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A Multi-Resolution Fast Filter Bank for Spectrum Sensing in Military Radio Receivers K. G. Smitha and A. P. Vinod
Abstract—In this paper, we propose a multi-resolution filter bank (MRFB)-based on the fast filter bank design for multiple resolution spectrum sensing in military radio receivers. The proposed method overcomes the constraint of fixed sensing resolution in spectrum sensors based on conventional discrete Fourier transform filter banks (DFTFB). The flexibility in realizing multiple sensing resolution spectrum sensor is achieved by suitably designing the prototype filter and efficiently selecting the varying resolution subbands without hardware re-implementation. Design examples show that the sensing performance of proposed MRFB is comparable to that of conventional fixed resolution DFTFB. The complexity comparison shows that the proposed MRFB architecture has a gate count reduction of 36.5% over the DFTFB. The proposed MRFB architecture achieves an average power reduction of 20.8% over DFTFB. Index Terms—Fast filter bank, low complexity, multi-resolution filter bank (MRFB), reconfigurability, variable sensing resolution.
I. INTRODUCTION Real-time spectrum sensing of wideband signals whose radio channels (frequency bands) have distinct bandwidths corresponding to different wireless communication standards is an often requirement in military radio (MR) communications. The conventional method for sensing the multiple bandwidth radio channel is to have a fixed sensing resolution using discrete Fourier transform filter banks (DFTFB), where resolution is fixed as per the bandwidth of the channel that has the smallest bandwidth among all the channels of multiple standards. This method will sense a wider bandwidth channel by adding together the smaller bands of fixed resolution. But when the input signal is having channels of varying bandwidths, the conventional method of fixed sensing using the smallest sensing resolution becomes complex as the method needs to utilize the most stringent specification for a relaxed bandwidth. This will increase the dynamic power and delay in obtaining the output. Conventionally, there are three techniques used for spectrum sensing: matched filtering, energy detection, and cyclostationary feature detection [1]. Energy detection is the most widely used method as it requires no priori knowledge of the input signal. DFTFB-based energy detector is found to be more promising in terms of accuracy over the low level power spectral density (PSD) portions of the band [2]. The DFTFB approach in [3], which uses an optimal prolate sequence window as a prototype filter, offers improved sensing accuracy than the periodogram method with reduced complexity. In this paper, for simplicity we are using energy detection based spectrum sensor, as it can be used with least knowledge of the input signal. Low complexity dynamic spectrum estimation of a wideband signal with different channel bandwidths, is hardly addressed in literature. The work till date in spectrum sensing focused mainly on improving estimation accuracy by suitably designed architectures. Recent multiple resolution spectrum sensing schemes in [4]–[6] senses the total Manuscript received September 22, 2010; revised February 09, 2011; accepted April 20, 2011. The authors are with the School of Computer Engineering, Nanyang Technological University, 639798 Singapore (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVLSI.2011.2151214
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bandwidth initially using a coarse resolution. Fine resolution sensing is done only on portion of interesting bands. This approach saves sensing time and power when compared to the scheme which senses the whole bandwidth with highest resolution. The multiple resolution schemes in [4]–[6] are analog sensing techniques, which does not conform to the targeted digital platform, software defined radio (SDR), on which MR will be implemented. In an MR, the spectral occupancy as well as the bandwidths of channels could vary simultaneously. Hence the identical analysis resolution (sensing resolution) at a given time used in the existing approaches is insufficient for signals with time-varying channel occupancy. Multiple sensing resolution can be achieved in the digital domain using modulated perfect reconstruction filter banks (MPRB) [7] or cosine modulated filter banks (CMFB) [8]. These techniques have increased complexity when compared to DFTFB. In this paper, we propose a multi-resolution filter bank (MRFB) based on the fast filter bank (FFB) design for multiple resolution spectrum sensing in MR receivers. The proposed MRFB-based spectrum sensor can adapt to different sensing detection bandwidths for wideband spectrum sensing. The flexibility in realizing multiple sensing resolution spectrum sensor is achieved by suitably designing the prototype filter and efficiently selecting the desired sensing resolution without hardware re-implementation. The preliminary idea was presented in a conference paper [14]. The rest of this paper is arranged as follows. Section II presents the proposed MRFB architecture, the spectrum sensor and the complexity comparison with DFTFBs. Design example and implementation results is shown in Section III. Conclusions are given in Section IV. II. PROPOSED MULTI-RESOLUTION SPECTRUM SENSOR BASED ON FFB The proposed MRFB for spectrum sensing is a low complexity filter design approach based on FFB [10], with variable sensing resolution. FFB is a low complexity filter bank [10], proposed as an alternative to DFTFBs. The FFB consists of several subfilters of lower order arranged in a tree fashion. The FFB makes use of a technique called as frequency response masking (FRM) [9]. The basic idea behind the FRM technique [9] is to compose the overall sharp transition-band filter using several wide transition-band subfilters. However, the reconfigurability potential of FFB is hardly exploited in literature. In the proposed MRFB architecture, we modify the FFB design, by incorporating reconfigurability to each of the subfilters for varying the sensing resolution in MR receivers. A. FFB Architecture The FFB is suitable for the design of filter banks due to its reduced complexity [10]. The FFB follows a tree structure and it can be decomposed into several stages. For a k -stage FFB, we can realize 2k channels. The subfilters Hi;j (Z ), where j > 0 are modulated versions of prototype filter and together they form the basic structure of FFB [11]. Each stage is interpolated by a factor M and we can get both the original and complementary responses from each stage. A complementary filter can be obtained by subtracting the output of the (M + 1)-band response from a suitably delayed version of the input. If each of these (M + 1) bands is masked using suitably designed masking filters in k 0 1 stages, we can obtain 2k channels. In this paper, reconfigurabilty is incorporated into FFB architecture so that the modal filter response can be changed by varying the interpolation value according to the resolution required in the spectrum sensor. Using the proposed spectrum sensor, the sensing resolution can also be changed using software reconfiguration.
