This paper reports the implementation and theoretical model for analyzing an optical CDMA/DWDM hybrid system to reduce two major problems,the Inter-Symbol Interference(ISI)and the Four-Wave Mixing(FWM)effects and impr...This paper reports the implementation and theoretical model for analyzing an optical CDMA/DWDM hybrid system to reduce two major problems,the Inter-Symbol Interference(ISI)and the Four-Wave Mixing(FWM)effects and improve the performance of optical subscriber access networks by using Zero Cross-Correlation(ZCC)optical codes,which helps to reduce the effect of the Multiple Access Interference(MAI).A squeezing method is used in the proposed hybrid system to completely suppress the ISI.In this method,the sequence interval of the signature code is squeezed into a duration of less than one-bit.The hybrid system is capable of accommodating 120 optical CDMA users carried by only 10 DWDM wavelengths spaced by 0.2 nm with 60 Gb/s/wavelength transmitted over 105.075 km of optical fiber.The result shows that the optimum interval of the code sequence is a quarter(i.e.,25%)of the bit duration.Moreover,the results reveal that the CDMA technology based on the spread spectrum is capable of increasing the nonlinear tolerance of the proposed hybrid system as the energy of bits is distributed over the chip sequence code.Also,the number of ones/weight and the positions between them have a significant effect on the performance of the proposed hybrid system.展开更多
In this paper,we propose a novel iterative scheme for exploiting transmit diversity using parallel independent Inter-Symbol Interference (ISI) channels. In this adaptive iterative scheme,we use EXtrinsic Information T...In this paper,we propose a novel iterative scheme for exploiting transmit diversity using parallel independent Inter-Symbol Interference (ISI) channels. In this adaptive iterative scheme,we use EXtrinsic Information Transfer (EXIT) chart tool to choose appropriate iterative method from Itera-tive Combining (IC),used as parallel concatenation turbo-like scheme,and Turbo Equalization (TE),used as serial concatenation turbo-like scheme. It is show that the proposed iterative scheme provides excellent performance both analytically and through simulations without any compute complexity increase comparable to IC.展开更多
The Chaotic Baseband Wireless Communication System(CBWCS)is expected to eliminate the Inter-Symbol Interference(ISI)caused by multipath propagation by using the optimal decoding threshold that is the sum of the ISI ca...The Chaotic Baseband Wireless Communication System(CBWCS)is expected to eliminate the Inter-Symbol Interference(ISI)caused by multipath propagation by using the optimal decoding threshold that is the sum of the ISI caused by past decoded bits and the ISI caused by future transmitting bits.However,the current technique is only capable of removing partial effects of the ISI,because only past decoded bits are available for the suboptimal decoding threshold calculation.The unavailability of the future information needed for the optimal decoding threshold is an obstacle to further improve the Bit Error Rate(BER)performance.In contrast to the previous method using Echo State Network(ESN)to predict one future bit,the proposed method in this paper predicts the optimal decoding threshold directly using ESN.The proposed ESN-based threshold prediction method simplifies the symbol decoding operation by avoiding the iterative prediction of the output waveform points using ESN and accumulated error caused by the iterative operation.With this approach,the calculation complexity is reduced compared to the previous ESN-based approach.The proposed method achieves better BER performance compared to the previous method.The reason for this superior result is twofold.First,the proposed ESN is capable of using more future symbols information conveyed by the ESN input to obtain more accurate threshold rather than the previous method in which only one future symbol was available.Second,the proposed method here does not need to estimate the channel information using Least Squared(LS)method,which avoids the extra error caused by inaccurate channel information estimation.Simulation results and experiment based on a wireless open-access research platform under a practical wireless channel show the effectiveness and superiority of the proposed method.展开更多
A novel dual-band antenna is proposed for mitigating the multi-path interference in the global navigation satellite system(GNSS) applications. The radiation patches consist of a shortedannular-ring reduced-surface-w...A novel dual-band antenna is proposed for mitigating the multi-path interference in the global navigation satellite system(GNSS) applications. The radiation patches consist of a shortedannular-ring reduced-surface-wave(SAR-RSW) element and an inverted-shorted-annular-ring reduced-surface-wave(ISAR-RSW)element. One key feature of the design is the proximity-coupled probe feeds to increase impedance bandwidth. The other is the defected ground structure band rejection filters to suppress the interaction effect between the SAR-RSW and the ISAR-RSW elements. In addition, trans-directional couplers are used to obtain tight coupling. Measurement results indicate that the antenna has a larger than 10 d B return loss bandwidth and a less than 3 d B axial-ratio(AR) bandwidth in the range of(1.164 – 1.255) GHz and(1.552 – 1.610) GHz. The gain of the passive antenna in the whole operating band is more than 7 d Bi.展开更多
