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# Channel Estimation - Science topic

Explore the latest questions and answers in Channel Estimation, and find Channel Estimation experts.
Questions related to Channel Estimation
Question
In a signal is to be transmismitted, first pilot symbols are added and then through Mach-zehnder modulator it has to be transmitted for optical communication purposes. So, for pilot symbols, they have to be go through Mach-Zehnder modulator. The output of Mach-Zehnder modulator is E_out=cos(phi); Where phi= ((U+U_dc)/U_pi)*pi. and here, U_dc, U_pi and pi are constant. And U is the information after inserting pilots. This signal E_out is sent through the channel h.
Now, my question is that how should I estimate the channel because the pilot are gone through Mach-Zehnder modulator before the channel. and How should I extract the pilots and estimate the channel? Thank you.
If we see the series expansion of cos function then how can we find the linear interval? After first term every term is non-linear. I am attaching the series expansion of cos function. If I am missing something in this concept please let me know.
Question
According to my knowledge, the channel estimation is to analyze the channel realization based on the pilot signal, and the channel prediction is to obtain it based on past channel realizations.
Therefore, the channel prediction can be utilized when the pilot signal is contaminated. In other words, the channel prediction is only deserved in the situation when the pilot signals are crashed so that the channel estimation doesn’t work.
Did I understand right? Thank you for your valuable responses in advance.
I would describe it somewhat differently. In my vocabulary, channel estimation refers to the general concept of utilizing received signals to estimate the channel response. The estimation could be based on pilots, pilots+data or only data (the latter two are known as semi-blind and blind estimation).
Since the channel is changing over time, we need to estimate the channel repeatedly in a wireless system. Normally, we are only trying to estimate the current channel response, but one could also try to estimate future channel responses. This is what we call channel prediction. To succeed, you need an accurate model of the time variations. A Kalman filter is one method that can be used to predict future channels.
Question
I have read in a paper that a variable 'x' is the rotation angle of the user's antenna array with respect to moving direction. I am wondering how can we calculate this variable x?
Following information may not be useful but just in case it is necessary. Let us assume that BS has M ULA and user has N ULA.
You are referring to eqn 1 of the paper "Angular-Domain Selective Channel Tracking and Doppler Compensation for High-Mobility mmWave Massive MIMO". This is an equation which describes a wireless channel consisting of plane waves. The terms of interest are f_d,t which is the maximum Doppler frequency offset, \theta_t,q and \eta_t.
As f_d,t is a frequency, it must be multiplied by time somehow as it is in the argument of exp(). I cannot see any time in the formula but it might be that DFO is normalised per symbol time so that the factor 2 \pi f_d,t i produces the increasing phase offset with symbol index as required.
The index q is over all possible propagation paths. These arrive at the antenna in the plane of travel of the antenna from multiple different angles. Hence there are generally many such paths and hence values of q. The total number is L_t where t counts the times frames. \theta_t,q and L_t change from frame to frame. \eta_t is the orientation of the antenna with respect to the direction of motion. This changes with time because the user is rotating the antenna during motion.
The term cos(\theta_t,q + \eta_t) is what is confusing you.
THE IMPORTANT THING TO NOTE IS THAT DOPPLER SHIFT IS:
1. ZERO FOR RAYS ARRIVING AT PERPENDICULAR INCIDENCE TO THE DIRECTION OF MOTION
2. MAXIMUM FOR THOSE ARRIVING FROM THE DIRECTION OF MOTION and
3. MINIMUM FOR THOSE ARRIVING OPPOSITE TO THE DIRECTION OF MOTION
This is handled by the cosine. You will need to consult a Physics text for this.
In order to compute the total angular effect of the Doppler you must add \theta_t,q and \eta_t.
Question
It is known that for optimal RIS control, perfect CSI of all the links between BS and MS through the RIS is required. Therefore, channel estimation and corresponding message feedback methods will be needed at the BS/MS.
Few studies suggest a two-stage channel estimation approach for RIS-aided MIMO channels, using iterative re-weighted method for estimating channel parameters sequentially.
Will this be a good way to go about it, or there is/are better methods.
If there is no specific channel structure, then you will have to transmit pilots using N different RIS configurations, in order to excite all dimensions of the channel.
However, if there is some channel structure (e.g., spatial sparsity) one might be able to reduce the pilot signaling.
Question
Let us say that we have a estimated channel at the BS, denoted by H_e, and actual channel, denoted by H_a. How can we calculate spectral efficiency of a SU-mMIMO system using this information?
More specifically, I have a BS equipped with 64 transmit antennas and a UE equipped with 1 receive antenna.
You said mMIMO in the question (= MU-MIMO) and the mentioned SU-MIMO in the text. Which setup do you have in mind?
For MU-MIMO, I would recommend my book: massivemimobook.com
For SU-MIMO, I would recommend the paper "Capacity and power allocation for fading MIMO channels with channel estimation error" by You and Goldsmith.
Question
In OFDM, First we modulate our message signal and then we take the IFFT of that signal to load the message on subcarrirers. And after that the cyclic prefix is added to combat the frequency selective nature of channel. What should be the length of the cyclic prefix?
The length of the cyclic prefix should be at least equal to the number of channel taps minus one, so that the linear channel filtering appears as if it is a cyclic convolution.
Question
In the literature, I have seen path-loss models, e.g., air-to-ground (ATG). Such models obtain received power by using: Pr=Pt-PL. However, none of these models provide the method to obtain 'H'.
I am interested to obtain 'H' using UAV communication environment. For instance, 'H' must be the combination of line-of-sight (LoS) and non-LoS (NLoS) components.
I suggest you check the paper attached on this topic (Zeng, Fanhui, et al. "UAV-assisted data dissemination scheduling in VANETs." -- Eq(3), Eq(4), and Eq(5)). Specifically, the average path loss can of the UAV link can be modeled by combining the LoS and NLoS links, which is: L=P_{LoS}/d^a+\epsilon*P_{NLoS}d^a (Eq(5)), where P_{L}=1/(1+Eexp(-D[\theta-E])) (Eq(5))denotes the probability of the LoS link.
Question
Pilot signals are used for channel estimation in communication links. How much ratio of lengths can effectively represent channel estimate especially in OFDM case?
Check this reference, it will give you an idea on the length of pilot symbols as well as the arrangement:
Question
I am able to generate Rayleigh coefficients as per the following code (function) in python using H=(1/sqrt(2))*(randn(N)+randn(N)*1i)
def RAYLEIGH(d, etaa, num_symbols):
// Input arguments (Distance, pathloss exponent and samples required (depends on data if fast fading)//
c=1/(d**etaa);
h1 = np.sqrt(c); //(Pathloss is multiplied with Rayleigh coefficient)
h = h1*((np.random.randn(num_symbols)+1j*np.random.randn(num_symbols))/np.sqrt(2));
g = (np.absolute(h))**2; // Magnitude
return h.tolist(), g.tolist(); // Return as a list
How to generate the Rician Coefficients given d (distance), etaa (path loss exponent) on the same lines.