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Fig. 1. Reconfigurable MRFB-based spectrum sensor architecture.
B. Proposed MRFB Architecture The output response of the FFB depends on the interpolated modal filter response. If the interpolation factors of the modal filter can be changed with the corresponding masking filter stages of FFB, a filter bank with channels of different bandwidths can be realized. Reconfigurable FRM techniques in [12], [13] can be used to make the FFB architecture suitable to obtain frequency bands of different bandwidths. The methods in [12] and [13] uses reconfigurable FRM techniques for channel filter realization. The proposed method is for designing a reconfigurable multi-resolution filter bank for spectrum sensing. The architecture for proposed MRFB using four stage FFB is shown in Fig. 1. along with energy detector for spectrum sensing and summing circuitry. The proposed MRFB architecture can be explained using an example. The normalized frequency band edge specification of the 1st stage filter called the modal filter is chosen as follows: passband edge fpb = 0:4 and stopband edge fsb = 0:6. The length of the filters can be obtained from the expression (1)
N
3 (103p3 s ) 0 1 = 02 3(log fsb 0 fpb )
(1)
where p is the peak passband ripple (PPR), s is the peak stopband ripple (PSR), and fsb 0 fpb is the normalized transition band width (TBW). Assume p = 0.1 dB and s = 040 dB for all the subfilters in Fig. 1. From (1), the length of the filter N is obtained as 19. The band edge of masking filters of the respective stages are designed according to the relaxed specifications (2) [11]
i
= 1 02i0
(2)
where i is the number of stages starting from 0 for the modal filter to 3 for the last stage filter. We can note that as the number of stages in the tree structure increases, the TBW decreases, which will reduce the
complexity of the filter. The length of the masking filters are 11, 7, and 5, respectively, obtained using (1) and (2). Fig. 2(a) shows the reconfigurable 1st stage filter architecture. The subsequent stages will be similar to the first stage by removing the delays Z 04 , Z 02 , and Z 01 , respectively. The complementary delay for the first stage is shown in Fig. 2(b). Using the select lines S[1:0] and enable lines en(0 : 2) shown in Figs. 1 and 2, the MRFB architecture can be reconfigured for obtaining variable bandwidth output. When S[1:0] is “11”, en(0 : 2) = 1, we obtain 16 channels or 8 real channels, each of bandwidth (BW ), 0.05. Similarly when S[1:0] is “10”, en(0 : 1) = 1 and en(2) = 0 we obtain four real channels of BW, 0.1; when S[1:0] is “01”, en(0) = 1 and en(1 : 2) = 0, we obtain two real channels of BW, 0.2; when S[1:0] is “00”, en(0 : 2) = 0, we obtain 1 channel of BW, 0.4. Using the enable signals en(0), en(1), and en(2), the dynamic power dissipation can be controlled as the “en” signals along with the AND gates in Fig. 1 provide gating for the next level of filters. If we require only 4 real channels with BW = 0:1, we can disable the last stage of MRFB in Fig. 1 by setting en(0 : 1) = 1 and en(2) = 0. This will enable us to speed-up spectrum sensing as it is not required to wait till the end of the fourth stage. We can note that, the rising edge ffre g and falling edges fffe g for 16-channel, 8-channel, 4-channel, and 2-channel FFB and DFTFB follow a relation for the real channels as shown in (3)
ffre ; ffe g =
3 BW (2n 0 1)3 BW 2 ; (2n 0 1) 2 + BW
(3)
where BW is the bandwidth of the corresponding FFB when total signal bandwidth is (0fs; f s) and n is the channel number. In this we can note that by adding together two adjacent channels of 16-channel FFB, it is not possible to get the same rising and falling edge specification for the similar channel in 8-channel FFB. For example, if we add together the channel 1 and channel 2 of 16-channel FFB, Y f4; 1g + Y f4; 2g, the ffre ; ffe g of the resultant channel is ff s=16; 5f s=16g
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Fig. 2. Reconfigurable filter architectures for first stage filter. (a) First stage output. (b) Complementary delays for the first stage.