A signal detection algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) sys- tem in the presence of fast time-varying channel. The channel is represented by a piece-wise linear variant mod...A signal detection algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) sys- tem in the presence of fast time-varying channel. The channel is represented by a piece-wise linear variant model with normalized Doppler frequency of less than 0.2. The channel parameters are extracted through ISI/ICI (inter-symbol in- terference/inter-carrier interference) cancellation and circular convolution reconstruction. Meanwhile, an improved OFDM symbol detection algorithm is also proposed based on circular convolution reconstruction. The channel state in- formation in the OFDM symbol duration can be obtained accurately from the adjacent two block pilots in a linear model. The simulation results show that the proposed method can not only track the channel variation, but also promise better performance gain in the OFDM symbol detection. Furthermore, the bit error ratio (BER) is close to the perform- ance with the perfect channel state information.展开更多
Pattern Time Delay Shift Coding (PDS) scheme is robust for underwater acoustic communication. The digital information are encoded in the time delay shift values of the Pattern, so the PDS scheme belongs to the Pulse P...Pattern Time Delay Shift Coding (PDS) scheme is robust for underwater acoustic communication. The digital information are encoded in the time delay shift values of the Pattern, so the PDS scheme belongs to the Pulse Position Modulation (PPM). Several Patterns are selected for code division that the communication system could have a high ability to mitigate the inter-symbol interference (ISI) caused by multipath channel. Four communication channels work on the same time divided by different frequency, which lead to 1000bits/s of the data rate of communication. The simulation experiments show that the PDS system could adapt to many underwater acoustic channels for high data rate and high reliability.展开更多
A new method called joint Matched Filter (MF) combining and turbo equalization is proposed for wireless communications over Inter-Symbol Interference (ISI) channels with diversity reception. This method takes diversit...A new method called joint Matched Filter (MF) combining and turbo equalization is proposed for wireless communications over Inter-Symbol Interference (ISI) channels with diversity reception. This method takes diversity combining and equalization as integrity and need just one turbo equalizer for all diversity branches. Computer simulations prove that our method can take advantage of turbo equalization and diversity reception to combat fading of wireless channels.展开更多
This letter presents the principles of Coded Orthogonal Frequency Division Multiplexing (COFDM) system and focuses on the effect of the Guard Interval (GI) on the systemperformance. The role of the GI parameter period...This letter presents the principles of Coded Orthogonal Frequency Division Multiplexing (COFDM) system and focuses on the effect of the Guard Interval (GI) on the systemperformance. The role of the GI parameter period to solve the problem of interferences that occur at the receiver is discussed. A new COFDM concept with a Variable GI (VGI) is proposed in order to improve the Bit Error Rate (BER) performance in the presence of multipaths with variable delays. A series of simulations have been carried out on the BER performance as a function of GI, maximum delay spread, and Signal-to-Noise Ratio (SNR), with QPSK as modulation scheme over multipath fading and Additive White Gaussian Noise (AWGN). The results show that the optimum values of the GI parameter approximately equal to the maximum delay spread, and the proposed system with VGI provides a better performance compared with the fixed length GI.展开更多
Recently, two expressions (for the noiseless and noisy case) were proposed for the residual inter-symbol interference (ISI) obtained by blind adaptive equalizers, where the error of the equalized output signal may be ...Recently, two expressions (for the noiseless and noisy case) were proposed for the residual inter-symbol interference (ISI) obtained by blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. However, those expressions are not applicable for biased input signals. In this paper, a closed-form approximated expression is proposed for the residual ISI applicable for the noisy and biased input case. This new proposed expression is valid for blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. The new proposed expression depends on the equalizer’s tap length, input signal statistics, channel power, SNR, step-size parameter and on the input signal’s bias. Simulation results indicate a high correlation between the simulated results and those obtained from our new proposed expression.展开更多
An increasing demand for high data rate transmission and protection over bandlimited channels with severe inter-symbol interference has resulted in a flurry of activity to improve channel equalization, In conjunction ...An increasing demand for high data rate transmission and protection over bandlimited channels with severe inter-symbol interference has resulted in a flurry of activity to improve channel equalization, In conjunction with equalization, channel coding-decoding can be employed to improve system performance. In this letter, the performance of the three stage turbo-equalization-decoding employing log maximum a posteriori probability is experimentally evaluated by a fading simulator. The BER is evaluated using various information sequence and interleaver sizes taking into account that the communication medium is a noisy inter symbol interference channel.展开更多
