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?
Hi Zhu,
The application of LS should be in the context where the number of variables should be smaller than or equal to that of equation. In this sense, the number of training sequence should be larger than or equal to the number of transmit antennas.
Please refer to the papers how much training is needed in multiple-antenna wireless links and Training based MIMO channel estimation: a study of estimator tradeoffs and optimal training signals.
I hope my answer can help address your questions.
Regards.
Jiguang
Hi ............. I think may be the problem is when u are using direct inversion like " inv( S * S' )" then your matrix ( S * S' ) should be full ranked or it must not have any zero eigenvalues, so i think u have to choose your 'S' such a way( S is full ranked) that ( S * S' ) does not not have any zero eigenvalue or null space. if u randomly choose S in each trial in your MATLAB simulation then there is always certain probability that your 'S' will be low ranked. Hope this will help u......................
Hi Faisal Ahmed Siddiky,
I think that your comment is right. The random S cannot promise that the matrix inverse is full rank. As for Training-based transmission, Choosing the particular sequence as the training is reasonable.
Kind regards
- To have a meaningful information of the sequence optimization problem,we need to limit the maximum total transmit power of the antenna array. In practice ,knowledge of the unknown channel is often obtained by sending known training symbols to the receiver . During the training period ,we obtain the best linear unbiased estimates of the channel parameters based on the received training block. we determine the optimal training sequence set that minimizes the mean square error of the channel estimator under a total transmit power constraint. In oder to obtain the advantage of the optimal training sequence design , long-term statistics of the interference correlation are needed at the transmitter . Hence ,this information need to be estimated at the receiver and fed back to the transmitter.
yes it happens because as N=T then it reaches full rank then condition number reduces and the warning condition goes.
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.
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