You can create the channel directly with Matlab using the "comm.RicianChannel" then apply this filter to your signal
Question
Hello all, I am working on MU-MIMO DL Block Diagonalization Precoding in Multi-Antenna receivers case and comparing it to zero forcing precoding.
I have following questions, could you please help in understanding.
1) In case of MU-MIMO Downlink, what is the actual cause of Multi-User interference or Inter-User Interference?
- Is it due to the fact that BS simultaneously transmitting signals to the users!
or
- due to Channel distortion!
I understand that in case of same channel, MUI can occur, but I also read that each transmit antennas at BS as a particular channel towards each receive antennas at the user side. Therefore in this case, how is MUI occuring? Is my understanding of channels between transmit and receive antennas correct?
2) In case of MU-MIMO downlink Zero Forcing Precoding, literature says its disadvantages are
i) inversion of ill-conditioned channel matrix causes noise amplification
How is noise amplification caused in precoding?
(However, In case of ZF Receiving, I understood Noise amplification problem, as h ->0, n/h -> Infinity )
ii) extra power might be required to transmit separate signals to closely spaced antennas of a single user, if channels of these antennas are highly correlated!
So, Block Diagonalization is preferred in multi- antenna recievers, as it only removes MUI and it does not suppress Inter-Antenna Interference as in case of ZF Precoding.
Could you please help in understanding disadvantages of ZF Precoding in MU-MIMO DL multi-antenna recievers case.
Thank You.
1) The cause is that multiple signals are transmitted at the same time and frequency, but with different spatial directivity. In theory, zero-forcing and block-diagonalization can cancel that interference but in practice, the cancellation will be only partial due to imperfect channel state information.
2) You are right, it won't lead to noise amplification. I have also noticed how this term is misused in the literature. What is meant is that interference suppression between users with very similar channel will lead to a large loss in signal power at the desired receiver. Hence, the SNR becomes bad. For this reason, zero-forcing is only recommended when you have high SNRs and well separated channels. Otherwise, there are regularized zero-forcing methods that perform better.
Question
Geometry Based Stochastic Channel Modelling or Spatial Channel Modeling (SCM) methods such as:
- 3GPP-SCM, SCM-E
- Winner (I and II)
produce channel coefficients as a matrix H (may on path or at time) between transmitter and receiver antennas.
Then H associated with CSI matrix. But CSI of real channel assume several components (CQI - SNR, PMI, RI). Also, it is referred sometimes as a matrix of complex numbers (gain and phase)...
How generated channel coefficients are related with CSI?
How Channel State Information (CSI) could be obtained from matrix generated by Spatial Channel Modeling?
H matrix always includes only the complex channel coefficients between transmitter and receiver antennas. Channel models (spatial, stochastic, or deterministic) try to estimate that matrix.
CSI, on the other hand, is the set of information that the receiver calculates using that real H matrix coefficients. It measures SNR, determines the correct precoder matrix, rank, layer, etc. based on the network's algorithm, and reports to the transmitter with their corresponding indicators in a CSI reporting.
Question
I have a complex channel matrix 'H' and I want to quantize it in such a way so that the quantization error is minimum. In particular, how to select the dynamic range (the maximum and minimum interval) of the quantization level. Also, what is the best way of finding the appropriate values of each quantized point?
A MATLAB code-based supported answer would be icing on the cake. :)
-------
Below is what I am doing, at the moment, but it is not the best way.
Example:
H =
[-0.9767 + 1.0234i, -1.0477 - 0.4223i;
1.0364 + 0.0454i , 0.0095 - 0.4758i;
0.2724 - 0.4980i , -0.4430 - 0.7466i;
-0.7302 + 0.7945i , -0.2508 + 0.1906i]; %Matrix H having 4 rows and 2 columns
H = H.';
H = reshape(H,1,[]);
partition = [0:1]; % Quantization levels
codebook = [0:2]; %Values for each quantized point.
[index,Q_H_real] = quantiz(real(H),partition,codebook); % Quantized real of H.
[index,Q_H_Im] = quantiz(imag(H),partition,codebook); % Quantized img. of H.
Q_H=Q_H_real+i*Q_H_Im;
%Fig. 1. Plot real part of H and its quantized version
stem(real(H),'b');
hold on
stem(Q_H_real,'r')
legend('Original (Real Part) H','Quantized (Real Part) H')
title('Quantization of Real Part of H')
%Fig. 2. Plot Imaginary part of H and its quantized version
figure;
stem(imag(H),'b');
hold on
stem(Q_H_Im,'r')
legend('Original (Img Part) H','Quantized (Img Part) H')
title('Quantization of Imaginary Part of H')
Attached is the outcome of the above code. There is a huge quantization error.
You have to understand how this quantiz function works and what exactly are the arguments used for. Your "partition" vector will decide what are the bounds of the quantization grid, and the "codebook" will decide what value to output for every "window" defined in the partition vector, including what value to output when the signal is below the lowest bound and when it's above the highest bound. I think the examples on the link I gave you are pretty much self-explanatory and give a good idea of how it's done. From there, I think this function is pretty versatile and can be used for your purpose. You could, of course, adapt your bounds via the partition vector, according as you said to the dynamic range of your signal.
Question
I am new to ML/DL domain and my area of research is channel estimation in Massive MIMO. I would like to know a few things:
1) Can we use ML/DL algorithms to get optimal channel estimates in Massive MIMO?
2) Are they computationally efficient so that we could implement them in the real world?
3) What is the best way for me to start in this area?
Thanks
In my experience that we can ML or DL in real-Time for example we used in Computer vision sector for Autonomous vehicles or Robotics in generally by using Embedded Systems.
For starting, i suggest you to search implementation for real-time in Course, we can find it in Udemy, and we can see some examples in TensorFlow of DL.
Site web:
I hope that be Clair for you.-
Question
I have a channel matrix, H, which contains the complex entries. I want to obtain the quantization of this matrix. For instance,
H=[1+2i,2-3i;5+3i,9-8i]; Q(H)?
Where Q is a quantization function. I found something on google but it is only to deal with a vector having real numbers. The code is given below.
t = [0:.1:2*pi]; % Times at which to sample the sine function
sig = sin(t); % Original signal, a sine wave
partition = [-1:.5:1]; % 2 bit quantizer
codebook = [-1.5:.5:1]; % 2 bit quantizer
[index,quants] = quantiz(sig,partition,codebook); % Quantize.
plot(t,sig,'x',t,quants,'.')
legend('Original signal','Quantized signal');
I am not sure I understand what is quantization in this context. But if you want real values out of your channel matrix, I have 2 ideas.
(1) Separate the matrix into two, one for amplitude of the H (|H|) and other for phase of H (angle(H)). Since they are real values. you can quantize them to nearest value to lower the resolution of the information.
(2) Create a time-frequency plot of the each individual channel vectors (row or column depending on your assignment. You can use different methods like STFT, WT or CT, then quantize the time and frequency information separately. Finally, recombine them again.