In low-frequency elastic wave through-the-earth communication system,because of multipath transmission caused by characteristics of the layered earth,the time domain equalizer is different from other wireless communic...In low-frequency elastic wave through-the-earth communication system,because of multipath transmission caused by characteristics of the layered earth,the time domain equalizer is different from other wireless communication systems.A modified LMS algorithm of variable step size is proposed based on improvement of traditional LMS.On the base of principle and simulation analysis,the improved Least Mean Square(LMS)algorithm is analyzed and the performances are compared between the improved LMS algorithm and traditional LMS algorithm.In the improved algorithm,the contradiction between convergence speed and the steady-state error is considered at the same time.Therefore,the improved algorithm has good convergence properties and channel-tracking performance.展开更多
This paper treats the digital design of a probabilistic energy equalizer for impulse radio (IR) UWB receiver in high data rate (100Mbps). The aim of this study is to bypass certain complex mathematical function as a c...This paper treats the digital design of a probabilistic energy equalizer for impulse radio (IR) UWB receiver in high data rate (100Mbps). The aim of this study is to bypass certain complex mathematical function as a chi-squared distribution and reduce the computational complexity of the equalizer for a low cost hardware implementation. As in Sub-MAP algorithm, the max* operation is investigated for complexity reduction and tested by computer simulation with fixed point data types under 802.15.3a channel models. The obtained re-sults prove that the complexity reduction involves a very slight algorithm deterioration and still meet the low-cost constraint of the implementation.展开更多
As an important secure routing mechanism, multi-path routing is one of the major ways to improve network efficiency and to guarantee the network security, which ensures the reliability of data transmission by using ba...As an important secure routing mechanism, multi-path routing is one of the major ways to improve network efficiency and to guarantee the network security, which ensures the reliability of data transmission by using backup paths when the primary one is unavailable due to local node or link failures. Most current studies on multi-path routing mechanism are based on experiments or simulations. The resulta are usually specific application scenarios oriented heuristic algorithms, lacking universal significance. In this paper, a theoretic analysis is performed on the relationship between the multi-path routing policy, the network efficiency and its survivability. Starting with point-to-point communication network, an impactoriented analysis is made on the network interference under multi-path routing mechanism. Based on the analysis, the upper-limit of network performance under interference impact is also discussed.展开更多
In this paper,a Doppler scaling fast Fourier transform(Doppler-FFT)algorithm for filter bank multi-carrier(FBMC)is proposed,which can efficiently eliminate the impact of the Doppler scaling in satellite communicat...In this paper,a Doppler scaling fast Fourier transform(Doppler-FFT)algorithm for filter bank multi-carrier(FBMC)is proposed,which can efficiently eliminate the impact of the Doppler scaling in satellite communications.By introducing a Doppler scaling factor into the butterfly structure of the fast Fourier transform(FFT)algorithm,the proposed algorithm eliminates the differences between the Doppler shifts of the received subcarriers,and maintains the same order of computational complexity compared to that of the traditional FFT.In the process of using the new method,the Doppler scaling should be estimated by calculating the orbital data in advance.Thus,the inter-symbol interference(ISI)and the inter-carrier interference(ICI)can be completely eliminated,and the signal to interference and noise ratio(SINR)will not be affected.Simulation results also show that the proposed algorithm can achieve a 0.4 d B performance gain compared to the frequency domain equalization(FDE)algorithm in satellite communications.展开更多
Recently,the nested Mach–Zehnder interferometer[Phys.Rev.Lett.111,240402(2013)]was modified by adding Dove prisms in a paper[Quantum Stud.:Math.Found.2,255(2015)],and an interesting result is that,after the Dove pris...Recently,the nested Mach–Zehnder interferometer[Phys.Rev.Lett.111,240402(2013)]was modified by adding Dove prisms in a paper[Quantum Stud.:Math.Found.2,255(2015)],and an interesting result is that,after the Dove prisms were inserted,a signal at the first mirror of the nested interferometer was obtained.But,according to the former original paper,the photons have never been present near that mirror.In this work,we interpret this result naturally by resorting to the three-path interference method.Moreover,we find that even though the photons have been somewhere,they can hide the trace of being there.展开更多
基金This work was supported by Multimedia University(Malaysia),project SAP ID:MMUI/160092.