TABLE I COMPLEXITY COMPARISON
Fig. 3. Channel Y f4; 1g + Y f4; 2g of 16-FFB and Y f3; 1g of 8-FFB.
which is not equivalent to Y f3; 1g = ffs=8; 3fs=8g. From Fig. 3, we can note that the BW for both (Y f4; 1g + Y f4; 2g) and Y f3; 1g are same which is fs=4, but the ffre ; ffe specifications vary for the summation outputs. The proposed MRFB architecture can generate Y f3; 1g at an earlier stage. Using the summing circuitry shown in Fig. 1, Y f4; 1g+ Y f4; 2g can also be obtained, thus achieving multiple resolution sensing with varying rising and falling edges. Extraction of lower resolution signal at an earlier stage help us to reduce dynamic power and time for energy calculation. C. Comparison of Complexity The comparison of complexity of our proposed MRFB architecture with that of the DFTFB approach is presented in this section. As DFTFB is a uniform filter bank, for a fair comparison, we have considered 16-channel DFTFB (16 uniform bandwidth channels) and 16-channel proposed MRFB (16 uniform bandwidth channels). For a 16-channel proposed MRFB as shown in Figs. 1 and 2, the minimum normalized bandwidth, BWmin = fp =Mmax = 0:4=8 = 0:05, where fp is the passband width of the modal filter and Mmax is the maximum M value. For the example given in the paper, fpb = 0:4 and fsb = 0:6 for 16-channel MRFB. This means the proposed MRFB, when realized to extract 16 channels, can have passband edge (fp ) = 0:05 = 0:4=8 (fpb interpolated by 8) and stopband edge (fs ) = 0:075 = 0:6=8 (fsb interpolated by 8). Taking the same specifications for 16 point DFTFB, the prototype filter should have the specification of fpb = 0:05 and fsb = 0:075. Then the order of the prototype filter (1) is 156. Table I shows the complexity comparison in terms of multiplications (mult.) for a 16 fixed channel DFTFB and proposed MRFB architecture with Bmin = 0:05. The total complexity of a DFTFB is equal to the cost of the prototype filter (N multiplications for an N -tap filter) and that of the fast Fourier transform (FFT) computation (S log2 S multiplications for S -point FFT needed to extract S channels). For the
proposed MRFB architecture, we need only lower order filters for the masking filters due to the relaxed specifications as shown in [11]. Hence the total number of multiplications for the proposed MRFB is 109, which includes the whole set of filter multiplications for the 16 channel MRFB implementation. The MPRB method [7] requires almost twice the complexity of DFTFB as it needs analysis and synthesis filter banks. The CMFB method [8] requires S 2 multiplications when compared to the S log2 S multiplications for S -point FFT needed to extract S channels in DFTFB’s. Hence the total complexity of both MPRB and CMFB is almost double of DFTFB. From the total number of multiplications shown in Table I, the proposed MRFB architecture has a complexity reduction of 50.5% over DFTFB, 75.2% over MPRB, and 73.54% over CMFB. For the proposed MRFB architecture, the same architecture can be reused for 16-, 8-, 4-, and 2-channel outputs without any increase in complexity. The only additional complexity is that of the multiplexers and delays which is only 7.5% of the total complexity. III. DESIGN EXAMPLE AND IMPLEMENTATION RESULTS A. Design Example In this section, we present a design example to demonstrate the variable spectrum sensing in a multi-mode communication environment, where two predefined standards, standard S1 with channel bandwidth 25 kHz and standard S2 with channel bandwidth 100 kHz, exists at two different time intervals. Consider that the S1 channels exists during the time instance t0 and S2 channels exists during the time instance t1 , where t1 > t0 . The input signal bandwidth is chosen as 400 kHz. The sensing resolution of the MRFB can be set to S[1:0] = “11”, in order to obtain eight real subbands, each of bandwidth corresponding to S1 standard, 25 kHz. The S2 channels can be sensed using MRFB sensor
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TABLE II HARDWARE AND RECONFIGURATION COST COMPARISON
Fig. 4. Input spectrum example for time instance t and t .
