Compressive sensing (CS) is a new attractive technique adopted for Linear Time Varying channel estimation. orthogonal frequency division multiplexing (OFDM) was proposed to be used in 4G and 5G which supports high data rate requirements. Different pilot aided channel estimation techniques were proposed to better track the channel conditions, which consumes bandwidth, thus, considerable data rate reduced. In order to estimate the channel with minimum number of pilots, compressive sensing CS was proposed to efficiently estimate the channel variations. In this paper, a novel delay dictionary-based CS was designed and simulated to estimate the linear time varying (LTV) channel. The proposed dictionary shows the suitability of estimating the channel impulse response (CIR) with low to moderate Doppler frequency shifts with acceptable bit error rate (BER) performance.
Method for Converter Synchronization with RF InjectionCSCJournals
This paper presents an injection method for synchronizing analog to digital converters (ADC). This approach can eliminate the need for precision routed discrete synchronization signals of current technologies, such as JESD204. By eliminating the setup and hold time requirements at the conversion (or near conversion) clock rate, higher sample rate systems can be synchronized. Measured data from an existing multiple ADC conversion system was used to evaluate the method. Coherent beams were simulated to measure the effectiveness of the method. The results show near theoretical coherent processing gain.
Analysis Predicted Location of Harmonic Distortion in RF Upconverter StructureTELKOMNIKA JOURNAL
A new mathematical analysis to predict the magnitude size of the distortion products from the
signal up-conversion process output is presented. The signal up-conversion process converts the digital
baseband from the analog baseband into a radio frequency signal. When the signal baseband involves
frequency offsetting then occurring a number of distortion products which can reduce the dynamic range
so it is difficult to meet the spectrum mask requirements within the operating band. This paper will focus on
methods of new mathematical analysis using a continuous frequency range and only applies to a single
side band tone, with constant amplitude into any value of frequency offsets. The novel contribution to the
analysis starts at generating the gate signal and convolution of the gate signal into the reference carrier
signal. The results show very close between the simulation results and the calculation of the predicted
location of the distortions.
In this paper, we analyzed a numerical evaluation of the performance of MIMO radio systems in the LTE network environment. Downlink physical layer of the OFDM-MIMO based radio interface is considered for system model and a theoretical analysis of the bit error rate of the two space-time codes (SFBC 2×1 and FSTD 4×2 codes are adopted by the LTE norm as a function of the signal to noise ratio. Analytical expressions are given for transmission over a Rayleigh channel without spatial correlation which is then compared with Monte-Carlo simulations. Further evaluated channel capacity and simulation results show throughput almost reaches to the capacity limit.
Method for Converter Synchronization with RF InjectionCSCJournals
This paper presents an injection method for synchronizing analog to digital converters (ADC). This approach can eliminate the need for precision routed discrete synchronization signals of current technologies, such as JESD204. By eliminating the setup and hold time requirements at the conversion (or near conversion) clock rate, higher sample rate systems can be synchronized. Measured data from an existing multiple ADC conversion system was used to evaluate the method. Coherent beams were simulated to measure the effectiveness of the method. The results show near theoretical coherent processing gain.
Analysis Predicted Location of Harmonic Distortion in RF Upconverter StructureTELKOMNIKA JOURNAL
A new mathematical analysis to predict the magnitude size of the distortion products from the
signal up-conversion process output is presented. The signal up-conversion process converts the digital
baseband from the analog baseband into a radio frequency signal. When the signal baseband involves
frequency offsetting then occurring a number of distortion products which can reduce the dynamic range
so it is difficult to meet the spectrum mask requirements within the operating band. This paper will focus on
methods of new mathematical analysis using a continuous frequency range and only applies to a single
side band tone, with constant amplitude into any value of frequency offsets. The novel contribution to the
analysis starts at generating the gate signal and convolution of the gate signal into the reference carrier
signal. The results show very close between the simulation results and the calculation of the predicted
location of the distortions.
In this paper, we analyzed a numerical evaluation of the performance of MIMO radio systems in the LTE network environment. Downlink physical layer of the OFDM-MIMO based radio interface is considered for system model and a theoretical analysis of the bit error rate of the two space-time codes (SFBC 2×1 and FSTD 4×2 codes are adopted by the LTE norm as a function of the signal to noise ratio. Analytical expressions are given for transmission over a Rayleigh channel without spatial correlation which is then compared with Monte-Carlo simulations. Further evaluated channel capacity and simulation results show throughput almost reaches to the capacity limit.
Singular Value Decomposition: Principles and Applications in Multiple Input M...IJCNCJournal
The authors discuss the importance of using the singular value decomposition (SVD) in computing the capacity of multiple input multiple output (MIMO) and in estimation the channel gain from the transmitter to the receiver. Examples that show how the SVD simplifies computing the MIMO channel capacity are discussed. Numerical results that show what factors determine the performance of using SVD in channel
estimation are also discussed.
Performance Analysis of Ultra Wideband Receivers for High Data Rate Wireless ...graphhoc
For high data rate ultra wideband communication system, performance comparison of Rake, MMSE and Rake-MMSE receivers is attempted in this paper. Further a detail study on Rake-MMSE time domain equalizers is carried out taking into account all the important parameters such as the effect of the number of Rake fingers and equalizer taps on the error rate performance. This receiver combats inter-symbol interference by taking advantages of both the Rake and equalizer structure. The bit error rate performances are investigated using MATLAB simulation on IEEE 802.15.3a defined UWB channel models. Simulation results show that the bit error rate probability of Rake-MMSE receiver is much better than Rake receiver and MMSE equalizer. Study on non-line of sight indoor channel models illustrates that bit error rate performance of Rake-MMSE (both LE and DFE) improves for CM3 model with smaller spread compared to CM4 channel model. It is indicated that for a MMSE equalizer operating at low to medium SNR values, the number of Rake fingers is the dominant factor to improve system performance, while at high SNR values the number of equalizer taps plays a more significant role in reducing the error rate.
Improved Timing Estimation Using Iterative Normalization Technique for OFDM S...IJECEIAES
Conventional timing estimation schemes based on autocorrelation experience perfor- mance degradation in the multipath channel environment with high delay spread. To overcome this problem, we proposed an improvement of the timing estimation for the OFDM system based on statistical change of symmetrical correlator. The new method uses iterative normalization technique to the correlator output before the detection based on statistical change of symmetric correlator is applied. Thus, it increases the detection probability and achieves better performance than previously published methods in the multipath environment. Computer simulation shows that our method is very robust in the fading multipath channel.
A COMPARATIVE PERFORMANCE STUDY OF OFDM SYSTEM WITH THE IMPLEMENTATION OF COM...ijcsa
This paper presents a comparative performance analysis of wireless orthogonal frequency division multiplexing (OFDM) system with the implementation of comb type pilot-based channel estimation algorithm over frequency selective multi-path fading channels. The Minimum Mean Square Error (MMSE) method is used for the estimation of channel at pilot frequencies. For the estimation of channel at data frequencies different interpolation techniques such as low-pass, linear, and second order interpolation are employed. The OFDM system simulation has been carried out with Matlab and the performance is analyzed in terms of bit error rate (BER) for various signal mapping (BPSK, QPSK, 4QAM, 16QAM, and 64QAM) and channel (Rayleigh and Rician) conditions. The impact of selecting number of channel taps on the BER performance is also investigated.