Question
I need to implement the closed form solution in order to compute DFE Filters coefficient in matlab/Octave. Attached you can find the theoretical part that I've found in Proakis...
But I am having a hard time computing the Feedforward filters.
Any help will be really appreciated
Hello Abraham
for the point on initialization : the central coefficient of the FF filter is initialized to one (the other coefficients of the FF part to 0), and for the BW filter, all coefficient are initialized with 0.
>> hFF = zeros(LFF,1);
>> hFF((LFF-1)/2) = 1.;
>> hFB= zeros(LFB,1);
For the point on ".. hFB on the other hand is never used" : The backward coefficients are used in the filtering operation :
>> out(n) = hFF'*MemFF + hBW'*MemBW;
and the BW coefficents are updated with the following instruction :
>> hBW = hBW + stepsize * error * MemBW;
I think that all was OK in the code that can be foud in my last post.
Pascal
Question
I am doing a simple channel estimation using Least squares algorithm in a SISO system using QAM modulation.
I am new to this and I do not know what kind of results I have to plot.
I wrote a Matlab code which estimates channel using Least squares algorithm and plots the average mean square error between original channel and estimated coefficients Versus the SNR.
I am attaching the Matlab code and the plot for your reference. Kindly let me know what kind of results that I have to plot.
Ready to give more details if you want.
Dear Balaji,
As the colleagues hinted this is the performance characteristics which you have to obtain to judge the effectiveness of the channel estimation algorithm.
It would be also useful if you use other estimation algorithms for sake of comparison and getting confidence in your results.
May be an other important performance parameters is to determine the bit error rate versus the S/N ratio as this will be the ultimate goal of the estimation accuracy.
Best wishes
Question
What are the different methods or techniques with which we could evaluate the performance of channel estimation algorithms in wireless communications systems, especially in Massive MIMO OFDM systems?
The channel estimation algorithms are evaluated by calculating the the bit error rate versus the signal to noise ratio Pe vs. Eb/N0.
In order to carry out this calculation you need to build the system in form of functional block diagram. Then expressing the signal symbols at the output of the transmitter, inserting the channel transmission matrix according to the channel model. Then model the reliever and assuming at its input specific noise power.
Having the S/N to ratio at the receiver one can calculates the bit error rate.
Then one changes the estimation method and recalculate the bit error rate and assess the results.As an example the zero forcing method, minimum mean square error and the maxim liklihood methods.
There are many papers treating this problem using matlab.
Best wishes
Question
Hello, i'm having a project where I must implement ofdm simulation with mmse estimator for the rayleigh channel. Although the estimation seems tolerant, i'm getting no improve with ber, even for simulation of 10000 symbols.
I have attached the paper i'm trying to implement, with the matlab code and some representative figures to see exactly what i'm doing
I can't understand if i'm missing something very important when estimating the channel or when using specific pilot symbols or in somewhere else..
Anastasia
Hello Tesla;
I have same question.
Question
In mmWaves electromagnetic channels (≥30GHz), the channel models might be known, but they are too complex and/or change too fast to estimate with reasonable accuracy ?
why the channel models changes too fast ?
It all depends on how fast mobility that you are considering. You need to estimate the channel once every time you have moved a particular fraction of a wavelength, for example, wavelength/4.
If you compare 3 GHz and 30 GHz systems where the users move at the same velocity, you will have to estimate the channel 10 times more often at 30 GHz. But if you are instead only supporting low-mobility users at 30 GHz (10 times slower movement) the system will work just fine.
I recommend you to read our paper:
Emil Björnson, Liesbet Van der Perre, Stefano Buzzi, Erik G. Larsson, “Massive MIMO in Sub-6 GHz and mmWave: Physical, Practical, and Use-Case Differences,” IEEE Wireless Communications, To appear. https://arxiv.org/pdf/1803.11023
Question
In wireless Communication, what is the deference between the two terms;
1- Channel Estimation
2- Detection/ Decision making
Dear Abdelwahab,
I agree with the colleges and add, the channle estimation is to measure the channel transmission properties in time domain it is h(t) and in the frequency domain it is H(f). Modern communication relay on the estimation of the channel characteristics to remove the distortion in the received signal in a process called equalization.
Detection; is the identification of a specific signal in the received signal. Extraction of the modulating signals form the carrier is called detection or demodulation.
Signal detection in the presence of interference and noise is one of the most demanding task in the communication systems. In fact, one receives the symbols, detect them which means determine there magnitude and phase. and then decode them in a bi nary form in a process called demapping.
Correlators and matched filters are two devices used to detect the symbols from the received signals.
In the logic symbols one has to classify the logic symbols either logic one or zero.
Every logic symbol is represented by a range of values. If the values are greater than certain threshold the logic value will be one other wise it will be zero. Decision is always required when we have to classify the symbols as they have discrete values.
Best wishes
Question
QuaDRiGa (QUAsi Deterministic Radio channel GenerAtor). Is it possible to apply QuaDRiGa channel models for simulating massive MIMO.
This thesis i think answers your question
Quasi-deterministic channel modeling and experimental validation in cooperative and massive MIMO deployment topologies
Question
In  the authors consider linearly independent channel covariance matrices, however, they do not mention if it is symmetric or not.
Therefore, I'd like to know if the covariance matrix for that case is symmetric.
 Emil Björnson, Jakob Hoydis, and Luca Sanguinetti,"Pilot contamination is not a fundamental asymptotic limitation in massive MIMO",  IEEE International Conference on Communications (ICC), May 2017.
Thanks and Kind Regards,
Felipe
Thanks for the answers!
Question
In TDD, by having K users and length of pilots=K, we would have orthogonal pilots which results in no pilot contamination. By reducing the length of pilots, we can transmit more symbols and of course we would have pilot contamination. So is there any trade off between the length of pilots and number of data symbols? Given (length of pilots+number of data symbols=total number of symbols in each coherence time). Thanks!
I think you have already pointed out the tradeoff in your post. Yes, there is a tradeoff and an optimal number of pilots. I guess what you are looking for is an equation for the optimal pilot length? I don't think such an equation exists in general because the optimal number depends a lot on the propagation scenario and processing scheme. Here are some reasons for that:
* If there is strong spatial correlation, users with very different correlation properties can use the same pilot without causing much interference.
* ZF benefits more from longer pilots than MRC, since ZF uses the estimates for interference suppression.
Here are things that come to my mind:
Figure 7 in "Energy and Spectral Efficiency of Very Large Multiuser MIMO Systems" shows the optimal number numerically: https://arxiv.org/pdf/1112.3810.pdf
The pilot reuse factor is optimized in https://arxiv.org/pdf/1505.01181.pdf with MRC and in https://arxiv.org/pdf/1709.06060.pdf with ZF. The criteria is energy efficiency and not rate, but I would guess that the number that maximizes energy efficiency is basically the same as the one maximizing the sum rate.
There are probably other works that study this as well.
Question
i have collect emg signal from 2 extensor and 2 flexor muscle for 10 motion. Is that each muscle represented one axis and input for classifier? I means i have 10 motion x 4 features ( one muscle for 1 features) for input of classifier, is that correct?