by taking S[1:0] = “01” and 2 real subbands is realized, each of bandwidth corresponding to S2 standard, 100 kHz. Thus the same MRFB spectrum sensor can be reconfigured to meet both the specifications. B. Functionality Test The S1 =S2 example is functionally verified by inputting a signal whose spectrum is shown in Fig. 4 to the MRFB-based sensor. The input signals in Fig. 4 are signals at two time instances t0 and t1 . When the input signal at t0 in Fig. 4 is fed to the proposed spectrum sensor with S[1:0] = “11”, high energy is estimated indicating spectrum occupancy results for subband-1 of BW 25 kHz as shown in Fig. 5(a). The input spectrum shown in Fig. 4 at t1 , has band edges at 56 and 144 kHz, spreads over 5 subbands-2, 3, 4, 5, and 6 for the given selector set to S[1:0] = “11”. The band edges for the summed channel of subbands 2, 3 4, 5, and 6 are 37.5 and 162.5 kHz. With S[1:0] = “11”, the subband 2 with band edges {37.5 kHz, 62.5 kHz} and subband 6 with band edges {137.5 kHz, 162.5 kHz} have less amount of signal and there is a possibility of failure in detection if the threshold of the energy detection in not accurately set. This can be reduced if we set the select value S[1:0] = “01” for the input at t1 . In the case of S[1:0] = “01”, high energy is estimated indicating spectrum occupancy results for only subband-1 with band edges {50 kHz, 150 kHz} as shown in Fig. 5(b). In this example, the signal at t1 can be sensed at a faster rate by setting the S[1:0] = “01” and en(2) =“0”, thus utilizing only fewer number of stages. C. Performance Evaluation In this section, we present the simulation results to demonstrate the performance of the proposed MRFB based energy spectrum sensing scheme. The performance of the of the proposed method can be evaluated using Pd , probability of detection and Pfa , probability of false alarm. Pd is the probability of detecting a signal on the considered frequency band, when it was truly sent and Pfa is the probability that the detection incorrectly decides the presence of a signal when there was no signal sent in that frequency band. Both the MRFB and DFTFB based systems using energy detector are made to detect the same signal in the
set to “11”. Fig. 5. (a) Output spectrum at t of the MRFB sensor with S set to “01”. (b) Output spectrum at t of the MRFB sensor with S
presence of noise. The values of Pd and Pfa are calculated and plotted for two different values of signal-to-noise power ratio (SNR), 015 and 020 dB, in Fig. 6. The Fig. 6 shows that, the performance characteristics of the proposed MRFB-based spectrum sensor is as good as the DFTFB-based spectrum sensors. D. Implementation Results The proposed 16-channel MRFB architecture is implemented and compared with the 16-channel DFTFB. The architecture was implemented on Xilinx Virtex 2v3000ff1152–4 FPGA associated with dual DSP-FPGA Signalmaster kit provided by lyrtech. It was tested using real time Gaussian noise as input signal. The proposed 16-channel MRFB architecture offers an average gate count reduction of 36.5% over 16-channel DFTFB as shown in Table II. The average reduction of power consumption achieved using the proposed 16-channel MRFB over 16-channel DFTFB is 20.8%. We have also shown the reconfiguration cost of the proposed architecture to 8-channel MRFB and have compared it with fixed sensing DFTFB spectrum sensor where wider resolution is made by adding the finer resolutions. The result shows that there is a 5% reduction in dynamic power and 8% reduction in delay when compared to 16-channel MRFB.
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Fig. 6. Plot of P versus P
for multiple SNR.
IV. CONCLUSION In this paper we have proposed a spectrum sensing technique based on MRFB, which can have variable sensing resolutions and can adapt to different sensing bandwidths by software reconfiguration. Our proposed MRFB-based spectrum sensor is having a gate count reduction of 36.5% and power reduction of 20.8% over DFTFB based spectrum sensor.
REFERENCES [1] H. Arslan and T. Yucek, Spectrum Sensing for Cognitive Radio Applications, Book Chapter, Cognitive Radio, Software Defined Radio and Adaptive Wireless Systems. New York: Springer, 2007. [2] B. F-Boroujeny, “Filter bank spectrum sensing for cognitive radios,” IEEE Trans. Signal Process., vol. 56, no. 5, pp. 1801–1811, May 2008.