文摘This paper reports the implementation and theoretical model for analyzing an optical CDMA/DWDM hybrid system to reduce two major problems,the Inter-Symbol Interference(ISI)and the Four-Wave Mixing(FWM)effects and improve the performance of optical subscriber access networks by using Zero Cross-Correlation(ZCC)optical codes,which helps to reduce the effect of the Multiple Access Interference(MAI).A squeezing method is used in the proposed hybrid system to completely suppress the ISI.In this method,the sequence interval of the signature code is squeezed into a duration of less than one-bit.The hybrid system is capable of accommodating 120 optical CDMA users carried by only 10 DWDM wavelengths spaced by 0.2 nm with 60 Gb/s/wavelength transmitted over 105.075 km of optical fiber.The result shows that the optimum interval of the code sequence is a quarter(i.e.,25%)of the bit duration.Moreover,the results reveal that the CDMA technology based on the spread spectrum is capable of increasing the nonlinear tolerance of the proposed hybrid system as the energy of bits is distributed over the chip sequence code.Also,the number of ones/weight and the positions between them have a significant effect on the performance of the proposed hybrid system.
基金Supported by the National Natural Science Foundation of China (No.60372030)China Ministry of Education Foundation for Visiting Scholar (No.[2003]406)Key Project of Provincial Scientific Foundation of Shandong (No.Z2003G02).
文摘In this paper,we propose a novel iterative scheme for exploiting transmit diversity using parallel independent Inter-Symbol Interference (ISI) channels. In this adaptive iterative scheme,we use EXtrinsic Information Transfer (EXIT) chart tool to choose appropriate iterative method from Itera-tive Combining (IC),used as parallel concatenation turbo-like scheme,and Turbo Equalization (TE),used as serial concatenation turbo-like scheme. It is show that the proposed iterative scheme provides excellent performance both analytically and through simulations without any compute complexity increase comparable to IC.
文摘The Chaotic Baseband Wireless Communication System(CBWCS)is expected to eliminate the Inter-Symbol Interference(ISI)caused by multipath propagation by using the optimal decoding threshold that is the sum of the ISI caused by past decoded bits and the ISI caused by future transmitting bits.However,the current technique is only capable of removing partial effects of the ISI,because only past decoded bits are available for the suboptimal decoding threshold calculation.The unavailability of the future information needed for the optimal decoding threshold is an obstacle to further improve the Bit Error Rate(BER)performance.In contrast to the previous method using Echo State Network(ESN)to predict one future bit,the proposed method in this paper predicts the optimal decoding threshold directly using ESN.The proposed ESN-based threshold prediction method simplifies the symbol decoding operation by avoiding the iterative prediction of the output waveform points using ESN and accumulated error caused by the iterative operation.With this approach,the calculation complexity is reduced compared to the previous ESN-based approach.The proposed method achieves better BER performance compared to the previous method.The reason for this superior result is twofold.First,the proposed ESN is capable of using more future symbols information conveyed by the ESN input to obtain more accurate threshold rather than the previous method in which only one future symbol was available.Second,the proposed method here does not need to estimate the channel information using Least Squared(LS)method,which avoids the extra error caused by inaccurate channel information estimation.Simulation results and experiment based on a wireless open-access research platform under a practical wireless channel show the effectiveness and superiority of the proposed method.
