including CC (Brandes), CC (GA), and CC (DE).

Figure 8 .
Figure 8.The PSD comparison between the proposed technique and existing techniques including ACC and ASW.

Figure 9 .
Figure 9.The PSD comparison between the proposed technique and existing techniques including CC (Brandes), CC (GA), and CC (DE).

Figure 10 .
Figure 10.The PSD comparison between the proposed technique and existing techniques including ACC and ASW.

Figure 11 .
Figure 11.The PSD comparison between the proposed technique and existing techniques including CC (Brandes), CC (GA), and CC (DE).

Figure 13 .
Figure 13.The PSD comparison between the proposed technique and existing techniques including CC (Brandes), CC (GA), and CC (DE).

Table 1 .
Comparison of sidelobe suppression between existing and proposed techniques.

Table 2 .
Comparison of sidelobe suppression between existing and proposed techniques.

Table 3 .
Comparison of sidelobe suppression between existing and proposed techniques.

Table 5 .
Comparison of sidelobe suppression between existing and proposed techniques.