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[3] F. Sheikh and B. Bing, “Cognitive spectrum sensing and detection using polyphase DFT filter banks,” in Proc. IEEE Consumer Commun. Network. Conf., 2008, pp. 973–977. [4] Y. Hur, L. Park, W. Woo, K. Lim, C.-H. Lee, H. S. Kim, and L. Laskar, “A wideband analog multi-resolution spectrum sensing (MRSS) technique for cognitive radio (CR) systems,” in Proc. Int. Symp. Circuits Syst., 2006, pp. 4090–4093. [5] N. M. Neihart, S. Roy, and D. L. Allstot, “A parallel, multi-resolution sensing technique for multiple antenna cognitive radios,” in Proc. Int. Symp. Circuits Syst., 2007, pp. 2530–2533. [6] Q. Zhang, A. B. J. Kokkeler, and G. J. M. Smit, “An efficient multiresolution spectrum sensing method for cognitive radio,” in Proc. 3rd Int. Conf. Commun. Network. China, 2008, pp. 1226–1229. [7] W. A. Abu-Al-Saud and G. L. Stuber, “Efficient wideband channelizer for software radio systems using modulated PR filter banks,” IEEE Trans. Signal Process., vol. 52, no. 10, pp. 2807–2820, Oct. 2004. [8] B. Li, L. Ge, and J. Zheng, “An efficient channelizer based on nonuniform filter banks,” in Proc. 8th Int. Conf. Signal Process., 2006, pp. 16–20. [9] Y. C. Lim, “Frequency-response masking approach for the synthesis of sharp linear phase digital filters,” IEEE Trans. Circuits Syst., vol. 33, no. 4, pp. 357–364, Apr. 1986. [10] Y. C. Lim and B. F-Boroujeny, “Fast filter bank (FFB),” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 39, no. 5, pp. 316–318, May 1992. [11] Y. C. Lim and B. F-Boroujeny, “Analysis and optimum design of the FFB,” in Proc. Int. Symp. Circuits Syst., 1994, pp. 509–512. [12] R. Mahesh and A. P. Vinod, “Reconfigurable frequency response masking filters for software radio channelization,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 55, no. 3, pp. 274–278, Mar. 2008. [13] K. G. Smitha, R. Mahesh, and A. P. Vinod, “A reconfigurable multistage frequency response masking filter bank architecture for software defined radio receivers,” in Proc. IEEE Int. Symp. Circuits Syst., 2008, pp. 85–88. [14] K. G. Smitha and A. P. Vinod, “A multi-resolution digital filter bank for spectrum sensing in military radio receivers,” in Proc. IEEE Int. Conf. Signal Process. Commun., 2010, pp. 1–5.
A Multi-Resolution Fast Filter Bank for Spectrum Sensing in Military Radio Receivers K. G. Smitha and A. P. Vinod
Abstract—In this paper, we propose a multi-resolution filter bank (MRFB)-based on the fast filter bank design for multiple resolution spectrum sensing in military radio receivers. The proposed method overcomes the constraint of fixed sensing resolution in spectrum sensors based on conventional discrete Fourier transform filter banks (DFTFB). The flexibility in realizing multiple sensing resolution spectrum sensor is achieved by suitably designing the prototype filter and efficiently selecting the varying resolution subbands without hardware re-implementation. Design examples show that the sensing performance of proposed MRFB is comparable to that of conventional fixed resolution DFTFB. The complexity comparison shows that the proposed MRFB architecture has a gate count reduction of 36.5% over the DFTFB. The proposed MRFB architecture achieves an average power reduction of 20.8% over DFTFB. Index Terms—Fast filter bank, low complexity, multi-resolution filter bank (MRFB), reconfigurability, variable sensing resolution.
I. INTRODUCTION Real-time spectrum sensing of wideband signals whose radio channels (frequency bands) have distinct bandwidths corresponding to different wireless communication standards is an often requirement in military radio (MR) communications. The conventional method for sensing the multiple bandwidth radio channel is to have a fixed sensing resolution using discrete Fourier transform filter banks (DFTFB), where resolution is fixed as per the bandwidth of the channel that has the smallest bandwidth among all the channels of multiple standards. This method will sense a wider bandwidth channel by adding together the smaller bands of fixed resolution. But when the input signal is having channels of varying bandwidths, the conventional method of fixed sensing using the smallest sensing resolution becomes complex as the method needs to utilize the most stringent specification for a relaxed bandwidth. This will increase the dynamic power and delay in obtaining the output. Conventionally, there are three techniques used for spectrum sensing: matched filtering, energy detection, and cyclostationary feature detection [1]. Energy detection is the most widely used method as it requires no priori knowledge of the input signal. DFTFB-based energy detector is found to be more promising in terms of accuracy over the low level power spectral density (PSD) portions of the band [2]. The DFTFB approach in [3], which uses an optimal prolate sequence window as a prototype filter, offers improved sensing accuracy than the periodogram method with reduced complexity. In this paper, for simplicity we are using energy detection based spectrum sensor, as it can be used with least knowledge of the input signal. Low complexity dynamic spectrum estimation of a wideband signal with different channel bandwidths, is hardly addressed in literature. The work till date in spectrum sensing focused mainly on improving estimation accuracy by suitably designed architectures. Recent multiple resolution spectrum sensing schemes in [4]–[6] senses the total Manuscript received September 22, 2010; revised February 09, 2011; accepted April 20, 2011. The authors are with the School of Computer Engineering, Nanyang Technological University, 639798 Singapore (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVLSI.2011.2151214
1