基金supported by the National Natural Science Foundation of China(61071044)the Traffic Applied Basic Research Project of the Ministry of Transport of China(2010-329-225-030)+2 种基金the Doctor Startup Foundation of Liaoning Province(20141103)the Scientific Research Project of the Department of Education of Liaoning Province(L2013196)the Fundamental Research Funds for the Central Universities(2014YB05)
文摘A novel dual-band antenna is proposed for mitigating the multi-path interference in the global navigation satellite system(GNSS) applications. The radiation patches consist of a shortedannular-ring reduced-surface-wave(SAR-RSW) element and an inverted-shorted-annular-ring reduced-surface-wave(ISAR-RSW)element. One key feature of the design is the proximity-coupled probe feeds to increase impedance bandwidth. The other is the defected ground structure band rejection filters to suppress the interaction effect between the SAR-RSW and the ISAR-RSW elements. In addition, trans-directional couplers are used to obtain tight coupling. Measurement results indicate that the antenna has a larger than 10 d B return loss bandwidth and a less than 3 d B axial-ratio(AR) bandwidth in the range of(1.164 – 1.255) GHz and(1.552 – 1.610) GHz. The gain of the passive antenna in the whole operating band is more than 7 d Bi.
基金supported by the National Natural Science Foundation of China(Nos.61032002,71020107027,71001075,and 60902026)Chinese Important National Science & Technology Specific Projects(No.2011ZX03001-007-01)
文摘A signal detection algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) sys- tem in the presence of fast time-varying channel. The channel is represented by a piece-wise linear variant model with normalized Doppler frequency of less than 0.2. The channel parameters are extracted through ISI/ICI (inter-symbol in- terference/inter-carrier interference) cancellation and circular convolution reconstruction. Meanwhile, an improved OFDM symbol detection algorithm is also proposed based on circular convolution reconstruction. The channel state in- formation in the OFDM symbol duration can be obtained accurately from the adjacent two block pilots in a linear model. The simulation results show that the proposed method can not only track the channel variation, but also promise better performance gain in the OFDM symbol detection. Furthermore, the bit error ratio (BER) is close to the perform- ance with the perfect channel state information.
文摘Pattern Time Delay Shift Coding (PDS) scheme is robust for underwater acoustic communication. The digital information are encoded in the time delay shift values of the Pattern, so the PDS scheme belongs to the Pulse Position Modulation (PPM). Several Patterns are selected for code division that the communication system could have a high ability to mitigate the inter-symbol interference (ISI) caused by multipath channel. Four communication channels work on the same time divided by different frequency, which lead to 1000bits/s of the data rate of communication. The simulation experiments show that the PDS system could adapt to many underwater acoustic channels for high data rate and high reliability.
基金Supported by the National Natural Science Foundation of China (No. 60572176)
文摘A new method called joint Matched Filter (MF) combining and turbo equalization is proposed for wireless communications over Inter-Symbol Interference (ISI) channels with diversity reception. This method takes diversity combining and equalization as integrity and need just one turbo equalizer for all diversity branches. Computer simulations prove that our method can take advantage of turbo equalization and diversity reception to combat fading of wireless channels.
文摘This letter presents the principles of Coded Orthogonal Frequency Division Multiplexing (COFDM) system and focuses on the effect of the Guard Interval (GI) on the systemperformance. The role of the GI parameter period to solve the problem of interferences that occur at the receiver is discussed. A new COFDM concept with a Variable GI (VGI) is proposed in order to improve the Bit Error Rate (BER) performance in the presence of multipaths with variable delays. A series of simulations have been carried out on the BER performance as a function of GI, maximum delay spread, and Signal-to-Noise Ratio (SNR), with QPSK as modulation scheme over multipath fading and Additive White Gaussian Noise (AWGN). The results show that the optimum values of the GI parameter approximately equal to the maximum delay spread, and the proposed system with VGI provides a better performance compared with the fixed length GI.
文摘Recently, two expressions (for the noiseless and noisy case) were proposed for the residual inter-symbol interference (ISI) obtained by blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. However, those expressions are not applicable for biased input signals. In this paper, a closed-form approximated expression is proposed for the residual ISI applicable for the noisy and biased input case. This new proposed expression is valid for blind adaptive equalizers, where the error of the equalized output signal may be expressed as a polynomial function of order 3. The new proposed expression depends on the equalizer’s tap length, input signal statistics, channel power, SNR, step-size parameter and on the input signal’s bias. Simulation results indicate a high correlation between the simulated results and those obtained from our new proposed expression.