Instead of using your raw EMG data as the inputs to your classifier, you might want to implement some feature extraction methods to them (such as wavelets or fourier) and use these features for each of your raw signal sets as the input vectors to your classifier. In this case you'll have a set of N features x 10 motions x 4 muscles as your total input set.
Question
1、  signal power
we compare different method BER-SNR SER-SNR. Send signal must pass a channel
the signal power is the signal power before channel or after channel?.I guess before
someone try to normalize channel .like fir channel we set some taps then h/norm(h)
other type channel the same way. However this cannot ensure the power is same before and
after channel. Another way channel is usually fading channel so the normalize is redundant or not?
cp occupy part of energy we can ignore it?
Does we consider the processing as a linear system  input output? Like channel cp is the middle  processing. We do not need to consider as signal power or not?
2、  in ofdm normalize the power for example qpsk  16qam the coefficient  are sqrt(2)
sqrt(10)  the average power of all subcarriers symbols is 1.this is due to the distribution of the qam signal like 16qam 1+3j 1-j 1+j… the average is sqrt(1+9) does it ?
3、  complex noise is not exist  in math we say the amplitude is abs(s),the phase is angel(s)
someone try to assign the ofdm signal to be conjugate so the symbol after ifft is real type then
noise type is real. However others does not then noise power divide into equal two parts this may have effect on the figure in SNR-BER?
4、  sparse channel in sparse channel estimation someone know the of the channel does this .of course we must sure Ncp>Nh we can assume the length of Nh is Ncp or much longer is ture?
5、  The practical system there are many procedure like synchronization interweave etc. in simulation we may ignore it? Practical system we use a few symbols to do channel estimation for extreme conditions we use all subcarriers to do estimation ,of course we assume the channel is time invariant or slow variant. Traditional typical pilot type should be useless
Thanks
Hi Xq Ye,
Have a look here.
I don't think it shows the power allocation. However, you can derive the SNR formula with or without the path loss.
I hope this will help.
Best regards,
Question
A signal is transmitted by the transmitter and multiple rays arrive at the receiver as a result of reflections (from the flat obstacles), diffraction (from the edges of obstacles) and scattering.
How do I find the number of clusters in this condition?
Question
For the Relaigh fading model, I want use four multipath components, each component has its delay and gain. Can the gain in dB of any of the individual multipath components be positive value? I can understand that it can be zero or maybe negative indicating reduction in its amplitude due to delay and effects of channel, but I can not understand how it can be positive. The overall signal resulting from the four components at the receiver may be with positive gain. This is reasonable, due to constructive addition of maybe inphase components, but how can a single component be with positive gain?
Propagation from one radio to another will always be a net loss.  You'll never receive more power than you transmit.  However, in talking about a channel model, the gains of clusters and taps are generally treated as relative values, absent the net path loss term.  The typical approach is to have the first cluster be the 0 dB reference and other clusters are usually less than that, indicating a decaying power delay profile. However, there's nothing preventing the shortest path having a lower signal than a longer path (e.g. through a wall vs. a strong reflection around the wall).  Thus, if the first cluster is 0 dB, then the second cluster would be positive.  That doesn't really mean anything physically.  It's all just an arbitrary reference normalized to the first cluster.
Note that for a faded multipath, you don't get gain due to "in phase" conditions.  You have to treat those as power sums, not voltage sums.  That's different than gain at the source due to beamforming, etc. where phase of the unfaded signal is used to provide gain (over an isotropic radiator) in the antenna array.
Question
I'm studying on "identification of channel coding". the received data encoded by one of the following channel coding, 'convolutional' , 'LDPC' , 'Reed-Solomon' and 'BCH'. i should extract a feature among the received data to identify the kind of channel coding blindly and decide that which one of the above channel coding is used for channel coding. I would like to help me to find a feature for blind identification of mentioned channel coding. Your help will be much appreciated. Looking forward to hearing back from you.
This is an interesting question!
One of the possible methods is the exploitation of the code rate which is the ratio of the original data bits to the coded data bits.
That is, if the code rate is k/n, for every k bits of original data, the coder generates totally n bits of data, of which n-k are parity bits.
If R is the gross bitrate or data signalling rate (inclusive of redundant error coding), the net bitrate (the useful bit rate exclusive of error-correction codes) is = R•k/n.
For example: The code rate of a convolutional code may typically be 1/2, 2/3, 3/4, 5/6, 7/8, etc., corresponding to that one redundant bit is inserted after every single, second, third, etc., bit. The code rate of the Reed Solomon block code denoted e.g. RS(204,188) is 188/204, corresponding to that 204 - 188 = 16 redundant bytes are added to each block of 188 bytes of useful information.
So, the code rate can work as an identifier since every channel code is identified by  a code rate. If the code rates are equal and this is very less probable, then one can revert to sorting the original message bits and the redundancy bits.
One of properties that can be exploited is the code structure itself which means the ordering of the original message bits and the parity bits. In convolutional codes they are added directly after the every message bit, in as a block codes they are added after the message symbols. Also the same holds to the LPDC code which is also a block code with low density parity. .
Identification is base on the unique features of the different encoding techniques.
In fact, an elaborate study is required to work out the differentiating features of the different coders. Which i introduced here is just some ideas.
wish you success
Question
I'm trying to implement the EVD-based channel estimation algorithm in massive MIMO using Matlab. The channel matrix G models fast fading H, large-scale fading D (shadow fading, path loss) by the formular: G = H*sqrt(D). But most of the papers on this method assume that we know D, and choose D = diag(0.98 0.63 0.47) or D = diag(0.98 0.85 0.75) for 3 UE as the papers below.
My first question is how can I determine these values of large-scle fading matrix?
And, if 3 UEs have similar positions, the coefficients can be similar or the same. The EVD-based algorithm cannot resolve the multiplicative factor ambiguity because of the invertible matrix. How can I resolve this problem?
References: H.Q. Ngo and E. Larsson, "EVD-based channel estimation in multicell multiuser MIMO systems with very large antenna arrays", Proc. IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), pp. 3249-3252, 2012.
Umut Ugurlu et. al, Coordinated optimization of EVD-based channel estimators in multi-cell massive MIMO networks, Communication Workshop (ICCW), 2015.
The large-scale fading coefficients are the variance of the channel coefficients. These represent that pathloss. Some theoretical papers assign some simple numbers to these parameters, but if you want to have a model you can for example choose the Hata model: https://en.wikipedia.org/wiki/Hata_model_for_urban_areas
And, if 3 UEs have similar positions, the coefficients can be similar or the same.
Yes, this is true.
Question
when we use pilot channel  estimation in matlab，the following questions：
suppose Ncp,Nch,Npi,Nall represent the length of CP,Channnel impulse response(CIR),pilot length, all subcarriers length,respectively.
1.the order of P/S and add CP
some one say before S/P，we add cp，while others are opposite.
we must ensure Ncp>=Nch
2、the order of add pilot ，most paper say that this step is after S/P,，that
means we must add pilot in parallel data，in matlab simulation we user
set A index of pilot ，but if we do this in parallel  data we must convert the index to fit the  parallel data.