Performance Analysis of Differential Beamforming in Decentralized NetworksIJECEIAES
This paper proposes and analyzes a novel differential distributed beamforming strategy for decentralized two-way relay networks. In our strategy, the phases of the received signals at all relays are synchronized without requiring channel feedback or training symbols. Bit error rate (BER) expressions of the proposed strategy are provided for coherent and differential M-PSK modulation. Upper bounds, lower bounds, and simple approximations of the BER are also derived. Based on the theoretical and simulated BER performance, the proposed strategy offers a high system performance and low decoding complexity and delay without requiring channel state information at any transmitting or receiving antenna. Furthermore, the simple approximation of the BER upper bound shows that the proposed strategy enjoys the full diversity gain which is equal to the number of transmitting antennas.
Discrete-wavelet-transform recursive inverse algorithm using second-order est...TELKOMNIKA JOURNAL
The recursive-least-squares (RLS) algorithm was introduced as an alternative to LMS algorithm with enhanced performance. Computational complexity and instability in updating the autocolleltion matrix are some of the drawbacks of the RLS algorithm that were among the reasons for the intrduction of the second-order recursive inverse (RI) adaptive algorithm. The 2nd order RI adaptive algorithm suffered from low convergence rate in certain scenarios that required a relatively small initial step-size. In this paper, we propose a newsecond-order RI algorithm that projects the input signal to a new domain namely discrete-wavelet-transform (DWT) as pre step before performing the algorithm. This transformation overcomes the low convergence rate of the second-order RI algorithm by reducing the self-correlation of the input signal in the mentioned scenatios. Expeirments are conducted using the noise cancellation setting. The performance of the proposed algorithm is compared to those of the RI, original second-order RI and RLS algorithms in different Gaussian and impulsive noise environments. Simulations demonstrate the superiority of the proposed algorithm in terms of convergence rate comparedto those algorithms.
Emulation OF 3gpp Scme CHANNEL MODELS USING A Reverberation Chamber MEASUREME...IJERA Editor
The MIMO OTA way forward was approved at the 3GPP RAN4 #62bis meeting in Jeju (Korea) [1], and among
the remaining works to be accomplished it was highlighted that the channel model had to be validated across
methods in order to ensure that a minimal number of artifacts are inserted into the channel model by any given
methodology and that the different methods reproduce, and the DUT experiences, the same radio conditions
regardless of the methodology.The objective of this contribution is to validate the power delay profile (PDP) for
the 3GPP SCME Urban macro (UMA) and Urban micro (UMI) channel models emulated in a mode-stirred
reverberation chamber for the reverberation chamber
NEW BER ANALYSIS OF OFDM SYSTEM OVER NAKAGAMI-n (RICE) FADING CHANNELijcseit
Modern wireless communication systems support high speed multimedia services. These services require
high data rates with acceptable error rates. Orthogonal Frequency Division Multiplexing (OFDM) is a
capable candidate to solve this problem. In this paper, a new expression for the BER of OFDM system has
been derived over Nakagami–n (Rice) fading channels using characteristics function (CHF) approach. The
exact probability density function of first order of Nakagami-n (Rice) random vector is used to derive the
expression for the error rates of OFDM system. The BER derivation of Rician fading channel is slightly
more complex compared to the Nakagami–m distribution because the PDF of the Rician RV contains an
explicit term of a modified Bessel function of first kind. Earlier, this problem was solved by replacing the
Bessel function with its infinite series and exponential integral representation. Here we propose an integral
expression to remove the complexity of the expression.
Projected Barzilai-Borwein Methods Applied to Distributed Compressive Spectru...Polytechnique Montreal
Cognitive radio allows unlicensed (cognitive) users to use licensed frequency bands by exploiting spectrum sensing techniques to detect whether or not the licensed (primary) users are present. In this paper, we present a compressed sensing applied to spectrum-occupancy detection in wide-band applications. The collected analog signals from each cognitive radio (CR) receiver at a fusion center are transformed to discrete-time signals by using analog-to-information converter (AIC) and then employed to calculate the autocorrelation. For signal reconstruction, we exploit a novel approach to solve the optimization problem consisting of minimizing both a quadratic (l2) error term and an l1-regularization term. In specific, we propose the Basic gradient projection (GP) and projected Barzilai-Borwein (PBB) algorithm to offer a better performance in terms of the mean squared error of the power spectrum density estimate and the detection probability of licensed signal occupancy.
Modified Whitening Rotation based Joint Semi-blind Channel and Data Estimatio...IDES Editor
In this paper, we propose a novel joint semi-blind
channel and data estimation technique based on Whitening
Rotation (WR) method for Rayleigh flat fading Multiple Input
Multiple output (MIMO) channel using different receiver
antennas combinations. Here we divide newly proposed
technique in three steps. In the first step, we use conventional
Whitening Rotation based semi-blind channel estimation
technique, where MIMO channel matrix H can be decomposed
as H=WQ H . Whitening matrix W can be estimated blindly
using second order statistical information of received data
and unitary rotation matrix Q can be estimated exclusively
using Orthogonal Pilot Maximum Likelihood (OPML)
algorithm. In the second step, data symbols can be estimated
using estimated channel H and received output data by
applying maximum likelihood data estimation method.
Finally in the third step, Q can be re-estimated as a Q new
using OPML algorithm by considering estimated blind data
symbols itself as a pilot symbols for more statistical
information of unitary matrix and perform final channel
estimation H final=W Q new H . Simulation results are presented
under 4-PSK data modulation scheme for two transmitters
and different combinations of receiver antennas to support
proposed novel technique and they demonstrate improved BER
performance compared to conventional WR based optimal
technique and Rotation Optimization Maximum Likelihood
(ROML) based suboptimal semi-blind channel estimation
technique.
Orthogonal Frequency Division Multiplexing (OFDM) is of great interest for the development of
the fifth-generation technology. It is the cornerstone of Multiple-input multiple-output (MIMO) systems.
Even though inter carrier interference (ICI) and inter symbol interference (ISI) have been processed for
the fourth-generation standards, they still present a huge problem for the fifth-generation standards. This
paper explores the tradeoff between the length of the cyclic prefix and the performances of the OFDM
system. It also studies the effect of carrier frequency offset (CFO) on OFDM systems. A blind frequency
offset estimator that uses the correlations between the remodulated sequence in the receiver side and
the conventional received symbol is presented and a closed form solution is derived. The proposed
estimator is derived under short interval when the correlation is high, so it has low computational
complexity. Lin and Beek’s estimators are used for comparison. Simulations demonstrate the effectiveness
of the proposed estimator under Rayleigh fading channel.
An identification of the tolerable time-interleaved analog-todigital convert...IJECEIAES
High-speed Terahertz communication systems has recently employed orthogonal frequency division multiplexing approach as it provides high spectral efficiency and avoids inter-symbol interference caused by dispersive channels. Such high-speed systems require extremely high-sampling time-interleaved analog-to-digital converters at the receiver. However, timing mismatch of time-interleaved analog-to-digital converters significantly causes system performance degradation. In this paper, to avoid such performance degradation induced by timing mismatch, we theoretically determine maximum tolerable mismatch levels for orthogonal frequency division multiplexing communication systems. To obtain these levels, we first propose an analytical method to derive the bit error rate formula for quadrature and pulse amplitude modulations in Rayleigh fading channels, assuming binary reflected gray code (BRGC) mapping. Further, from the derived bit error rate (BER) expressions, we reveal a threshold of timing mismatch level for which error floors produced by the mismatch will be smaller than a given BER. Simulation results demonstrate that if we preserve mismatch level smaller than 25% of this obtained threshold, the BER performance degradation is smaller than 0.5 dB as compared to the case without timing mismatch.
