论文部分内容阅读
【摘要】In this paper ，We propose animproving algorithm ofthe EM about the OFDM system under the condition offast-moving for channel estimation improvement algorithm. This algorithm is greatly reduced computational complexity compared with the original algorithm and makes the SNR performance close than without jamming. On the development of mobile communications has a good theoretical significance.
【关键词】High-speed mobile condition Improving the EM algorithm
【中图分类号】G642 【文献标识码】A 【文章编号】2095-3089（2016）11-0245-03
Introduction：
OFDM technology was concerned of everyone who researching the high-speed mobile because it can be improving thetransmitted effectivelyspeed at the same time， avoiding kinds of interference and has good noise immunity， anti-multipath interference and high spectrum efficiency. However， in practice， especially when at the time under the condition of fast-moving， because the channel spectrum coverage， the orthogonality of channel will be destroyed， Channel signal interference （ICI） or distortion， the other wireless channel under high speed conditions will produce a large Doppler frequency shift， which will cause a time-varying carrier frequency offset and causeinterference between the carriers， in turn， dramatically reducing communications performance. Thirdly， due to rapidly changing channel under high speed conditions， producing time selective fading which slow the system performance.
For the above-mentioned reasons， we need to solve some questions：Firstly， we will need to estimate， track and calibrate time-varying carriers frequency offset caused by Doppler frequency shift. Secondly， we need to estimate precisely about rapidly time-varying channel. Thirdly， we must eliminate mutual interference between carrier problem. Finally， we need to overcome the problem of channel change caused by time selective fading.
In conclusion， we present an improved EM algorithm based on channel estimation， which solved the problem from traditional algorithm face to complexity and low signal to noise ratio （SNR） under the high-speed mobile condition.
I. Basic principle of OFDM system
1.1 The basic idea
Channels can be divided into several orthogonal channels， high-speed data signals converted into parallel low speed data streams and modulation on each channel to transmit. OFDM using DFT and IDFT method solves the problem that mutually orthogonal subcarriers and replies to the original data from the carrier signal and its basic model in figure [1]. Fig.1 The basic model of OFDM system
1.2 The orthogonal
It is non-overlapping that the frequency of each subcarriers in conventional frequency multiplexing methods. In order to reduce theICI， carriers needs to maintain enough frequency interval， thereby reducing the utilization of the frequency spectrum.In OFDM Systems， the subcarriers frequency is overlapped， so as to improve the utilization of the frequency spectrum， at the same time， as the subcarriers frequency spectrum orthogonality in the symbol period as a whole， so as to no distortion at the receiving end of recovery.
Established the period of OFDM symbol is NT.When the relationship between the various subcarriers frequencies for（k = 0，1，2...N-1）.In this formula， N represents the number of carriers， represents the lowest frequency used for transmitting， represents frequency separation between two adjacent carriers. the carriersunderorthogonality is established.
After the simulation， the spectrum of OFDM system in figure [2] below：
Fig.2 The spectrum of OFDM system
II.The algorithm of channel estimation for OFDM
2.1 The EM algorithm of channel estimation
The channel estimation of EM method using the previous channel impulse response （Channel Impluse Response， CIR） estimated values and receive pilot information， getting interference signal and noise variance estimate， we can get the current iteration of channel estimation values until convergence of system performance number of iterations using these estimate values and according to LS or MMSE criterion.
First， we define：
Given the unknown parameters and hypothesisobeys average value AH， covariance is matrixGaussian distribution， its
joint probability densityfunction of：
M represents the counts of OFDM number， assumptions within the M symbol cycle， h remains unchanged and is：
（2-3）
The request （2-2） in the maximum-likelihood formula is：
Getting the likelihood solution when is maximum， as follows：
The formula （2-5） into the equation （2-4）， omit irrelevant items， and get likelihood function of h， as follows：
However， the likelihood solution is usually difficult to obtain unless M is large enough. So we propose solution.
2.1.2 Improved EM algorithm for channel estimation
Based on the above analysis， we found that the maximum value of search is a very complex process， it is difficult to complete in practical situations. We hope that the above estimation algorithm is improved. 2.1.2.1 Channel multipath delay estimation
For EM channel estimation algorithm shortcomings， we will study the environment at high speed channel multipath delay estimation problem.First， in the case where there is no interference：
Wherein the vector
（2-8）
Matrix is K×L Van der Monde.
Secondly， in some cases with Interference：
When the interference power is strong， channel multipath delay is expected to bring a large error. We should suppress the contain larger interference before multipath delay estimation. P-th element of formula （2-8） can be written as：
Hypothesis the channel impluseresponse varianceis complex Gaussian distribution and are independence. （）， so obey the Gaussian distribution and average value is zero. Its variance is：
We used CME and improved dual threshold CME， the pilot subcarriers in the frequency domain channel estimation value is determined as follows：
sequence in ascending order， to obtain the column .
