Channel estimation for multicarrier systems

(in cooperation with CCPSR, NJIT, New Jersey)








  1. Introduction

The wireless radio channel can be parametrized as a combination of paths, each characterized by a delay and a complex amplitude. The amplitudes show fast temporal variations due to the mobility of terminals while the delays are almost constant over a large number of OFDM symbols (see figure). A possible approach is that of explicitly estimating and tracking the delays [Yang  '01]. To avoid the typical problems of non-linear parameter estimation (i.e, threshold effects and computational complexity), we propose to perform an unstructured tracking of the delays through a subspace tracking algorithm and the amplitudes by Kalman filtering or suboptimal (reduced complexity) techniques such as LMS or WLMS [Lindbom '01].




The idea has been applied first to OFDM systems over fast-varying fading channels. The channel estimation (tracking) in OFDM systems is generally based on the use of pilot subcarriers in given positions of the frequency-time grid. In particular, we consider the comb pilot pattern arrangement (see figure) which has been shown to satisfy different criteria of optimality such as mean square error on the channel estimate [Negi '98] and capacity [Adireddy '02].
In this framework, the traditional approach to channel estimation consists of two steps. Firstly, the least squares (LS) estimates of the channel gains over the pilot subcarriers are obtained by simply backrotating the received signal according to the knowledge of the pilot symbols. Then, the LS estimates are interpolated/smoothed over the entire frequency-time grid.





  2. Subspace tracking channel estimation

The Subspace Tracking (ST) algorithm (see figure-(a))  and the Subspace-Amplitude Tracking (SAT) algorithm (see figure-(b)) adaptively estimate the two time-varying terms of the multipath channel: delay-subspace and amplitudes.
The LS estimate over the pilot subcarriers is fed to a subspace tracker [Strobach '96] that udpates symbol by symbol the estimate of the delay-subspace basis and of its rank. The SAT technique also performs the tracking of the amplitudes (e.g., by LMS).

The ST and SAT algorithm can be applied to MIMO-OFDM or MC-CDMA systems by designing the training sequences as in [Jones '98].










Analysis and simulation show the relevant advantage of the unstructured tracking of the multipath delays compared to existing pre-interpolation techniques  in terms of mean square error (MSE) on the channel estimate.









The advantage can be quantified (for a large number of symbol n) as the ratio between the number of pilot subcarriers and the dimension of the delay-subspace. The algorithms do not assume any a priori knowledge  on the multipath channel. Even the dimension of the delay-subspace (which is related to degree of temporal diversity of the channel) is adaptively estimated symbol-by-symbol (see figure). However,  any a propri information on the statistics of the fading variation could be exploited by appropriate design of the amplitude tracker (e.g., Kalman filtering).

3.  Future work 

The delay-subspace (and amplitude) tracking algorithms can also be applied to OFDM systems over channels with larger coherence time that use a pilot arrangement such as that employed in Hiperlan/2 or IEEE802.11b. Preliminary results show that the techniques provide relevant performance improvement compared to known channel estimation algorithms also in this framework. A thourough study is under way.

  • [Yang '01] B. Yang, K. B. Letaief, R. S. Cheng, Z. Cao, “Channel estimation for OFDM transmission in multipath fading channels based on parametric channel modeling,” IEEE Trans. Comm., vol. 49, no.3, pp. 467-478, March 2001.
  • [Lindbom '01]  L. Lindbom, M. Sternad, A. Ahlen, “Tracking of the time-varying mobile radio channels-Part I: the Wiener LMS algorithm,” IEEE Trans. Comm., vol. 49, no. 12, pp. 2207-2217, Dec. 2001.
  • [Negi '98] R. Negi, J. Cioffi, “Pilot tone selection for channel estimation in a mobile OFDM system,” IEEE Trans. Consumer Electronics, vol. 44, pp. 1122-1128, Aug. 1998.
  • [Adireddy '02]  S. Adireddy, L. Tong, H. Viswanathan, “Optimal placement of training for frequency-selective block-fading channels,” IEEE Trans. Inform. Theory, vol. 48, no. 8, pp. 2338-2353, Aug. 2002.
  • [Strobach '96] Strobach, “Low-rank adaptive filters,” IEEE Trans. Signal Processing, vol. 44, no. 12, pp. 2932-2947, Dec. 1996.
  • [Jones '98] V. K. Jones, G. G. Raileigh, “Channel estimation for wireless OFDM systems,”  Proc. IEEE GLOBECOM’98, pp. 980-985.


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