Pilot based channel estimation improvement in orthogonal frequency-division m...IJECEIAES
Pilot based least square (LS) channel estimation is a commonly used channel estimation technique in orthogonal frequency-division multiplexing based systems due to its simplicity. However, LS estimation does not handle the noise effect and hence suffers from performance degradation. Since the channel coefficients are correlated in time and hence show a slower variation than the noise, it is possible to encode the channel using linear predictive coding (LPC) without the noise. In this work, the channel is estimated from the pilots using LS estimation and in a second step the channel’s LS estimation is encoded as LPC coefficients to produce an improved channel estimation. The estimation technique is simulated for space-time block coding (STBC) based orthogonal frequency-division multiplexing (OFDM) system and the bit error rate (BER) curves show improvement of the LPC estimation over the LS estimation of the channel.
Singular Value Decomposition: Principles and Applications in Multiple Input M...IJCNCJournal
The authors discuss the importance of using the singular value decomposition (SVD) in computing the capacity of multiple input multiple output (MIMO) and in estimation the channel gain from the transmitter to the receiver. Examples that show how the SVD simplifies computing the MIMO channel capacity are discussed. Numerical results that show what factors determine the performance of using SVD in channel
estimation are also discussed.
Performance Analysis of Ultra Wideband Receivers for High Data Rate Wireless ...graphhoc
For high data rate ultra wideband communication system, performance comparison of Rake, MMSE and Rake-MMSE receivers is attempted in this paper. Further a detail study on Rake-MMSE time domain equalizers is carried out taking into account all the important parameters such as the effect of the number of Rake fingers and equalizer taps on the error rate performance. This receiver combats inter-symbol interference by taking advantages of both the Rake and equalizer structure. The bit error rate performances are investigated using MATLAB simulation on IEEE 802.15.3a defined UWB channel models. Simulation results show that the bit error rate probability of Rake-MMSE receiver is much better than Rake receiver and MMSE equalizer. Study on non-line of sight indoor channel models illustrates that bit error rate performance of Rake-MMSE (both LE and DFE) improves for CM3 model with smaller spread compared to CM4 channel model. It is indicated that for a MMSE equalizer operating at low to medium SNR values, the number of Rake fingers is the dominant factor to improve system performance, while at high SNR values the number of equalizer taps plays a more significant role in reducing the error rate.
Improved Timing Estimation Using Iterative Normalization Technique for OFDM S...IJECEIAES
Conventional timing estimation schemes based on autocorrelation experience perfor- mance degradation in the multipath channel environment with high delay spread. To overcome this problem, we proposed an improvement of the timing estimation for the OFDM system based on statistical change of symmetrical correlator. The new method uses iterative normalization technique to the correlator output before the detection based on statistical change of symmetric correlator is applied. Thus, it increases the detection probability and achieves better performance than previously published methods in the multipath environment. Computer simulation shows that our method is very robust in the fading multipath channel.
A COMPARATIVE PERFORMANCE STUDY OF OFDM SYSTEM WITH THE IMPLEMENTATION OF COM...ijcsa
This paper presents a comparative performance analysis of wireless orthogonal frequency division multiplexing (OFDM) system with the implementation of comb type pilot-based channel estimation algorithm over frequency selective multi-path fading channels. The Minimum Mean Square Error (MMSE) method is used for the estimation of channel at pilot frequencies. For the estimation of channel at data frequencies different interpolation techniques such as low-pass, linear, and second order interpolation are employed. The OFDM system simulation has been carried out with Matlab and the performance is analyzed in terms of bit error rate (BER) for various signal mapping (BPSK, QPSK, 4QAM, 16QAM, and 64QAM) and channel (Rayleigh and Rician) conditions. The impact of selecting number of channel taps on the BER performance is also investigated.
Performance Analysis of Differential Beamforming in Decentralized NetworksIJECEIAES
This paper proposes and analyzes a novel differential distributed beamforming strategy for decentralized two-way relay networks. In our strategy, the phases of the received signals at all relays are synchronized without requiring channel feedback or training symbols. Bit error rate (BER) expressions of the proposed strategy are provided for coherent and differential M-PSK modulation. Upper bounds, lower bounds, and simple approximations of the BER are also derived. Based on the theoretical and simulated BER performance, the proposed strategy offers a high system performance and low decoding complexity and delay without requiring channel state information at any transmitting or receiving antenna. Furthermore, the simple approximation of the BER upper bound shows that the proposed strategy enjoys the full diversity gain which is equal to the number of transmitting antennas.
Discrete-wavelet-transform recursive inverse algorithm using second-order est...TELKOMNIKA JOURNAL
The recursive-least-squares (RLS) algorithm was introduced as an alternative to LMS algorithm with enhanced performance. Computational complexity and instability in updating the autocolleltion matrix are some of the drawbacks of the RLS algorithm that were among the reasons for the intrduction of the second-order recursive inverse (RI) adaptive algorithm. The 2nd order RI adaptive algorithm suffered from low convergence rate in certain scenarios that required a relatively small initial step-size. In this paper, we propose a newsecond-order RI algorithm that projects the input signal to a new domain namely discrete-wavelet-transform (DWT) as pre step before performing the algorithm. This transformation overcomes the low convergence rate of the second-order RI algorithm by reducing the self-correlation of the input signal in the mentioned scenatios. Expeirments are conducted using the noise cancellation setting. The performance of the proposed algorithm is compared to those of the RI, original second-order RI and RLS algorithms in different Gaussian and impulsive noise environments. Simulations demonstrate the superiority of the proposed algorithm in terms of convergence rate comparedto those algorithms.
Emulation OF 3gpp Scme CHANNEL MODELS USING A Reverberation Chamber MEASUREME...IJERA Editor
The MIMO OTA way forward was approved at the 3GPP RAN4 #62bis meeting in Jeju (Korea) [1], and among
the remaining works to be accomplished it was highlighted that the channel model had to be validated across
methods in order to ensure that a minimal number of artifacts are inserted into the channel model by any given
methodology and that the different methods reproduce, and the DUT experiences, the same radio conditions
regardless of the methodology.The objective of this contribution is to validate the power delay profile (PDP) for
the 3GPP SCME Urban macro (UMA) and Urban micro (UMI) channel models emulated in a mode-stirred
reverberation chamber for the reverberation chamber
NEW BER ANALYSIS OF OFDM SYSTEM OVER NAKAGAMI-n (RICE) FADING CHANNELijcseit
Modern wireless communication systems support high speed multimedia services. These services require
high data rates with acceptable error rates. Orthogonal Frequency Division Multiplexing (OFDM) is a
capable candidate to solve this problem. In this paper, a new expression for the BER of OFDM system has
been derived over Nakagami–n (Rice) fading channels using characteristics function (CHF) approach. The
exact probability density function of first order of Nakagami-n (Rice) random vector is used to derive the
expression for the error rates of OFDM system. The BER derivation of Rician fading channel is slightly
more complex compared to the Nakagami–m distribution because the PDF of the Rician RV contains an
explicit term of a modified Bessel function of first kind. Earlier, this problem was solved by replacing the
Bessel function with its infinite series and exponential integral representation. Here we propose an integral
expression to remove the complexity of the expression.
