Back in 2013, a partnership project was started between Nutaq and the Institut National de la Recherche Scientifique (National Institute for Scientific Research, or INRS) on Doppler spread estimation for next-generation wireless communication systems. The project itself is based on a paper published by researchers Faouzi Bellili and Sofiène Affes


The newly developed estimator is able to accurately estimate the extremely low normalized Doppler frequencies that are typical of next-generation wireless systems. It is applicable to most used Doppler types without any a priori knowledge of their models and, hence, exhibits an unprecedented robustness in regards to their power spectral density (PSD) shape.

The other advantage of the new estimator is its relatively low computational cost. In contrast to all previous maximum-likelihood (ML) implementations, the new estimator does not involve any numerical matrix inversion. It also outperforms other state-of-the-art estimators over a wide range of the normalized Doppler spread, more so at the very useful low-value regions that are typical of current and next-generation high-data-rate systems.

Without going into the details of the proof, the main challenge proposed by the estimator is to maximize the following log-likelihood function (LLF) with respect to the unknown Doppler spread σd:

This equation requires the inversion of a large-sized matrix which is the covariance matrix Rĥ  (σd). The computational complexity of such an operation increases quickly with the number of processed samples. I won’t go deeply in the details of the proof, but basically, by using a second-order Taylor series approximation of the covariance matrix, they achieved an elegant approximation of the LLF:

Such an equation is much more easily handled by an FPGA-like processor architecture. That’s exactly what this partnership is all about: implementing the maximization of the above LLF in a PicoSDR system.

I recently visited the institute to bring myself up to date on the project. Their implementation is based on Nutaq’s Model-Based Design Kit (MBDK) solution. The simulation phase is complete and they are now at the hardware-in-the-loop (HIL) testing stage. For the moment, a simple sine wave is generated by the PicoSDR, sent to a channel emulator, and then received back from Doppler estimation in the PicoSDR FPGA. After the validation phase, they plan on replacing the sine wave with Nutaq’s OFDM reference design to get a good idea on the behaviour of the algorithm in a real-world situation.

This is one of Nutaq’s many interesting partnership projects that strive to answer the wireless communication challenges of tomorrow.


[1] F. Bellili and S. Affes ”A low-cost and robust maximum likelihood Doppler spread estimator” accepted for publication in Proc. of IEEE GLOBECOM’13, Atlanta, GA, USA, Dec. 9-13, 2013, to appear.