3、the relationship of Npilot ，Nall，in matlab firstly we produce random bit data they a few steps，we have a index of pilot they we replace orign index
modulate data by the pilot data。so in fact the Npilot data is included in all data ，may this call  replace ，when use insert that means add extra data，the length is increase ，does it？
4、how to estimation ，most paper select the pilot data，Xp，Yp，these are serial data。I guess we may estimate in serial data，some paper is in parallel data？
there are  different type  pilot ，if we use interpret function in matlab we
must sure the beginning and the ending data must be pilot data，only in this way can every data be equalization ，does it？
if estimation in parallel data comb-type or block-type may be invalid?
5、cp ，when we do experiment we find is the cp data is zero ,it cannot affect data if not,some data can not use.
6\pliot Does pilot must be bigger than modulate data or less or donnot mind？
7、SNR the signal power is must be the signal after channel，not before channel.
when calculate ser or ber does pilot data should be remove from data?
8\ MMSE comparsion we must cal h_est,but Npilot is nor equal to Nch,
so if u want compare different ways ,does we need to interpert the different
way like h_ls,h_mmse,h_ch to the length of the receive signal?
i try find all  ways i can access but no ebook or paper refers the bellowing
questions
may i need total exact of 802.11 or DVB ofdm matlab code?
Dear,
1/ Concerning CP insertion, Figs. 1 and 2 are equivalent, even though Fig. 2 seems better, since CP insertion is carried out in time domain, i.e. after IFFT and P/S. However, in matlab, both figures are the same.
2/ OFDM is adapted to pilot insertion in frequency domain, i.e. before IFFT and P/S. You can add pilot in time domain, but you lose the advantage of frequency multiplexing. Note that in matlab, yoyu have to foresee the index of your pilots before pilot insertion.
3/ I suggest to first create Nall-Npi data, then insert the Npi pilots. In that case, you won't have problem in your data/pilots index.
4/ Estimation and pilot insertion scheme mainly depends on the channel you consider: a time and frequenc-selective channel requires comb-type pilots, whereas a frequency selective channel rather requires a block type pilot scheme. By the way, channel estimation is performed in frequency domain, i.e. after FFT at the receiver. Depending on the pilot insertion, you may require to estimate the channel on pilot tones, then perform an interpolation in order to get the channel estimate over the whole time-frequency grid. In some cases, you even have to perform extrapolation, for instance if pilots are not at the edge of the frequency band.
5/ By definition, CP is a repetition of the last samples of the OFDM symbol (after P/S) at the beginning of the same symbol, so it may not be zeros. Do not confuse CP with guard interval (GI): CP is one type of GI, but GI can instead be composed of zero. In that case, it is not CP, but zero-padded GI.
6/ It depends on the system/standard you consider. If you define your own simulations parameters (i.e. not based on an existing standard), I suggest to define pilots with the same energy as the data symbols.
7/ It is indead better to calculate SNR at the output of the channel (in simulation). In that case, the energy of the signal must include the energy of the pilots. However, BER or SER is calculated after pilots removal, by definition. In fact, BER is assessed on symbols that carry information, which are a priori unknown at the receiver.
8/ MMSE compares the exact channel with the estimated one. The latter is obtained after the steps estimation + interpolation. In that way, the estimated channel is (at least) Nch, i.e. the same length as the channel. Note that channel estimation requires that Npi>=Nch, in order to trackall the channel variation.
I worked on channel estimation in OFDM context during my PhD, you could see my thesis (in English) here:
Vincent
Question
what operation is performed after channel estimation by using the estimated channel information at receiver?
It allows the receiver to set the taps in its equalizer, and, in two-way channels, it allows the two sides to negotiate a valid (optimal) spectral efficiency to use in the channel. The receiver has to do this to correctly decode the incoming data symbols.
Consider QAM in the channel. To decode QAM accurately, the receiver had to be able to determine the amplitude and the phase of each incoming symbol, because it is the combination of amplitude and phase that determines the bit values intended to be carried in each symbol. As symbols travel, they will be attenuated, usually by different amounts throughout their spectrum, due to range and to multipath effects. A signal that becomes attenuated by differing amounts across its spectrum, must necessarily be shifted in phase too. In a two-way communications channel, if channel estimation determines that the noise level is high in comparison with the signal strength, the two ends may elect to use a simpler constellation, to more successfully allow the symbols to be decoded. A simpler constellation carries fewer bits per symbol, but the symbols can be decoded more robustly, because phase and amplitude transitions are large as opposed to subtle.
So, channel estimation is required to compensate for the distortion introduced in the symbols, as they travel through the channel, and to take into account SNR. The receiver's equalizer has to untwist the incoming symbols back into their intended shape, in order to decode them accurately, and in two-way comms, channel estimation allows negotiation of an optimal constellation.
Question
Hello, Which neural networks topology is better for OFDM channel estimation? and how to implement it?
If you have no reference about a previous work, my advice is that you use a simple network such as the multilayer perceptron. You can check my profile if you need to download practical cases of application of this structure.
Good Luck!
Question
I am using some resource allocation schemes to find out the capacity. I need to find out the outage capacity. According to p(outage)=1-p(C<Cthreshold). How do I select Cthreshold and find p?
The outage capacity is of interest for slowly fading channels, where the SNR of the channel is a random variable that can take realizations close to zero. In this case the capacity is zero and we need an alternative capacity metric.
You need to pick an outage probability epsilon. We then look for a capacity that holds for (1-epsilon) of the SNR realizations. You can obtain the corresponding SNR_threshold  from the following equation:
Pr(SNR < SNR_threshold) = epsilon.
You then get the epilson-outage capacity as
C_epsilon = log2(1+SNR_threshold).
I recommend Section 5.4.1 in the book Fundamentals of Wireless Communications: https://people.eecs.berkeley.edu/~dtse/Chapters_PDF/Fundamentals_Wireless_Communication_chapter5.pdf
Question
I need to know the origin/root cause of the CEE.
e.g. We know that one of the causes is  imperfect channel estimation. But I want to know what are the factors that lead to this imperfect channel estimation.
- channel frequecny offset,
- Doppler effect,
- time synchronization mismatch
among other sources of distortion. More specifically to channel estimation in multicarrier systems, in the case of scattered pilots, interpolation along time and frequency axes is required to estimate the channel over all the carriers/symbols. Most of interpolation methods induce estimation errors as well.
Question
The warning message displayed on Matlab When I choose Least square estimation LS = S' * inv( S * S' ) to achieve the channel estimation, Matrix is singular to working precision. ". Then the estimation is incorrect. If I increase the training length, the number of this cases appearance declines.
In general, you need to have at least as many observations as you have unknown parameters to estimate. This will make your matrix S * S' invertible (if the observations are independent).
In special cases of Bayesian estimation, one can get away with fewer observations since we have prior information on the unknown parameters that says that they are strongly correlated.