Projected Barzilai-Borwein Methods Applied to Distributed Compressive Spectru...Polytechnique Montreal
Cognitive radio allows unlicensed (cognitive) users to use licensed frequency bands by exploiting spectrum sensing techniques to detect whether or not the licensed (primary) users are present. In this paper, we present a compressed sensing applied to spectrum-occupancy detection in wide-band applications. The collected analog signals from each cognitive radio (CR) receiver at a fusion center are transformed to discrete-time signals by using analog-to-information converter (AIC) and then employed to calculate the autocorrelation. For signal reconstruction, we exploit a novel approach to solve the optimization problem consisting of minimizing both a quadratic (l2) error term and an l1-regularization term. In specific, we propose the Basic gradient projection (GP) and projected Barzilai-Borwein (PBB) algorithm to offer a better performance in terms of the mean squared error of the power spectrum density estimate and the detection probability of licensed signal occupancy.
Modified Whitening Rotation based Joint Semi-blind Channel and Data Estimatio...IDES Editor
In this paper, we propose a novel joint semi-blind
channel and data estimation technique based on Whitening
Rotation (WR) method for Rayleigh flat fading Multiple Input
Multiple output (MIMO) channel using different receiver
antennas combinations. Here we divide newly proposed
technique in three steps. In the first step, we use conventional
Whitening Rotation based semi-blind channel estimation
technique, where MIMO channel matrix H can be decomposed
as H=WQ H . Whitening matrix W can be estimated blindly
using second order statistical information of received data
and unitary rotation matrix Q can be estimated exclusively
using Orthogonal Pilot Maximum Likelihood (OPML)
algorithm. In the second step, data symbols can be estimated
using estimated channel H and received output data by
applying maximum likelihood data estimation method.
Finally in the third step, Q can be re-estimated as a Q new
using OPML algorithm by considering estimated blind data
symbols itself as a pilot symbols for more statistical
information of unitary matrix and perform final channel
estimation H final=W Q new H . Simulation results are presented
under 4-PSK data modulation scheme for two transmitters
and different combinations of receiver antennas to support
proposed novel technique and they demonstrate improved BER
performance compared to conventional WR based optimal
technique and Rotation Optimization Maximum Likelihood
(ROML) based suboptimal semi-blind channel estimation
technique.
Orthogonal Frequency Division Multiplexing (OFDM) is of great interest for the development of
the fifth-generation technology. It is the cornerstone of Multiple-input multiple-output (MIMO) systems.
Even though inter carrier interference (ICI) and inter symbol interference (ISI) have been processed for
the fourth-generation standards, they still present a huge problem for the fifth-generation standards. This
paper explores the tradeoff between the length of the cyclic prefix and the performances of the OFDM
system. It also studies the effect of carrier frequency offset (CFO) on OFDM systems. A blind frequency
offset estimator that uses the correlations between the remodulated sequence in the receiver side and
the conventional received symbol is presented and a closed form solution is derived. The proposed
estimator is derived under short interval when the correlation is high, so it has low computational
complexity. Lin and Beek’s estimators are used for comparison. Simulations demonstrate the effectiveness
of the proposed estimator under Rayleigh fading channel.
An identification of the tolerable time-interleaved analog-todigital convert...IJECEIAES
High-speed Terahertz communication systems has recently employed orthogonal frequency division multiplexing approach as it provides high spectral efficiency and avoids inter-symbol interference caused by dispersive channels. Such high-speed systems require extremely high-sampling time-interleaved analog-to-digital converters at the receiver. However, timing mismatch of time-interleaved analog-to-digital converters significantly causes system performance degradation. In this paper, to avoid such performance degradation induced by timing mismatch, we theoretically determine maximum tolerable mismatch levels for orthogonal frequency division multiplexing communication systems. To obtain these levels, we first propose an analytical method to derive the bit error rate formula for quadrature and pulse amplitude modulations in Rayleigh fading channels, assuming binary reflected gray code (BRGC) mapping. Further, from the derived bit error rate (BER) expressions, we reveal a threshold of timing mismatch level for which error floors produced by the mismatch will be smaller than a given BER. Simulation results demonstrate that if we preserve mismatch level smaller than 25% of this obtained threshold, the BER performance degradation is smaller than 0.5 dB as compared to the case without timing mismatch.
Pilot based channel estimation improvement in orthogonal frequency-division m...IJECEIAES
Pilot based least square (LS) channel estimation is a commonly used channel estimation technique in orthogonal frequency-division multiplexing based systems due to its simplicity. However, LS estimation does not handle the noise effect and hence suffers from performance degradation. Since the channel coefficients are correlated in time and hence show a slower variation than the noise, it is possible to encode the channel using linear predictive coding (LPC) without the noise. In this work, the channel is estimated from the pilots using LS estimation and in a second step the channel’s LS estimation is encoded as LPC coefficients to produce an improved channel estimation. The estimation technique is simulated for space-time block coding (STBC) based orthogonal frequency-division multiplexing (OFDM) system and the bit error rate (BER) curves show improvement of the LPC estimation over the LS estimation of the channel.
Turbo Detection in Rayleigh flat fading channel with unknown statisticsijwmn
The turbo detection of turbo coded symbols over correlated Rayleigh flat fading channels generated
according to Jakes’ model is considered in this paper. We propose a method to estimate the channel
signal-to-noise ratio (SNR) and the maximum Doppler frequency. These statistics are required by
the linear minimum mean squared error (LMMSE) channel estimator. To improve the system convergence, we redefine the channel reliability factor by taking into account the channel estimation
error statistics. Simulation results for rate 1/3 turbo code and two different normalized fading rates
show that the use of the new reliability factor greatly improves the performance. The improvement
is more substantial when channel statistics are unknown.
MIMO Channel Estimation Using the LS and MMSE AlgorithmIOSRJECE
Wireless Communication Technology has developed over the past few yearsfor other objectives.The Multiple InputMultiple Output (MIMO) is one of techniques that is used to enhancethe data rates, in which multiple antennas are employed both the transmitter and receiver. Multiple signals are transmitted from different antennas at the transmitter using the same frequency and separated space. Various channel estimation techniques are employed in order to judge the physical effects of the medium present. In this paper, we analyze and implementvarious estimation techniques for MIMO Systems such as Least Squares (LS), Minimum Mean Square Error (MMSE),these techniques are therefore compared to effectively estimate the channel in MIMO System. The results demonstrate that SNR required to support different values of bit error rate varies depending on different low correlation between the transmitting and the receiving antennas .In addition, it is illustrated that when the number of transmitter and receiver antennas increases, the performance of TBCE schemes significantly improves. The Same behavior isalso observed for MIMO system. Performance of both MMSE and LSestimation are the same for allkinds of modulation at small value of SNR but the more we increase the SNR value the more performance gap goes on increasing.
CHANNEL ESTIMATION AND MULTIUSER DETECTION IN ASYNCHRONOUS SATELLITE COMMUNIC...ijwmn
In this paper, we propose a new method of channel estimation for asynchronous additive white Gaussian noise channels in satellite communications. This method is based on signals correlation and multiuser interference cancellation which adopts a successive structure. Propagation delays and signals amplitudes are jointly estimated in order to be used for data detection at the receiver. As, a multiuser detector, a single stage successive interference cancellation (SIC) architecture is analyzed and integrated to the channel estimation technique and the whole system is evaluated. The satellite access method adopted is the direct sequence code division multiple access (DS CDMA) one. To evaluate the channel estimation and the detection technique, we have simulated a satellite uplink with an asynchronous multiuser access.