bandwidth initially using a coarse resolution. Fine resolution sensing is done only on portion of interesting bands. This approach saves sensing time and power when compared to the scheme which senses the whole bandwidth with highest resolution. The multiple resolution schemes in [4]–[6] are analog sensing techniques, which does not conform to the targeted digital platform, software defined radio (SDR), on which MR will be implemented. In an MR, the spectral occupancy as well as the bandwidths of channels could vary simultaneously. Hence the identical analysis resolution (sensing resolution) at a given time used in the existing approaches is insufficient for signals with time-varying channel occupancy. Multiple sensing resolution can be achieved in the digital domain using modulated perfect reconstruction filter banks (MPRB) [7] or cosine modulated filter banks (CMFB) [8]. These techniques have increased complexity when compared to DFTFB. In this paper, we propose a multi-resolution filter bank (MRFB) based on the fast filter bank (FFB) design for multiple resolution spectrum sensing in MR receivers. The proposed MRFB-based spectrum sensor can adapt to different sensing detection bandwidths for wideband spectrum sensing. The flexibility in realizing multiple sensing resolution spectrum sensor is achieved by suitably designing the prototype filter and efficiently selecting the desired sensing resolution without hardware re-implementation. The preliminary idea was presented in a conference paper [14]. The rest of this paper is arranged as follows. Section II presents the proposed MRFB architecture, the spectrum sensor and the complexity comparison with DFTFBs. Design example and implementation results is shown in Section III. Conclusions are given in Section IV. II. PROPOSED MULTI-RESOLUTION SPECTRUM SENSOR BASED ON FFB The proposed MRFB for spectrum sensing is a low complexity filter design approach based on FFB [10], with variable sensing resolution. FFB is a low complexity filter bank [10], proposed as an alternative to DFTFBs. The FFB consists of several subfilters of lower order arranged in a tree fashion. The FFB makes use of a technique called as frequency response masking (FRM) [9]. The basic idea behind the FRM technique [9] is to compose the overall sharp transition-band filter using several wide transition-band subfilters. However, the reconfigurability potential of FFB is hardly exploited in literature. In the proposed MRFB architecture, we modify the FFB design, by incorporating reconfigurability to each of the subfilters for varying the sensing resolution in MR receivers. A. FFB Architecture The FFB is suitable for the design of filter banks due to its reduced complexity [10]. The FFB follows a tree structure and it can be decomposed into several stages. For a k -stage FFB, we can realize 2k channels. The subfilters Hi;j (Z ), where j > 0 are modulated versions of prototype filter and together they form the basic structure of FFB [11]. Each stage is interpolated by a factor M and we can get both the original and complementary responses from each stage. A complementary filter can be obtained by subtracting the output of the (M + 1)-band response from a suitably delayed version of the input. If each of these (M + 1) bands is masked using suitably designed masking filters in k 0 1 stages, we can obtain 2k channels. In this paper, reconfigurabilty is incorporated into FFB architecture so that the modal filter response can be changed by varying the interpolation value according to the resolution required in the spectrum sensor. Using the proposed spectrum sensor, the sensing resolution can also be changed using software reconfiguration.
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Fig. 1. Reconfigurable MRFB-based spectrum sensor architecture.
B. Proposed MRFB Architecture The output response of the FFB depends on the interpolated modal filter response. If the interpolation factors of the modal filter can be changed with the corresponding masking filter stages of FFB, a filter bank with channels of different bandwidths can be realized. Reconfigurable FRM techniques in [12], [13] can be used to make the FFB architecture suitable to obtain frequency bands of different bandwidths. The methods in [12] and [13] uses reconfigurable FRM techniques for channel filter realization. The proposed method is for designing a reconfigurable multi-resolution filter bank for spectrum sensing. The architecture for proposed MRFB using four stage FFB is shown in Fig. 1. along with energy detector for spectrum sensing and summing circuitry. The proposed MRFB architecture can be explained using an example. The normalized frequency band edge specification of the 1st stage filter called the modal filter is chosen as follows: passband edge fpb = 0:4 and stopband edge fsb = 0:6. The length of the filters can be obtained from the expression (1)
N
3 (103p3 s ) 0 1 = 02 3(log fsb 0 fpb )
(1)
where p is the peak passband ripple (PPR), s is the peak stopband ripple (PSR), and fsb 0 fpb is the normalized transition band width (TBW). Assume p = 0.1 dB and s = 040 dB for all the subfilters in Fig. 1. From (1), the length of the filter N is obtained as 19. The band edge of masking filters of the respective stages are designed according to the relaxed specifications (2) [11]
i
= 1 02i0
(2)
where i is the number of stages starting from 0 for the modal filter to 3 for the last stage filter. We can note that as the number of stages in the tree structure increases, the TBW decreases, which will reduce the