You can find some conditions for this in the following paper:
Emil Björnson, Björn Ottersten, “A Framework for Training-Based Estimation in Arbitrarily Correlated Rician MIMO Channels with Rician Disturbance,” IEEE Transactions on Signal Processing, vol. 58, no. 3, pp. 1807-1820, March 2010.
Question
And where I can find a good references about channel estimation in WiMAX or generally?
Hi
The receiver apply MMSE, LS or ML algorithm  on the piltot signal that coming from the transmitter.
The receiver knows the sequence of these pilot signal.
Question
Hi all,
I am designing a loop filter of DPLL in 802.11ac OFDM system. The DPLL tracking is achieved by pilot symbols inserted into OFDM symbols.
Importantly, the coefficients of loop filter significantly impact the PER ( packet error rate ) of the OFDM system.
So, does anyone know that how to design or determine the coefficients of the loop filter is able to maximize the performance of the OFDM system.
Many thanks
Jiajun Zhu
Hi, I have used the method proposed by Texas Instrument in their paper entitled 'getliterature.tsp.PDF' issued in 2005
Best regards
Question
Suppose we have two sensors which are close to each other and the first has its own measured signal value, how this sensor can have an idea, margin or estimate of the signal measured by the second sensor in the proximity, knowing that these sensors does not know the original signal power emitted by the station or physical phenomenon. Obviously, I am not asking for the solution where the second can send the measured value to the first sensor.
Alright. Any assumptions about the location of the primary signal source?
Question
can anyone suggest a way as how to approach in analysing a frequency selective Fading channel characteristics using matlab?
You can model your system using matlab files or you can build it in form of simulink blocks. The matlab m-files are based on the analytical mathematical model of the system.
Any communication system is built from the transmitter a receiver and a transmission channel. You model the three components of the system.
Assume that the receiver produces the transmit symbols S(t), the channel has an impulse response h(t), the receiver signal r(t) can be expressed by
r(t)= h(t)*  S(t) + n(t) , where * is the convolution process and n the noise power.
The role of the receiver is to find  a best estimate of S in spite of distortion by the channel and contamination by noise. Normally equalizers and matched filters are used for optimum detection.
These operation are performed using analytical formulas in the m-file formulation.
In case of Simullink you build all these components using their model in the library of elements and components  or even custom components.
wish you success
Important here to point out that the channel is modeled as an FIR filters.
The book digital communication systems by Glover and Grant helps you much to realize your project.
Question
Currently, my friend is working with adaptive channel estimation for high mobility, Zero Forcing, MMSE, ML estimation.
Since the channel estimation for high mobility is complicated, we are moving to non linear estimation like, ML estimation. But this estimation is also complicated.
He needs better ideas to improve the estimation with less complexity.
Channel Estimation is based on LS, ML, MAP, MMSE methods but it can be categorized to training-based, semi-blind and blind methods. Nowaday, pilot-aided methods are used for channel estimation of fast-varying channels.
Question
When a channel is not perfectly estimated. (Imperfect CSI)
If channel gain RHO=modulus of h square ~ alpha*beta.
Yes, there are. Why not? The channel gain (complex channel gain as a summation of multipath components) changes in time  as a result of time-varying nature of the propagation environment. For some certain assumptions, the envelope of the sum then follows the Gamma distribution.
Question
Hi all,
In linear MIMO ZF or MMSE, the LLR is calculated by detected signal power over both interference noise power and white noise power.
In nonlinear MIMO ZF-SIC and MMSE-SIC, the interference noise is cancelled by decision feedback. However, the cancellation may be incorrect, if the decision in the previous layer is error. Hence, the LLR, I think that, is calculated by detected signal power over both white noise power and error decision feedback variance.
However, I dont know how to calculate this LLR.
Does anyone know the solution or provide some references to me?
You can read earlier papers on turbo equalization, where calculation  of LLR to feed the channel decoder is clearly showed.  Hope this can help.
Question
I am working on channel estimation in Massive MIMO for millimeter wave, I know that coherent time has reduced due to higher frequency, but still in doubt about number of symbols can send.
The important variables are the coherence time, Tc, and the coherence bandwidth, Bc.
By the Nyquist sampling theorem, a waveform that lives in this time/frequency coherence block is specified by TcBc complex samples. This is how you compute the number of symbols.
For example: The coherence time Tc=5 ms and coherence bandwidth Bc=100 kHz leads to a coherence block with TcBc=500 samples/symbols.
If you need a reference for this, you can have a look at my paper:
Emil Björnson, Erik G. Larsson, Thomas L. Marzetta, “Massive MIMO: 10 Myths and One Grand Question,” IEEE Communications Magazine, Submitted for publication. (http://arxiv.org/pdf/1503.06854)
Question
When we use subspace based blind channel estimation technique for MIMO-OFDM channel estimation, we divide the singular vectors of the received signal into noise subspace and signal subspace, and declare the matrix which minimizes the dot product of itself with noise subspace as the estimated channel, similar to all other blind techniques this procedure also does not give the true channel but gives upto a matrix multiple of the true channel, what are the techniques available to remove such an ambiguity? ,I do not wish to use any pilot sequences
I think the technique to resolve the ambiguity is to send a pilot :)
I am not aware of any other technique. If the phases of the channel elements are uniformly distributed between 0 and 2pi, then you need to observe some kind of signal with a known phase to have a chance to estimate the phases.
Channel estimation that uses both blind techniques and pilots are often called semi-blind.
Question
Since there are very large number of antennas at the transmitter and receiver, we may need to estimate large number of channels, correspondingly we may need very large length pilot sequence to ensure orthogonality among pilot signals used for different transmission paths.
If you send pilots from the many base station antennas to the users, then you need many pilots (at least one per antenna). The original idea with massive MIMO is to send the pilots in the uplink direction only. Then you only need to have one pilot per user in the cell!
There are more details on this in my overview paper "Massive MIMO: 10 Myths and One Grand Question" (http://arxiv.org/abs/1503.06854)
I would say that pilot transmission is necessary to ensure reliable channel estimation, but blind techniques can be used on top of this (also called semi-blind in this context) to mitigate interference.
Question
In OFDM transmission, we usually use a Frequency Domain Equalization by IFFT/FFT for channel estimation and equalization.
But some authors could use Time Domain Equalization also. Could you please provide some details to help me to understand how they proceed to do that? Thank you :-)
Dear Sanya,
time domain equalization (TEQ) is a technique that is widely adopted in DSL, on Discrete Multitone Modulation (OFDM with bit loading). Equalization in the time domain is discussed in great detail in the book Fundamentals of DSL Technology, chapter 11, or in the lecture notes provided by Prof. John Cioffi, at the attached link, chapter 3.
Best regards,
Igor F.