Using the Channel State Information (CSI) at the transmitter is fundamental for the precoder
design in Multi-user Multiple Input Single Output (MU-MISO-OFDM) systems. In Frequency
Division Duplex (FDD) systems, CSI can be just available at the transmitter through a limited
feedback channel [1], where we assume that each user quantizes its channel direction with a
finite number of quantization bits. In this paper, we consider a scalar quantization (SQ) scheme
of the Channel Direction Information (CDI). Although vector quantization (VQ) schemes [2],
[3] still outperform this scalar scheme in terms of quantization error and Sum rate, the former
scheme suffers from an exponential search complexity and high storage requirements at the
receiver for high number of feedback bits.
Multi-carrier Equalization by Restoration of RedundancY (MERRY) for Adaptive ...IJNSA Journal
This paper proposes a new blind adaptive channel shortening approach for multi-carrier systems. The performance of the discrete Fourier transform-DMT (DFT-DMT) system is investigated with the proposed DST-DMT system over the standard carrier serving area (CSA) loop1. Enhanced bit rates demonstrated and less complexity also involved by the simulation of the DST-DMT system.
CS Based Channel Estimation for OFDM Systems under Long Delay Channels Using ...IJERA Editor
Orthogonal frequency division multiplexing (OFDM) is a technique which are used in the next-generation wireless communication. Channel estimation in the OFDM technique is one of the big challenges, ever since high-resolution channel estimation can significantly improve the equalization at the receiver and consequently enhance the communication performances. Channel computation using superimposed pilot sequences is also a fully new area, idea for using superimposed pilot sequences has been proposed by various authors for different applications. In this paper, we are introduced a high accurate, low complexity compressive sensing (CS) based channel estimation namely Auxiliary information based Subspace Pursuit (ASP) in TFT-OFDM systems. ASP based channel estimation in TFT-OFDM system is based on two steps. First is, by exploiting the signal structure of recently proposed TDM-OFDM scheme, the supporting channel information is obtained. Second is, we propose the supporting information based subspace pursuit (SP) algorithm to use a very small amount of frequency domain pilots embedded in the OFDM block used for the exact channel estimation. Moreover, the obtained auxiliary channel information is adopted to reduce the complexity of the conventional SP algorithm. Simulation results demonstrate a important reduction of the number of pilots relative to least-squares channel estimation and supporting high-order modulations like 256 QAM.
A novel and efficient mixed-signal compressed sensing for wide-band cognitive...Polytechnique Montreal
In cognitive radio (CR) networks, unlicensed (cognitive) users can exploit the licensed frequency bands by using spectrum sensing techniques to identify spectrum holes. This paper proposes a distributed compressive spectrum sensing scheme, in which the modulated wide-band converter can apply compressed sensing (CS) directly to analog signals at the sub-Nyquist rate and the central fusion receives signals from multiple CRs and exploits the multiple-measurements-vectors (MMV) subspace pursuit (M-SP) algorithm to jointly reconstruct the spectral support of the wide-band signal. This support is then used to detect whether the licensed bands are occupy or not. Finally, extensive simulation results show the advantages of the proposed scheme. Besides, we also compare the performance of M-SP with M-orthogonal matching pursuit (M-OMP) algorithms.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Classical Discrete-Time Fourier TransformBased Channel Estimation for MIMO-OF...IJCSEA Journal
In this document, we look at various time domain channel estimation methods with this constraint of null carriers at spectrumborders.We showin detail howto gauge the importance of the “border effect” depending on the number of null carriers, which may vary from one system to another. Thereby we assess the limit of the technique discussed when the number of null carriers is large. Finally the DFT with the truncated singular value decomposition (SVD) technique is proposed to completely eliminate the impact of the null subcarriers whatever their number. A technique for the determination of the truncation threshold for any MIMO-OFDM system is also proposed.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Performance evaluation of high mobility OFDM channel estimation techniques IJECEIAES
In wireless communication, Orthogonal Frequency Division Multiplexing (OFDM) has been adopted due to its robustness to multipath fading and high data rate transmissions. At the other hand, the performance of OFDM systems severely degraded due to multi-path fading and Doppler frequency shifts in mobile systems, which causes inter-carrier-interference (ICI). Thus, Estimation of channel parameters is required at the receiver using a pre designed estimator where pilot tones are inserted in each OFDM symbol. In this paper, a random pilot data are generated and inserted in each OFDM symbol at equally spaced locations. The performance test of Least Square (LS) and Linear Minimum Mean Square (LMMSE) estimation methods are proposed with Discrete Fourier Transform (DFT) based on both LS and LMMSE, where different ITU channel models are considered in order to compare their performance for data transmission in high mobile systems with different Doppler frequencies exceeds 200 Hz and minimal number of pilots.
Analysis of Space Time Codes Using Modulation TechniquesIOSR Journals
Abstract: In this Paper, Analysis of channel codes for improving the data rate and reliability of communication over fading channels using multiple transmit antennas has been considered. The codes, namely ’Space Time Codes’ render full diversity and amend coding gain. Performance criteria for designing such codes, under this assumption that the fading is slow and nonselective frequency, is also analysed. Under this research, Study of Frame Error Rate(FER) and outage capacity is compared for different no. Of transmit and receive antennas as well as for different modulation techniques. According to theoretical results FER decreases with increasing SNR and No. Of receiving antennas. Numerical and practical result shows that FER decreases with increasing SNR and no. Of receiving antennas. Keywords: Space time Block Codes ,Space time trellis Codes,Frame Error Rate(FER),Outage capacity,Pairwise Error Probability
Multi carrier equalization by restoration of redundanc y (merry) for adaptive...IJNSA Journal
This paper proposes a new blind adaptive channel shortening approach for multi-carrier systems. The
performance of the discrete Fourier transform-DMT (DFT-DMT) system is investigated with the proposed
DST-DMT system over the standard carrier serving area (CSA) loop1. Enhanced bit rates demonstrated
and less complexity also involved by the simulation of the DST-DMT system.
Performance analysis of adaptive filter channel estimated MIMO OFDM communica...IJECEIAES
Advanced Communication Systems are wideband systems to support multiple applications such as audio, video and data so and so forth. These systems require high spectral efficiency and data rates. In addition, they should provide multipath fading and inter-symbol interference (ISI) free transmission. Multiple input multiple output orthogonal frequency division multiplexing (MIMO OFDM) meets these requirements Hence, MIMOOFDM is the most preferable technique for long term evaluation advanced (LTEA). The primary objective of this paper is to control bit error rate (BER) by proper channel coding, pilot carriers, adaptive filter channel estimation schemes and space time coding (STC). A combination of any of these schemes results in better BER performance over individual schemes. System performance is analyzed for various digital modulation schemes. In this paper, adaptive filter channel estimated MIMO OFDM system is proposed by integrating channel coding, adaptive filter channel estimation, digital modulation and space time coding. From the simulation results, channel estimated 2×2 MIMO OFDM system shows superior performance over individual schemes.