Removing the before M value represents the， where m = 0， M is a given constant. We can get the lowest threshold as follows：
Step one： hypothesis m=m+1;
Step two： Update sequencein the following way：
Step three： Update ：
Step four： Whennumber of elements are no longer increase， go to step 5. Otherwise， repeat steps 1-3;
Step five：Getting a higher threshold according to the following formula：
Those greater than the lower threshold sequencecompared with the ， is greater than when it is considered that the subcarriers interference， otherwise ， we considered the subcarriers interference. For these disturbed guide pilot subcarriers， which channel frequency response is setting a constant value.
2.1.3 Simulation results and analysis
Figure [3] shows the improved EM channel estimation algorithm with SNR changing NMSE performance graphs， which disturbed the pilot subcarriers are five consecutive pilot subcarriers.As can be seen from the figure， this process at higher SNR situation there is a performance platform， which is due to the interference environment channel normalized performance of the platform presence delay estimation.
Figure [4] shows the performance plot of OFDM system which used of the improved EM channel estimation algorithms in the interference environment.From the figure， BER performance of the improved EM channel estimation algorithm and BER performance without interference is very close. Fig.3TheNMSE performance with SNR changing on improved EM channel estimation algorithm
Fig.4 TheBER performance of OFDM system in improved EM channel estimation
Ⅲ. In conclusion
We researched the channel estimation problem of OFDM system under the highspeed mobileinterference environment and improved the EM iterative channel estimation algorithm. We propose a channel time delay estimation algorithm， this algorithm including some with interference detection and suppression and channel delay estimation two parts.For some with interference detection， we analysis the statistical characteristics of frequency response value in the pilot and used CME algorithm detected that disturbed pilot subcarriers and suppression.For channel time delay estimation，we analysis the mathematical model of the pilot channel at the frequency domain response， use of ANP spectral estimation method to obtain the value of channel estimate time delay.The simulation results show that channel frequency response under the improved EM channel estimation algorithm NMSE performance and corresponding system BER performance and latency known when the estimated performance of the algorithm is very close.
References：
[1] Telatar E.， "Capacity of multi-antenna Gaussian channels" [J]. AT&T-Bell Labs Internal Tech. Memo. pp：1-28， June，1995.
[2] Foschini G. J.， "Layered space-time architecture for wireless communication in a fadingenviroment when using multi-element antennas" [J]. Bell Labs Tech. J.，
1996， vol. 1，no.2， pp：41-59.
[3] W.C.Jakes，“MierowaveMobileCollun切rlleations，，，JohnWiley，NewYork，1974.
[4] T. Star， J. Coiffi， and P. Silverman， Understanding DSL Technology[M]，.Upper Saddle River， NJ： Prentice Hall， Feb. 1999.
【关键词】High-speed mobile condition Improving the EM algorithm
【中图分类号】G642 【文献标识码】A 【文章编号】2095-3089（2016）11-0245-03
Introduction：
OFDM technology was concerned of everyone who researching the high-speed mobile because it can be improving thetransmitted effectivelyspeed at the same time， avoiding kinds of interference and has good noise immunity， anti-multipath interference and high spectrum efficiency. However， in practice， especially when at the time under the condition of fast-moving， because the channel spectrum coverage， the orthogonality of channel will be destroyed， Channel signal interference （ICI） or distortion， the other wireless channel under high speed conditions will produce a large Doppler frequency shift， which will cause a time-varying carrier frequency offset and causeinterference between the carriers， in turn， dramatically reducing communications performance. Thirdly， due to rapidly changing channel under high speed conditions， producing time selective fading which slow the system performance.
For the above-mentioned reasons， we need to solve some questions：Firstly， we will need to estimate， track and calibrate time-varying carriers frequency offset caused by Doppler frequency shift. Secondly， we need to estimate precisely about rapidly time-varying channel. Thirdly， we must eliminate mutual interference between carrier problem. Finally， we need to overcome the problem of channel change caused by time selective fading.
In conclusion， we present an improved EM algorithm based on channel estimation， which solved the problem from traditional algorithm face to complexity and low signal to noise ratio （SNR） under the high-speed mobile condition.
I. Basic principle of OFDM system
1.1 The basic idea
Channels can be divided into several orthogonal channels， high-speed data signals converted into parallel low speed data streams and modulation on each channel to transmit. OFDM using DFT and IDFT method solves the problem that mutually orthogonal subcarriers and replies to the original data from the carrier signal and its basic model in figure [1]. Fig.1 The basic model of OFDM system
1.2 The orthogonal
It is non-overlapping that the frequency of each subcarriers in conventional frequency multiplexing methods. In order to reduce theICI， carriers needs to maintain enough frequency interval， thereby reducing the utilization of the frequency spectrum.In OFDM Systems， the subcarriers frequency is overlapped， so as to improve the utilization of the frequency spectrum， at the same time， as the subcarriers frequency spectrum orthogonality in the symbol period as a whole， so as to no distortion at the receiving end of recovery.
