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.
Dear Dr. Björnson,
Many thanks for the valuable and useful information. Also so grateful for the papers and the explanations.
Best regards,
Manijeh
Also this is an old question, but for those who might be interested, our paper gives detailed answer to the same question:
An analytical framework for the incorporation of non-orthogonal pilots in massive MIMO systems
https://doi.org/10.1016/j.dcan.2024.02.002