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Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
A novel delay dictionary design for compressive sensing-based time varying channel estimation in OFDM systems
1. TELKOMNIKA Telecommunication, Computing, Electronics and Control
Vol. 18, No. 5, October 2020, pp. 2284~2291
ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018
DOI: 10.12928/TELKOMNIKA.v18i5.14223 2284
Journal homepage: http://journal.uad.ac.id/index.php/TELKOMNIKA
A novel delay dictionary design for compressive sensing-based
time varying channel estimation in OFDM systems
Maryam K. Abboud, Bayan M. Sabbar
College of Information Engineering, Al-Nahrain University, Iraq
Article Info ABSTRACT
Article history:
Received Sep 27, 2019
Revised May 5, 2020
Accepted May 14, 2020
Compressive sensing (CS) is a new attractive technique adopted for linear time
varying channel estimation. orthogonal frequency division multiplexing
(OFDM) was proposed to be used in 4G and 5G which supports high data rate
requirements. Different pilot aided channel estimation techniques were
proposed to better track the channel conditions, which consumes bandwidth,
thus, considerable data rate reduced. In order to estimate the channel with
minimum number of pilots, compressive sensing CS was proposed to
efficiently estimate the channel variations. In this paper, a novel delay
dictionary-based CS was designed and simulated to estimate the linear time
varying (LTV) channel. The proposed dictionary shows the suitability
of estimating the channel impulse response (CIR) with low to moderate
Doppler frequency shifts with acceptable bit error rate (BER) performance.
Keywords:
Channel estimation
Compressive sensing
LTV channel
OFDM
This is an open access article under the CC BY-SA license.
Corresponding Author:
Maryam K. Abboud,
College of Information Engineering,
Al-Nahrain University, Iraq.
Email: maryamkhalifa_90@yahoo.com
1. INTRODUCTION
The performance of high data rate transmissions over wireless fading channels severely degraded due
to the multi path effects which causes inter symbol interference (ISI). In order to combat the fading effects,
OFDM has been widely adopted to wireless transmission [1-8]. The multipath propagation causes a time
varying channel state information (CSI), which needed to be predicated or estimated using channel estimation
techniques in order to recover the transmitted signal. Pilot aided channel estimation is the widely used
technique begins from the traditional techniques such as, least square (LS) and linear minimum mean square
(LMMS), ending with many recent ones used to improve the estimation performance [2, 9].
Compressive sensing (CS) is one of the recent techniques adopted for channel estimation in OFDM
systems by exploiting channel sparsely representation with dictionary basis [10]. Several approaches have been
employed to construct matrices in order to represent the channel in a sparse manner such as, discrete Fourier
transform (DFT) and random dictionaries. These approaches do not consider the time variation property of
the channel since the time varying channel parameters aren't taken into account [11-14].
The main contribution of this paper is, the design of a novel delay dictionary-based CS technique to
overcome the problem of the dictionary proposed by [15] in estimating LTV channel in the presence of Doppler
frequency shifts. In [15], a sample spaced delay dictionary was proposed to recover the CSI using CS in
multiple input multiple output (MIMO)-OFDM system. The concept of the research based on estimate
the channel coefficients for a time varying channel considering the useful OFDM symbol duration regarding
the guard band, and tacking the delay profile into account. Considering channel delay parameters, the dictionary
proposed by [15] improves its ability to recover the CSI even when number of pilots reduced, while it fails
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in estimating LTV channel coefficients in the presence of Doppler effect since it exploits the time variability
characteristic of the channel. Which leads to a conclusion that, the dictionary proposed by [15] can't be applied
for channel estimation in LTV channels since it doesn't sense the Doppler effect of the channel.
The rest of this paper is organized as follows, in section 2, a brief introduction to CS theory introduced
with the required analysis of LTV channel and the proposed system model for sparse channel estimation.
Simulation tests, required system parameters, and test results are introduced in section 3. Finally, the main
concluded remarks and future work are listed in section 4.
2. LTV CHANNEL ANALYSIS AND ESTIMATION BASED CS THEORY
2.1. Compressive sensing
Since the idea behind signal sparsity appears, many publications of sparse signal representations and
compressive sensing introduced especially in signal processing community [16]. With compressive sensing,
a real finite signal 𝑥 ∈ 𝑅 𝑀
, can be expressed in an orthonormal basis;
x = ∑ 𝜓𝑖 𝜃𝑖
𝑀
1 (1)
where 𝜓 = [𝜓1 𝜓2 … 𝜓 𝑀] represents the orthonormal basis, and 𝜃 = [𝜃1 𝜃2 … 𝜃 𝑀] is the sparse vector where
the number of non-zero elements (K<<M) much smaller than the number of zero elements and named as
a K-sparse vector. Using matrix notations, 𝑥 = 𝜓𝜃, where 𝜓 of size M x M [17]. Consider a classical linear
measurement model where 𝑦 = 𝜙𝑥 = 𝜙𝜓𝜃. Where 𝜃 represent the k-sparse vector of size M x 1 to be
estimated using the effective measurement matrix 𝜙𝜓, where the measurement matrix 𝜙 is of size N x M, and
y is the measurement vector of size N x 1. Hence, each observation of y vector represents the projection of
vector x on a row of the sensing matrix 𝜙 as described in Figure 1 [18].
From the mathematical expression of CS in the Figure 1, it is clear that a non-linear system of
equations must be solved to recover the sparse vector 𝜃, where the number of observations N is much less than
number of unknowns M. Since 𝜙 matrix projecting the vector x, low value of incoherence is required to insure
mutually independent matrices and hence better CS performance. The maximum value amongst inner product
of the Orthonormal basis and the orthonormal measurement matrix defined as incoherence. Therefore, to
recover the sparse vector correctly from 𝑦 = 𝜙𝑥, the sensing matrix 𝜙 should be designed carefully [19, 20].
Figure 1. CS mathematical representation
2.2. System model and LTV channel
In this paper, the OFDM system of Figure 2 is considered. At the transmitter 𝑇𝑥 side of this system,
a stream of symbols x[k] (data d[k] and pilots p[k]) are mapped using binary phase shift keying (BPSK), where
x[k] split into data blocks after serial to parallel conversion. Each of these blocks represent OFDM block
contain data and pilot symbols. The length of each OFDM block is N subcarriers. A cyclic prefix (CP) of length
(𝐿 𝑐𝑝) is prepended to each OFDM block to prevent adjacent interference and considered as a guard band (𝐺𝑖).
After CP insertion, the OFDM block transmitted over an LTV channel which is a multipath propagation
channel. In the proposed work, the LTV channel has been assumed to have a finite impulse response with L
paths. The transmitter and receiver are assumed synchronized in both time and carrier frequency.