Question
Hello, I am looking for the recent works, thesis and publications that deal with channel estimation (wireless system)  based on neural network. Thank you
Question
Land Mobile Satellite Channel Modeling
"THREE STATE FONTAN LMS CHANNEL MODEL" does not include:
1. Polarization
2. MIMO
3. Deterministic evolution of the channel
4. Possibility to include 3D Polarimetric antennas at RX and TX
5. Spatially correlated propagation parameters
6. Possibility to reproduce / resimulate measurement tracks
7. Deterministic transition between segments with different propagation properties (like NLOS to LOS)
8. A reference implementation is available.
Cheers,
Kai
Question
Right now what i am doing is, i am extracting my pilots before AWGN and estimating the channel at receiver. But i wonder if there is some other way to obtain perfect CSI? Any hints and suggestions would be a great help. Thanks
Which fading distribution are you using in the MIMO channel? Normally, for any Fading channel, you need to include an equalizer to equalize the gains as it is a dispersive channel and this degrades the system a lot, resulting a BER of 0.5. You can learn more about equalizer on Mathworks. Hope I've enlightened you a bit. Regards.
Question
Please point out some papers which are relatively easy for starters particularly focusing on the problem formulation and mathematical background
there is nothing special in parameter estimation for MIMO systems. If I understand you correctly, you mean correlated states or, in other words, that the states cannot be decoupled. This is the standard case. The fisrt thing to start is to familiarize with the notion of observability:
You can also take a look at basics. For instance:
These lecture notes come along with examples in Matlab.
Question
I need a theoretical analysis of channel estimation in mimo-ofdm system.
This book give good fundamentals for MIMO - OFDM with matlab
MIMO-OFDM WIRELESS COMMUNICATIONS WITH MATLAB by  Yong Soo Cho
channel estimation - chapter 6
Question
The power line channel is an FIR filter with the coefficients being the weighting factors. The OSTBC combiner block has a channel estimation port.
Hi...
In this regard I will prefer to go for adaptive FIR filters for better results. Please try adaptive filters and do the simulation,compare the results with your present algorithms. You can find many equivalent simulation help from MATLAB file central.
Regards,
A.Kar
Question
When using channel measurements on simulation, it is common to have impulse responses with a ringing effect due to truncation in the frequency domain (due to  the measurement itself). This ringing in the impulse response, however, induces bit detection errors that don't normally occur with regular impulse responses (given the bit loading algorithm guarantees a low BER). My question is: where in the DMT chain such an impulse response would be problematic, as far as simulation is concerned?
EDIT: I previously called these impulse responses with ringing as non-causal. However, non-causal in this context is not strictly non-causal by definition (an impulse response in which a given sample depends on future samples), but an impulse response in which the amplitude goes first negative before reaching the positive peak, showing energy before being excited. This is a terminology that commonly appears for channel models, in which the RCLG parameters can be causal or non-causal (depending on the model). To avoid confusion, I decided to edit and remove this term. The point is, the impulse response Im using has this ringing effect, an oscillation before the peak. I believe the fact that this can cause detection errors is a known issue and that's why Im asking it here. My goal is to understand why I can't use such an impulse response for time-domain simulations, or, in case I can, what type of pre-processing (e.g. freq-domain windowing) should I apply.
Bit loading seems to be correct, ISI/ICI seems to be controlled, transmission PSDs are apparently correct, detection implementation is correct and assumes perfect channel knowledge. I don't immediately see where it is problematic. I also cannot explain why the bit errors occur at the lower frequencies.
EDIT2: Problem solved. The impulse responses had small but non-negligible ringing in its last samples, close the FFT size. Hence, when I was truncating the impulse responses to 99% of the energy, they were continuing with a length close to the FFT size. This was impractical for the cyclic prefix to cover enough dispersion such that ISI could be controlled. Hence, what was indeed constraining me was ISI/ICI, in contrast to what I said before. Ultimately, I took the ISI/ICI PSD into account in the bit loading computation and solved the problem. I won't delete the question because it can be helpful for someone.
Best regards to everyone who tried to help.
Measure the SNR at the receiver on each channel. Maybe there is a problem in your power allocation at the transmitter. DMT tries to keep the BER roughly constant across all carriers (although in practice there is obviously some variation) through a combination of bit loading and a water-pouring power allocation algorithm; if ISI/ICI is OK then your cyclic prefix looks like it is long enough, so the only reason BER would be unreasonably high is poor SNR on some carriers, which suggests insufficient power is being provided at some frequency. There is normally a lower threshold below which a particularly poor carrier is not used at all, maybe that is not being applied.
Question
Hello everybody, I want to realize a simulation on Matlab with cosimulation on VPI to make a plastic optical channel estimation that allows me to identify and compensate distortions. Does anyone know about a model for plastic optica fiber (POF)?.
I have read several papers and they show the way but there are a lot of doubts about the generation of the preamble in the TS based on Chu or complemetary Golay sequences. How can I perform this simulation acording with this kind of binary sequences or if anybody can make a citation of a reference where I can understand better the procedurement. I appreciate any support!
Hello,
For orthogonal frequency-division multiplexing(OFDM) systems, if you are looking for a synchronization method  that achieves low mean squared error (MSE) in timing offset estimation at five (5 x) times lower computational complexity compared to usual methods, I suggest you to have a look on the following paper (available on my researchgate page) :
Pramod Udupa, Olivier Sentieys, Pascal Scalart,, "A Novel Hierarchical Low Complexity Synchronization Method for OFDM Systems," in Vehicular Technology Conference (VTC Spring), 2013 IEEE 77th; 01/2013
I hope this wil helps,
Question
The reference I've read indicates that the minimum training frames should be greater or equal to the number of transmitter antennas. Herein, the training frames denote that S = [s1, s2, s3, ... sN], where si is a nTx*1 vector and N is total number training frames.
When I choose Least square estimation LS = S' * inv( S * S' ) to achieve the channel estimation, I find that sometimes Matlab displays "Warning: Matrix is singular to working precision. ". Then the estimation is incorrect. If I increase the training length, the number of this cases appearance declines.
So, what is the problem in this case? How can I determine the training length to avoid the problem in reality?
On the basis of required accuracy of the channel estimation, optimal training sequences of minimum length are determined and it is given by
NP ≥ NT (L + 1) + L
Where, Where, Np = the number of training symbols per transmit antenna and per frame.
The training sequences very much effect the channel capacity, and by implementing the Optimal training sequence length improved MSE and capacity both.
Question
As for training sequence, we can use the known simples to estimate the channel and then cancel ISI. However, in reality, there are not only frequency-selective channel but also carrier frequency offset.
In that case, channel estimation does not work in my simulation when I introduce carrier frequency offset. Probably, I need to cancel the carrier frequency offset firstly for promising reliable channel estimation.
However, the phase has been distored by frequency selective channel. Hence, the normal methods to estimate frequency offset does not work.
How can I cancel the carrier frequency offset before channel estimation ?
Otherwise, how can I combine carrier frequency offset estimation and channel estimation at the same time?
Many thanks
Sorry I forgot to answer the question about channel estimation. The short answer is that it is the most practical to remove the dopper shift before processing the received signal.