Established the period of OFDM symbol is NT.When the relationship between the various subcarriers frequencies for（k = 0，1，2...N-1）.In this formula， N represents the number of carriers， represents the lowest frequency used for transmitting， represents frequency separation between two adjacent carriers. the carriersunderorthogonality is established.
After the simulation， the spectrum of OFDM system in figure [2] below：
Fig.2 The spectrum of OFDM system
II.The algorithm of channel estimation for OFDM
2.1 The EM algorithm of channel estimation
The channel estimation of EM method using the previous channel impulse response （Channel Impluse Response， CIR） estimated values and receive pilot information， getting interference signal and noise variance estimate， we can get the current iteration of channel estimation values until convergence of system performance number of iterations using these estimate values and according to LS or MMSE criterion.
First， we define：
Given the unknown parameters and hypothesisobeys average value AH， covariance is matrixGaussian distribution， its
joint probability densityfunction of：
M represents the counts of OFDM number， assumptions within the M symbol cycle， h remains unchanged and is：
（2-3）
The request （2-2） in the maximum-likelihood formula is：
Getting the likelihood solution when is maximum， as follows：
The formula （2-5） into the equation （2-4）， omit irrelevant items， and get likelihood function of h， as follows：
However， the likelihood solution is usually difficult to obtain unless M is large enough. So we propose solution.
2.1.2 Improved EM algorithm for channel estimation
Based on the above analysis， we found that the maximum value of search is a very complex process， it is difficult to complete in practical situations. We hope that the above estimation algorithm is improved. 2.1.2.1 Channel multipath delay estimation
For EM channel estimation algorithm shortcomings， we will study the environment at high speed channel multipath delay estimation problem.First， in the case where there is no interference：
Wherein the vector
（2-8）
Matrix is K×L Van der Monde.
Secondly， in some cases with Interference：
When the interference power is strong， channel multipath delay is expected to bring a large error. We should suppress the contain larger interference before multipath delay estimation. P-th element of formula （2-8） can be written as：
Hypothesis the channel impluseresponse varianceis complex Gaussian distribution and are independence. （）， so obey the Gaussian distribution and average value is zero. Its variance is：
We used CME and improved dual threshold CME， the pilot subcarriers in the frequency domain channel estimation value is determined as follows：
sequence in ascending order， to obtain the column .
Removing the before M value represents the， where m = 0， M is a given constant. We can get the lowest threshold as follows：
Step one： hypothesis m=m+1;
Step two： Update sequencein the following way：
Step three： Update ：
Step four： Whennumber of elements are no longer increase， go to step 5. Otherwise， repeat steps 1-3;
Step five：Getting a higher threshold according to the following formula：
Those greater than the lower threshold sequencecompared with the ， is greater than when it is considered that the subcarriers interference， otherwise ， we considered the subcarriers interference. For these disturbed guide pilot subcarriers， which channel frequency response is setting a constant value.
2.1.3 Simulation results and analysis
Figure [3] shows the improved EM channel estimation algorithm with SNR changing NMSE performance graphs， which disturbed the pilot subcarriers are five consecutive pilot subcarriers.As can be seen from the figure， this process at higher SNR situation there is a performance platform， which is due to the interference environment channel normalized performance of the platform presence delay estimation.
Figure [4] shows the performance plot of OFDM system which used of the improved EM channel estimation algorithms in the interference environment.From the figure， BER performance of the improved EM channel estimation algorithm and BER performance without interference is very close. Fig.3TheNMSE performance with SNR changing on improved EM channel estimation algorithm
Fig.4 TheBER performance of OFDM system in improved EM channel estimation
Ⅲ. In conclusion
We researched the channel estimation problem of OFDM system under the highspeed mobileinterference environment and improved the EM iterative channel estimation algorithm. We propose a channel time delay estimation algorithm， this algorithm including some with interference detection and suppression and channel delay estimation two parts.For some with interference detection， we analysis the statistical characteristics of frequency response value in the pilot and used CME algorithm detected that disturbed pilot subcarriers and suppression.For channel time delay estimation，we analysis the mathematical model of the pilot channel at the frequency domain response， use of ANP spectral estimation method to obtain the value of channel estimate time delay.The simulation results show that channel frequency response under the improved EM channel estimation algorithm NMSE performance and corresponding system BER performance and latency known when the estimated performance of the algorithm is very close.
References：
[1] Telatar E.， "Capacity of multi-antenna Gaussian channels" [J]. AT&T-Bell Labs Internal Tech. Memo. pp：1-28， June，1995.
[2] Foschini G. J.， "Layered space-time architecture for wireless communication in a fadingenviroment when using multi-element antennas" [J]. Bell Labs Tech. J.，
1996， vol. 1，no.2， pp：41-59.
[3] W.C.Jakes，“MierowaveMobileCollun切rlleations，，，JohnWiley，NewYork，1974.
[4] T. Star， J. Coiffi， and P. Silverman， Understanding DSL Technology[M]，.Upper Saddle River， NJ： Prentice Hall， Feb. 1999.