The multipath fading channel response is expressed as follows [21, 22];
ℎ( 𝑡) = ∑ 𝑎𝑖 ∗ 𝛿(𝑡 − 𝜏𝑖)𝐿−1
𝑖=0 (2)
where, the ith path of wireless environment is characterized by a propagation delay (𝜏𝑖) and attenuation
(𝑎𝑖). The received baseband signal r(t) is modeled by two components, amplitude and phase, which can be
expressed as;
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𝑟( 𝑡) = ∑ 𝑎𝑖 ∗ 𝛿( 𝑡 − 𝜏𝑖) ∗ 𝑒−𝑗2𝜋𝑓𝑐 𝜏 𝑖𝐿−1
𝑖=0 (3)
where, 𝑒−𝑗2𝜋𝑓𝑐 𝜏 𝑖 is the complex phase factor, and for a narrow band transmission;
𝛿( 𝑡 − 𝜏𝑖) = 𝛿( 𝑡) [23]. Hence;
ℎ( 𝑡) = ∑ 𝑎𝑖 𝑒−𝑗2𝜋𝑓𝑐 𝜏 𝑖𝐿−1
𝑖=0 (4)
The time varying property of the channel implies that channel coefficients changed over time. This changing
is related to the change in the frequency of the received signal, which related to the relative movement between
the transmitter and the receiver, Hence, the corresponding channel delay (𝜏𝑖) is changing [21, 22];
𝜏𝑖( 𝑡) = 𝜏𝑖 −
𝑣 cos 𝜃𝑡
𝑐
(5)
where 𝜏𝑖( 𝑡) is a function of distance, and hence;
ℎ( 𝑡) = ∑ 𝑎𝑖 𝑒−𝑗2𝜋𝑓𝑐∗[𝜏 𝑖−
𝑣 cos 𝜃𝑡
𝑐
]𝐿−1
𝑖=0 (6)
ℎ( 𝑡) = ∑ 𝑎𝑖 𝑒−𝑗2𝜋𝑓𝑐 𝜏 𝑖𝐿−1
𝑖=0 𝑒 𝑗2𝜋𝑓𝑐
𝑣 cos 𝜃𝑡
𝑐 (7)
where, 𝑓𝑐
𝑣 cos 𝜃
𝑐
is the Doppler frequency 𝑓𝑑 = 𝑓𝑑𝑚𝑎𝑥 cos 𝜃, where 𝑓𝑑𝑚𝑎𝑥 = 𝑓𝑐
𝑣
𝑐
is the maximum Doppler shift
(𝑓𝑑𝑚𝑎𝑥). Assuming that the movement of the mobile system is uniformly distributed from 0 ≤ θ ≤ π rad, and θ
is normalized. Thus, the channel impulse response is;
ℎ( 𝑡) = ∑ 𝑎𝑖 𝑒−𝑗2𝜋𝑓𝑐 𝜏 𝑖𝐿−1
𝑖=0 𝑒 𝑗2𝜋𝑓 𝑑 𝑡
(8)
Since this component (𝑒 𝑗2𝜋𝑓 𝑑 𝑡
) is a function of time, as a result, the channel coefficients h(t) are time varying.
Such a time varying channel is known as a time selective channel. How fast or slow the channel changes
depends on the channel coherence time (𝑇𝑐) where the channel is approximately constant during
𝑇𝑐 [21].
At the other hand, in order to estimate the time variant channel coefficients using CS technique,
the sensing matrix should be designed with atoms related to the two effecting parameters (𝜏𝑖 𝑎𝑛𝑑 𝑓𝑑) of
the LTV channel of (8). This will lead to compute the rate of change of the wireless channel by analyzing
the correlation between channel coefficients. Assume that 𝑎𝑖( 𝑡) is the channel coefficient at the ith path
at time t;
𝑎𝑖( 𝑡) = 𝑎𝑖 𝑒−𝑗2𝜋𝑓𝜏 𝑖 𝑒 𝑗2𝜋𝑓 𝑑 𝑡
(9)
Thus, to compute the correlation between 𝑎𝑖( 𝑡) and 𝑎𝑖( 𝑡 + ∆𝑡), the expectation of 𝑎𝑖( 𝑡) and 𝑎𝑖( 𝑡 + ∆𝑡),
𝐸{𝑎𝑖( 𝑡) 𝑎𝑖( 𝑡 + ∆𝑡)} should be computed [24];
𝑎𝑖( 𝑡) = 𝑎𝑖 𝑒−𝑗2𝜋𝑓𝜏 𝑖 𝑒 𝑗2𝜋𝑓 𝑑 𝑡
(10)
𝑎𝑖( 𝑡 + ∆𝑡) = 𝑎𝑖 𝑒−𝑗2𝜋𝑓𝜏 𝑖 𝑒 𝑗2𝜋𝑓 𝑑(𝑡+∆𝑡)
(11)
thus;
𝛹(∆𝑡) = 𝐸{|𝑎𝑖|2
∗ 𝑒 𝑗2𝜋𝑓 𝑑∆𝑡
} (12)
where 𝛹(∆𝑡) refer to the correlation function between 𝑎𝑖( 𝑡) and 𝑎𝑖( 𝑡 + ∆𝑡). Let |𝑎𝑖|2
normalized to be 1, thus,
𝛹(∆𝑡) = 𝐸{ 𝑒 𝑗2𝜋𝑓 𝑑∆𝑡} (13)
which summarized as;
𝛹(∆𝑡) = 𝐽0(2𝜋𝑓𝑑∆𝑡) (14)
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where 𝑓𝑑 represents the maximum Doppler frequency and 𝐽0 is the Bessel function of 0th
order. Finally,
the autocorrelation function 𝛹(∆𝑡) of LTV channel can be expressed in terms of coherence time [25];
𝛹(∆𝑡) = 𝐽0(
𝜋
2
.
∆𝑡
𝑇𝑐
) (15)
where; ∆𝑡 = 𝑥𝑇𝑐, 𝑥 = 1,2,3 … …., and, 𝑇𝑐 =
1
4𝑓 𝑑
.
Figure 2. OFDM System Model
2.3. Sparse channel estimation
Since CS has gained a much popularity in communications, recently, it is one of the small numbers of
strong paths used for channel estimation. It assumes that sparse signals can be approximated with a small
number of measurements compared to the large number required with Shannon-Nyquist rate [1]. Hence, to
estimate the channel vector ℎ ∈ 𝐶 𝑁×1
from y measurements, a CS problem of section (2.1) should be solved,
where y is expressed as follows;
𝑦 = 𝐴ℎ + 𝑛 (16)
n: AWGN noise with zero mean and variance 𝜎2
𝑛 =
𝑁0
2
𝐴: The sensing matrix
The sparse representation of data in terms of atoms is the main objective of the dictionary design,
which later used to reconstruct the sparse signal, where ℎ assumed to be K-sparse CSI and its energy uniformly
distributed among a small number of taps without any prior knowledge of their location, which must be
estimated with effective sensing. It is clear from (15) that channel coefficients are changed with respect to the
channel coherence time. Therefore, in this paper, the dictionary matrix is designed in a manner in which the
two delay parameters of the autocorrelation function are taken into account. The equispaced pilot subcarriers
p[k] are embedded within the data subcarriers d[k] of the OFDM system of Figure 2, where the number of
training pilots is 𝑁𝑝, and ∆𝑡 is assumed to be a taped delay profile along the OFDM symbol. Where;
∆𝑡 = [0, 𝑖 ×
𝛼
𝑁
, 𝛼] 𝑖 = 1, 2, 3, … , 𝑁 (17)
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𝛼 represent the minimum channel tap spacing which equals to (𝐺𝑖 × 𝑇𝑠 −
𝐺 𝑖×𝑇𝑠
𝑇𝑐×𝑁
), and 𝐺𝑖 is the guard interval
which assumed to be the CP appended to each OFDM symbol in order to mitigate the ICI, and 𝑇𝑠 is the OFDM
sample time. An N x N dictionary matrix is constructed with atoms related to each subcarrier position ℓ𝑖 along
the OFDM block length 𝑇𝑆𝑦𝑚𝑏𝑜𝑙, and multiplied by the taped delay atoms 𝜏𝑖 of ∆𝑡.