基金the National Natural Science Foundation of China(No.60172048)
文摘An increasing demand for high data rate transmission and protection over bandlimited channels with severe inter-symbol interference has resulted in a flurry of activity to improve channel equalization, In conjunction with equalization, channel coding-decoding can be employed to improve system performance. In this letter, the performance of the three stage turbo-equalization-decoding employing log maximum a posteriori probability is experimentally evaluated by a fading simulator. The BER is evaluated using various information sequence and interleaver sizes taking into account that the communication medium is a noisy inter symbol interference channel.
基金supported by the National Natural Science Foundation of China(No.61071016)
文摘In low-frequency elastic wave through-the-earth communication system,because of multipath transmission caused by characteristics of the layered earth,the time domain equalizer is different from other wireless communication systems.A modified LMS algorithm of variable step size is proposed based on improvement of traditional LMS.On the base of principle and simulation analysis,the improved Least Mean Square(LMS)algorithm is analyzed and the performances are compared between the improved LMS algorithm and traditional LMS algorithm.In the improved algorithm,the contradiction between convergence speed and the steady-state error is considered at the same time.Therefore,the improved algorithm has good convergence properties and channel-tracking performance.
文摘This paper treats the digital design of a probabilistic energy equalizer for impulse radio (IR) UWB receiver in high data rate (100Mbps). The aim of this study is to bypass certain complex mathematical function as a chi-squared distribution and reduce the computational complexity of the equalizer for a low cost hardware implementation. As in Sub-MAP algorithm, the max* operation is investigated for complexity reduction and tested by computer simulation with fixed point data types under 802.15.3a channel models. The obtained re-sults prove that the complexity reduction involves a very slight algorithm deterioration and still meet the low-cost constraint of the implementation.
基金the National Basic Research Development Program of China (Grant No. 2003CB314805)the National Nature Science Foundation of China (Grant No. 60603022)
文摘As an important secure routing mechanism, multi-path routing is one of the major ways to improve network efficiency and to guarantee the network security, which ensures the reliability of data transmission by using backup paths when the primary one is unavailable due to local node or link failures. Most current studies on multi-path routing mechanism are based on experiments or simulations. The resulta are usually specific application scenarios oriented heuristic algorithms, lacking universal significance. In this paper, a theoretic analysis is performed on the relationship between the multi-path routing policy, the network efficiency and its survivability. Starting with point-to-point communication network, an impactoriented analysis is made on the network interference under multi-path routing mechanism. Based on the analysis, the upper-limit of network performance under interference impact is also discussed.
基金supported by the National Natural Science Foundation of China (No. 91438116)by the Program for New Century Excellent Talents in University of China (No. NCET-12-0030)+1 种基金by the National Hi-Tech R&D Program of China (No. 2015AA7014065)by the Shanghai Aerospace Science and Technology Innovation Fund (No. SAST2015089)
文摘In this paper,a Doppler scaling fast Fourier transform(Doppler-FFT)algorithm for filter bank multi-carrier(FBMC)is proposed,which can efficiently eliminate the impact of the Doppler scaling in satellite communications.By introducing a Doppler scaling factor into the butterfly structure of the fast Fourier transform(FFT)algorithm,the proposed algorithm eliminates the differences between the Doppler shifts of the received subcarriers,and maintains the same order of computational complexity compared to that of the traditional FFT.In the process of using the new method,the Doppler scaling should be estimated by calculating the orbital data in advance.Thus,the inter-symbol interference(ISI)and the inter-carrier interference(ICI)can be completely eliminated,and the signal to interference and noise ratio(SINR)will not be affected.Simulation results also show that the proposed algorithm can achieve a 0.4 d B performance gain compared to the frequency domain equalization(FDE)algorithm in satellite communications.
基金supported by the National Natural Science Foundation of China(No.11804225)sponsored by Shanghai Gaofeng&Gaoyuan Project for University Academic Program Development。
文摘Recently,the nested Mach–Zehnder interferometer[Phys.Rev.Lett.111,240402(2013)]was modified by adding Dove prisms in a paper[Quantum Stud.:Math.Found.2,255(2015)],and an interesting result is that,after the Dove prisms were inserted,a signal at the first mirror of the nested interferometer was obtained.But,according to the former original paper,the photons have never been present near that mirror.In this work,we interpret this result naturally by resorting to the three-path interference method.Moreover,we find that even though the photons have been somewhere,they can hide the trace of being there.