complexity of the filter. The length of the masking filters are 11, 7, and 5, respectively, obtained using (1) and (2). Fig. 2(a) shows the reconfigurable 1st stage filter architecture. The subsequent stages will be similar to the first stage by removing the delays Z 04 , Z 02 , and Z 01 , respectively. The complementary delay for the first stage is shown in Fig. 2(b). Using the select lines S[1:0] and enable lines en(0 : 2) shown in Figs. 1 and 2, the MRFB architecture can be reconfigured for obtaining variable bandwidth output. When S[1:0] is “11”, en(0 : 2) = 1, we obtain 16 channels or 8 real channels, each of bandwidth (BW ), 0.05. Similarly when S[1:0] is “10”, en(0 : 1) = 1 and en(2) = 0 we obtain four real channels of BW, 0.1; when S[1:0] is “01”, en(0) = 1 and en(1 : 2) = 0, we obtain two real channels of BW, 0.2; when S[1:0] is “00”, en(0 : 2) = 0, we obtain 1 channel of BW, 0.4. Using the enable signals en(0), en(1), and en(2), the dynamic power dissipation can be controlled as the “en” signals along with the AND gates in Fig. 1 provide gating for the next level of filters. If we require only 4 real channels with BW = 0:1, we can disable the last stage of MRFB in Fig. 1 by setting en(0 : 1) = 1 and en(2) = 0. This will enable us to speed-up spectrum sensing as it is not required to wait till the end of the fourth stage. We can note that, the rising edge ffre g and falling edges fffe g for 16-channel, 8-channel, 4-channel, and 2-channel FFB and DFTFB follow a relation for the real channels as shown in (3)
ffre ; ffe g =
3 BW (2n 0 1)3 BW 2 ; (2n 0 1) 2 + BW
(3)
where BW is the bandwidth of the corresponding FFB when total signal bandwidth is (0fs; f s) and n is the channel number. In this we can note that by adding together two adjacent channels of 16-channel FFB, it is not possible to get the same rising and falling edge specification for the similar channel in 8-channel FFB. For example, if we add together the channel 1 and channel 2 of 16-channel FFB, Y f4; 1g + Y f4; 2g, the ffre ; ffe g of the resultant channel is ff s=16; 5f s=16g
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Fig. 2. Reconfigurable filter architectures for first stage filter. (a) First stage output. (b) Complementary delays for the first stage.
TABLE I COMPLEXITY COMPARISON
Fig. 3. Channel Y f4; 1g + Y f4; 2g of 16-FFB and Y f3; 1g of 8-FFB.
which is not equivalent to Y f3; 1g = ffs=8; 3fs=8g. From Fig. 3, we can note that the BW for both (Y f4; 1g + Y f4; 2g) and Y f3; 1g are same which is fs=4, but the ffre ; ffe specifications vary for the summation outputs. The proposed MRFB architecture can generate Y f3; 1g at an earlier stage. Using the summing circuitry shown in Fig. 1, Y f4; 1g+ Y f4; 2g can also be obtained, thus achieving multiple resolution sensing with varying rising and falling edges. Extraction of lower resolution signal at an earlier stage help us to reduce dynamic power and time for energy calculation. C. Comparison of Complexity The comparison of complexity of our proposed MRFB architecture with that of the DFTFB approach is presented in this section. As DFTFB is a uniform filter bank, for a fair comparison, we have considered 16-channel DFTFB (16 uniform bandwidth channels) and 16-channel proposed MRFB (16 uniform bandwidth channels). For a 16-channel proposed MRFB as shown in Figs. 1 and 2, the minimum normalized bandwidth, BWmin = fp =Mmax = 0:4=8 = 0:05, where fp is the passband width of the modal filter and Mmax is the maximum M value. For the example given in the paper, fpb = 0:4 and fsb = 0:6 for 16-channel MRFB. This means the proposed MRFB, when realized to extract 16 channels, can have passband edge (fp ) = 0:05 = 0:4=8 (fpb interpolated by 8) and stopband edge (fs ) = 0:075 = 0:6=8 (fsb interpolated by 8). Taking the same specifications for 16 point DFTFB, the prototype filter should have the specification of fpb = 0:05 and fsb = 0:075. Then the order of the prototype filter (1) is 156. Table I shows the complexity comparison in terms of multiplications (mult.) for a 16 fixed channel DFTFB and proposed MRFB architecture with Bmin = 0:05. The total complexity of a DFTFB is equal to the cost of the prototype filter (N multiplications for an N -tap filter) and that of the fast Fourier transform (FFT) computation (S log2 S multiplications for S -point FFT needed to extract S channels). For the
proposed MRFB architecture, we need only lower order filters for the masking filters due to the relaxed specifications as shown in [11]. Hence the total number of multiplications for the proposed MRFB is 109, which includes the whole set of filter multiplications for the 16 channel MRFB implementation. The MPRB method [7] requires almost twice the complexity of DFTFB as it needs analysis and synthesis filter banks. The CMFB method [8] requires S 2 multiplications when compared to the S log2 S multiplications for S -point FFT needed to extract S channels in DFTFB’s. Hence the total complexity of both MPRB and CMFB is almost double of DFTFB. From the total number of multiplications shown in Table I, the proposed MRFB architecture has a complexity reduction of 50.5% over DFTFB, 75.2% over MPRB, and 73.54% over CMFB. For the proposed MRFB architecture, the same architecture can be reused for 16-, 8-, 4-, and 2-channel outputs without any increase in complexity. The only additional complexity is that of the multiplexers and delays which is only 7.5% of the total complexity. III. DESIGN EXAMPLE AND IMPLEMENTATION RESULTS A. Design Example In this section, we present a design example to demonstrate the variable spectrum sensing in a multi-mode communication environment, where two predefined standards, standard S1 with channel bandwidth 25 kHz and standard S2 with channel bandwidth 100 kHz, exists at two different time intervals. Consider that the S1 channels exists during the time instance t0 and S2 channels exists during the time instance t1 , where t1 > t0 . The input signal bandwidth is chosen as 400 kHz. The sensing resolution of the MRFB can be set to S[1:0] = “11”, in order to obtain eight real subbands, each of bandwidth corresponding to S1 standard, 25 kHz. The S2 channels can be sensed using MRFB sensor
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TABLE II HARDWARE AND RECONFIGURATION COST COMPARISON
Fig. 4. Input spectrum example for time instance t and t .