𝑇𝑆𝑦𝑚𝑏𝑜𝑙 = ( 𝑁 + 𝐺𝑖) 𝑇𝑠, is the OFDM symbol time including 𝐺𝑖. Therefore, the dictionary 𝐷 𝑁×𝑁 is represented
as follows;
𝐷 =
[
𝑒
−
𝑗2𝜋 ℓ1 𝜏1
𝑇 𝑆𝑦𝑚𝑏𝑜𝑙 ⋯ 𝑒
−
𝑗2𝜋 ℓ1 𝜏 𝑁
𝑇 𝑆𝑦𝑚𝑏𝑜𝑙
⋮ ⋱ ⋮
𝑒
−
𝑗2𝜋 ℓ 𝑁 𝜏1
𝑇 𝑆𝑦𝑚𝑏𝑜𝑙 ⋯ 𝑒
−
𝑗2𝜋 ℓ 𝑁 𝜏 𝑁
𝑇 𝑆𝑦𝑚𝑏𝑜𝑙 ] 𝑁×𝑁
(18)
where the rows of dictionary matrix D are refer to the subcarriers positions along the OFDM symbol, while
columns are refer to the delay vector of each subcarrier. Regarding sensing matrix. A construction, an 𝑁𝑝 rows
are selected from D related to pilot locations, and multiplied by 𝑁𝑝 × 𝑁 matrix of pilot data using dot
product multiplication;
𝐴 =
[
𝑒
−
𝑗2𝜋 ℓ1 𝜏1
𝑇 𝑆𝑦𝑚𝑏𝑜𝑙 ⋯ 𝑒
−
𝑗2𝜋 ℓ1 𝜏 𝑁
𝑇 𝑆𝑦𝑚𝑏𝑜𝑙
⋮ ⋱ ⋮
𝑒
−
𝑗2𝜋 ℓ 𝑁 𝑝 𝜏1
𝑇 𝑆𝑦𝑚𝑏𝑜𝑙 ⋯ 𝑒
−
𝑗2𝜋 ℓ 𝑁 𝜏 𝑁
𝑇 𝑆𝑦𝑚𝑏𝑜𝑙 ] 𝑁 𝑝×𝑁
. [
𝑒−𝑗𝜋 𝑃1 ⋯ 𝑒−𝑗𝜋 𝑃1(𝑁)
⋮ ⋱ ⋮
𝑒−𝑗𝜋 𝑃 𝑁 𝑝 ⋯ 𝑒
−𝑗𝜋 𝑃 𝑁 𝑝(𝑁)
]
𝑁 𝑝×𝑁
(19)
𝑃𝑖 is the pilot symbol used for estimation considering equally likely symbols of [0, 1], and
𝑖 = 1,2,3, … . , 𝑁𝑝. Different sparse signal recovery algorithms can be applied to solve the CS problem in
a number of iterations to minimize CS error with respect to D. Once the channel dominant taps estimated
(i.e. recovering of the sparse vector 𝜃), the whole CIR is built at all locations simply from ℎ̂ = 𝐷 × 𝜃, and
the equalization process implemented.
3. SIMULATION TEST AND RESULTS
In this paper, the OFDM system of Figure 2 compares the test results of both least square (LS) and basis
pursuit (BP) based channel estimation techniques. Different OFDM system parameters are listed in
Table 1. In addition to AWGN noise, a 6 tap LTV channel is considered as a Rayleigh fading channel with paths
delays and power vectors standardized by ITU channel model of Table 2. Basis pursuit (BP) algorithm is used to
solve the convex optimization problem with MatLab for sparse signal recovery, where it uses the 𝑙1_𝑛𝑜𝑟𝑚 to
regularize the problem [9]. The performance test of OFDM system was shown in the form of bit error rate (BER)
versus signal to noise ratio (SNR), where SNR is determined by the corresponding (
Eb
No
⁄ ) in dB.
Table 1. OFDM system parameters
Parameter Value
Number of transmitted bits
Modulation
Sampling Time (Ts)
OFDM Subcarriers
Number of pilots
Cyclic prefix length (𝐿 𝑐𝑝)
Maximum Doppler shift (𝑓𝑑)Hz
64000, 128000, 256000
BPSK
1 µsec
64, 128, 256
16, 13
16
0, 10, 20, 40
In Figure 3, the BER performance of OFDM system over a multipath indoor channel environment
using LS and BP is presented. In addition to compare the estimation performance of BP over LS algorithm,
the purpose of this test is to show the ability of the proposed dictionary to recover the CSI with different
delay parameters for both indoor and outdoor environments. In the present test, BP performance outperforms
LS technique by about 4.5 dB at a BER of 10−3
with 16 pilots out of 64 subcarriers and zero Doppler
frequency. In Figure 4, LS and BP algorithms are tested over a multipath outdoor channel environment of
Table 2. In this test, the OFDM block containing 64 subcarriers and the number of pilot subcarriers used is
16. Different Doppler shifts are considered in order to test the recovering ability of the proposed dictionary
in the presence of Doppler effects.
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2289
Figure 3. BER performance with
𝑓𝑑 = 0 𝐻𝑧, 𝑁𝑝 = 16, 𝑎𝑛𝑑 𝑁 = 64
Figure 4. BER performance with
𝑁𝑝 = 16, 𝑎𝑛𝑑 𝑁 = 64
Table 2. ITU Channel Models [26]
Indoor Outdoor
Delay (ns) Power (dB) Delay (ns) Power (dB)
0 0 0 0
50 -3 310 -1.5
110 -10 710 -9.0
170 -18 1090 -10.0
290 -26 1730 -15.0
310 -32 2510 -20.0
As could be noticed, CS based channel estimation algorithm improves the estimation performance
as compared to LS algorithm even with Doppler effect. By comparing BP performance for both 𝑓𝑑 = 0 𝐻𝑧,
and 𝑓𝑑 = 10 𝐻𝑧, it is clear that as 𝑓𝑑 increased to 10 Hz, the performance test degraded by about 15 dB at
a BER of 10−3
. At the other hand, BP performance degraded when 𝑓𝑑 increased more than 10 Hz and become
worse than LS unless the number of pilots used for estimation increased, which in turn improves
LS performance. The same test was repeated with a lower number of pilots, where 13 pilots was inserted within
the OFDM block at equally spaced locations instead of 16 pilots as shown in Figure 5. The test shows that
the BP performance degraded but still much better than LS. This observation leads to the possibility of using
reduced number of pilots for channel estimation without sacrificing the accuracy of channel estimation, when
the rate of change of channel coefficients increasing according to Doppler shift effects.
Figure 5. BER performance with 𝑁𝑝 = 13, 𝑎𝑛𝑑 𝑁 = 64
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Another test considering different subcarrier numbers and Doppler shifts is shown in Figure 6.
The test results proved that BP exceeded LS performance. But this superiority is still limited by the amount of
Doppler shift and number of pilots, where it is degraded when 𝑓𝑑 increased above than 20 𝐻𝑧 and 40 𝐻𝑧 for
128 and 256 OFDM subcarriers respectively with 16 pilots. This degradation is shown in Figure 7, where LS
and BP algorithms are tested with, 𝑓𝑑 = 30 𝐻𝑧 for 𝑁 = 128, and 𝑓𝑑 = 50 𝐻𝑧 for 𝑁 = 256. Finally,
it could be concluded that, as the amount of Doppler shift increase, the estimation performance degraded due
to the Doppler effect on the channel. This degradation manifests itself when the number of subcarriers
increased, where the subcarrier bandwidth will be decreased, so, it is more sensitive to the Doppler and requires
an additional process to eliminate carrier frequency offset (CFO).
Figure 6. BER performance with
𝑁𝑝 = 16, 𝑁 = 128 𝑎𝑛𝑑 256
Figure 7. BER performance with 𝑁𝑝 = 16
4. CONCLUSIONS AND FUTURE WORKS
In this paper, the proposed dictionary design was tested to achieving the desired results of BP based
CS algorithm in estimating of CIR of a LTV channel. At the other hand, this performance is limited to the low
to moderate Doppler frequency shifts. The future work may be carried to extend the current work to be used
for estimation of LTV channel with high mobility or high Doppler frequency shifts.
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