As you are aware, a well-designed testing signal (training signal) must be sent over the channel and its signal properly recieved and analyzed at the receiver. The receiver must have an exact replica of the initial transmitted signal. It is equivalent to measuring the impulse respone of the channel although we often use the Fourier Transform equivalent and do the analysis in the frequency domain, i. e., use the transfer function. Doppler shift of the transmitted signal affects all parts of the signal spectrum but if we send a signal that has a carrier component, we can correct for doppler shift by estimating the received carrier frequency as compared to the local receiver clock.
Question
DS-CDMA is divided into uplink and downlink communications.
As for uplink, the users suffer from different channel impulse responses (CIRs). How the receiver estimates these CIRs and cancel it?
As for downlink, does the receiver only know own signature waveform? If say yes, how does it uses multiuser detection to cancel CIR and multiuser interference (MUI)?
LMS and RLS are popular methods for channel estimation. However, in the DS-CDMA system, there are not only CIR but also MUI. How can we let LMS and RLS adapt to this situation?
Many thanks.
RAKE receiver performs correlation function Rxy(tau) x, being received signal and y the code of the user. If the user signal is present in the received signal, Rxy(tau) has a maximuma at every repetition (multipath) of the signal, provided that the delay of the repetition is greater than the width of autocorrelation function Ryy(tau) of the code.
Question
I wanna to establish a inverse modelling to get a equalizer to combat the multipath channel. However, I found a problem that the training of LMS algorithm is very unstable under the Rayleigh multipath channel generated randomly.
So far, I found that in some coefficients of Rayleigh multipath the training seem to be stable, but in some coefficients of Rayleigh multipath the training is bad.
I think that the step size of LMS algorithm is a critical point, but I can't find some references to give an accurate value of the step size. Normally, they only give a range of the value which I have followed.
Does anyone know the problem?
Does My model perhaps is incorrect?
Many thanks
Jiajun
As stated in the earlier comments, to maintain the stability property the step-size of the adaptive algorithm (equalizer here) should be lower than 2/lambda_max, where lambda_max is the maximum eigenvalue of the covariance matrix R=E[uu^H], where u is the tap input vector. This upper bound is only a first approximation and it shoud be in reality lower by a factor of 1/10 in order to ensure stability whatever the experimental conditions are.
In your experiment, the properties of this covariance matrix R may change when varying the parameters of the Rayleigh multipath channel and in some configuration the fixed step-size is greater than the maximum allowed value. That is the reason why "...in some coefficients of Rayleigh multipath the training is bad".
To ensure stability, several algorithms are usually proposed :
1- use of of Normalized algorithm (i.e. NLMS) instead of the standard LMS. Then you will be independent of the energy variations in the tap input vector u.
2- use of standard approaches for computing the variable step-size such as (main relevant papers):
1. V. John Mathews, Zhenhua Xie, "A Stochastic Gradient Adaptive Filter with Gradient Adaptive Step Size," IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 41, NO. 6, JUNE 1993.
2. Raymond H. Kwong, Edward W. Johnston, "A Variable Step Size LMS Algorithm", IEEE TRANSACTIONS ON SIGNAL PROCESSING. VOL 40, NO 7. JULY 1992.
3. Tyseer Aboulnasr, K. Mayyas " A Robust Variable Step-Size LMS-Type Algorithm: Analysis and Simulations," IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 45, NO. 3, MARCH 1997.
4. Pooi Yuen Kam, Keng Hong Chua, and Xiaofeng Yu, "Adaptive Symbol-by-Symbol Reception of MPSK on the Gaussian Channel with Unknown Carrier Phase Characteristics," IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 46, NO. 10, OCTOBER 1998.
5. Jacob Benesty, Hernán Rey, Leonardo Rey Vega, and Sara Tressens, "A Nonparametric VSS NLMS Algorithm," IEEE SIGNAL PROCESSING LETTERS, VOL. 13, NO. 10, OCTOBER 2006.
Regards
Question
I want to design a Decision Feedback Equalizer (DFE) to combat the multipath channel.
Does anyone know some references about the principles of Decision Feedback
Equalizer (DFE) ?
Further, What is the advantages of DFE compared with normal equalizer?
Many thanks
Dear
I think this video is interesting.
Question
Hi,
I have the delay profile and losses for indoor channel model A. How can I make time varying using Monte Carlo method?
Thanks.
For each path, you get a vector. If you consider (as usual) a channel as being constant during one OFDM symbol duration, then each sample of these vectors corresponds to one OFDM symbol. More precisely, you will do the delayed sum of all the k^th samples of each path for the k^th OFDM symbol.
Concerning the variation of the channel, since you consider a very low speed, you have to consider a very large number of OFDM symbols to see the variations.
Question
Complex equalizers are needed in GSM while LTE resort to simpler equalization techniques due to its narrow band sub-channels. How to explain this difference in a simple way?
@Magnus .... i have very limited knowledge of electronics, especially amplifiers. I may not be able to answer your question properly. Recently, i published a paper in Globecom 2013 in which i dealt with Class C amplifier. At the output of IFFT amplifier, OFDMA waveform is very fluctuating thanks to additions and multiplications operations of IFFT. So high peaks in the waveform drives the amplifier into saturation region but we want our amplifier to be work in linear region where output and input has linear relation (imagine ohm's curve of I and V). But once your amplifier is driven into saturation region, it starts producing harmonics meaning that your input power is dissipated into unwanted harmonics. This means you have reduced your transmitted power. Hence, S/N is reduced at receiver and BER is increased. But in SC-FDMA and together with QPSK, our amplifier remains in linear region. Not sure how Class AB will act in such case.
@ismat ... you summarised everything right. and i second with what you have said about MIMO and OFDMA/WCDMA.
Question
.
Dear Folks,
Indeed, it depends, but there are so many different scenarios to consider that I am unable to give you an exhaustive answer here, but you would find a lot of related information in my book on QAM. Some sample chapters are enclosed here, but ALL chapters are available at IEEE Xplore on line.
Most importantly, in the recently discovered spatial modulation star-qam performs better then square qam with gray mapping!!!
With best wishes
Lajos
Question
Can wavelet transforms be applied to adaptive filter applications like linear prediction, echo cancellation, equalization, channel estimation etc?
Yes you can use it
only change you are creating is instead of filter coefficients adapted over time( normal time domain adaptive filters), you can adapt wavelet coefficients to adapt over time( transform domain adaptive filters)
Question
Done via a single transmit antenna (like in spatial modulation) with minimum number of rx antennas.
May be these articles will are useful to you:
1) C. Fragouli, N. Al-Dhahir, and W. Turin, “Training-Based Channel Estimation for Multiple-Antenna Broadband Transmission,” IEEE Transactions on Wireless Communications, vol. 2, no. 2, pp. 384–391, March 2003
2) Oomke Weikert and Udo Zolzer, “Efficient MIMO Channel Estimation With Optimal Training Sequences”
Question
BER calculation every time I use the Rayleigh multipath-fading simulator in Simulink (v2012a MATLAB) it induces a BER of about 50% in my communications model. I have tried changing all of the parameters in the simulator, but nothing seems to help. Even if I reduce the numbers of paths to one, and increase the gain dramatically it still produces the same result. Does anyone have experience with this simulator?