by taking S[1:0] = “01” and 2 real subbands is realized, each of bandwidth corresponding to S2 standard, 100 kHz. Thus the same MRFB spectrum sensor can be reconfigured to meet both the specifications. B. Functionality Test The S1 =S2 example is functionally verified by inputting a signal whose spectrum is shown in Fig. 4 to the MRFB-based sensor. The input signals in Fig. 4 are signals at two time instances t0 and t1 . When the input signal at t0 in Fig. 4 is fed to the proposed spectrum sensor with S[1:0] = “11”, high energy is estimated indicating spectrum occupancy results for subband-1 of BW 25 kHz as shown in Fig. 5(a). The input spectrum shown in Fig. 4 at t1 , has band edges at 56 and 144 kHz, spreads over 5 subbands-2, 3, 4, 5, and 6 for the given selector set to S[1:0] = “11”. The band edges for the summed channel of subbands 2, 3 4, 5, and 6 are 37.5 and 162.5 kHz. With S[1:0] = “11”, the subband 2 with band edges {37.5 kHz, 62.5 kHz} and subband 6 with band edges {137.5 kHz, 162.5 kHz} have less amount of signal and there is a possibility of failure in detection if the threshold of the energy detection in not accurately set. This can be reduced if we set the select value S[1:0] = “01” for the input at t1 . In the case of S[1:0] = “01”, high energy is estimated indicating spectrum occupancy results for only subband-1 with band edges {50 kHz, 150 kHz} as shown in Fig. 5(b). In this example, the signal at t1 can be sensed at a faster rate by setting the S[1:0] = “01” and en(2) =“0”, thus utilizing only fewer number of stages. C. Performance Evaluation In this section, we present the simulation results to demonstrate the performance of the proposed MRFB based energy spectrum sensing scheme. The performance of the of the proposed method can be evaluated using Pd , probability of detection and Pfa , probability of false alarm. Pd is the probability of detecting a signal on the considered frequency band, when it was truly sent and Pfa is the probability that the detection incorrectly decides the presence of a signal when there was no signal sent in that frequency band. Both the MRFB and DFTFB based systems using energy detector are made to detect the same signal in the
set to “11”. Fig. 5. (a) Output spectrum at t of the MRFB sensor with S set to “01”. (b) Output spectrum at t of the MRFB sensor with S
presence of noise. The values of Pd and Pfa are calculated and plotted for two different values of signal-to-noise power ratio (SNR), 015 and 020 dB, in Fig. 6. The Fig. 6 shows that, the performance characteristics of the proposed MRFB-based spectrum sensor is as good as the DFTFB-based spectrum sensors. D. Implementation Results The proposed 16-channel MRFB architecture is implemented and compared with the 16-channel DFTFB. The architecture was implemented on Xilinx Virtex 2v3000ff1152–4 FPGA associated with dual DSP-FPGA Signalmaster kit provided by lyrtech. It was tested using real time Gaussian noise as input signal. The proposed 16-channel MRFB architecture offers an average gate count reduction of 36.5% over 16-channel DFTFB as shown in Table II. The average reduction of power consumption achieved using the proposed 16-channel MRFB over 16-channel DFTFB is 20.8%. We have also shown the reconfiguration cost of the proposed architecture to 8-channel MRFB and have compared it with fixed sensing DFTFB spectrum sensor where wider resolution is made by adding the finer resolutions. The result shows that there is a 5% reduction in dynamic power and 8% reduction in delay when compared to 16-channel MRFB.
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Fig. 6. Plot of P versus P
for multiple SNR.
IV. CONCLUSION In this paper we have proposed a spectrum sensing technique based on MRFB, which can have variable sensing resolutions and can adapt to different sensing bandwidths by software reconfiguration. Our proposed MRFB-based spectrum sensor is having a gate count reduction of 36.5% and power reduction of 20.8% over DFTFB based spectrum sensor.
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