Blind Estimation of Multiple Carrier Frequency Offsets

arXiv:0707.0463v1 [cs.IT] 3 Jul 2007 BLIND ESTIMATION OF MULTIPLE CARRIER FREQUENCY OFFSETS Yuanning Yu, Athina P. Petropulu, H. Vincent Poor+ and Visa Koivunen+ Electrical & Computer Engineering Department, Drexel University +School of Engineering and Applied Science, Princeton University ABSTRACT Multiple carrier-frequency offsets (CFO) arise in a distributed antenna system, where data are transmitted simultaneously from multiple antennas. In such systems the received signal contains mul- tiple CFOs due to mismatch between the local oscillators of trans- mitters and receiver. This results in a time-varying rotation of the data constellation, which needs to be compensated for at the receiver before symbol recovery. This paper proposes a new approach for blind CFO estimation and symbol recovery. The received base-band signal is over-sampled, and its polyphase components are used to formulate a virtual Multiple-Input Multiple-Output (MIMO) prob- lem. By applying blind MIMO system estimation techniques, the system response is estimated and used to subsequently transform the multiple CFOs estimation problem into many independent sin- gle CFO estimation problems. Furthermore, an initial estimate of the CFO is obtained from the phase of the MIMO system response. The Cramer-Rao Lower bound is also derived, and the large sample performance of the proposed estimator is compared to the bound. keywords-Multi-user Systems, Distributed Antenna Systems, Carrier Frequency Offset, Blind MIMO System Identification 1. INTRODUCTION In any communication system, the received signal is corrupted by carrier-frequency offsets (CFOs) due to the Doppler shift and/or lo- cal oscillators drift. The CFO causes a frequency shift and a time- varying rotation of the data symbols, which need to be compensated for at the receiver before symbol recovery. This can be achieved via pilot symbols. However, in the case of mobile systems and rich scat- tering environments the effects of CFO become time varying and even small errors in the CFO estimate tend to cause large data re- covery errors. This necessitates transmission of pilots rather often, a process that lowers data throughput. In this paper we deal with CFO estimation without the need for pilot symbols. In single user sys- tems, or in multi-antenna systems in which the transmitters are phys- ically connected to the same oscillator, there is only one CFO that needs to be estimated. This is typically done via a decision feedback Phase Lock Loop (PLL) at the receiver end. The PLL is a closed- loop feedback control system that uses knowledge of the transmitted constellation to adaptively track both the frequency and phase off- set between the equalized signal and the known signal constellation. However, depending on the constellation used during transmission, the PLL can have an M-fold symmetric ambiguity, resulting in a lim- ited CFO acquisition range, i.e., |Fk| < 1/(8Ts) for 4QAM signals, where Ts is the symbol period. Moreover, the PLL typically requires a long convergence time. Alternatively, several methods have been This work has been supported by NSF under grant Nos. ANI-03-38807, CNS-06-25637 and CNS-04-35052, and by the Office of Naval Research un- der Grant ONR-N-00014-07-1-0500. proposed [2], [4], [5], [7] [9] that blindly estimate the CFOs and recover the transmitted symbols using second-order cyclic statistics of the over-sampled received signal. Blind CFO estimation has also been studied in the context of orthogonal frequency-division multi- plexing (OFDM) systems, where the CFO destroys the orthogonality between the carriers (see [3] and the references therein). In a spatially distributed antenna system where data are transmit- ted simultaneously from multiple antennas, the received signal con- tains multiple CFOs, one for each transmit antenna. A PLL does not work in that case as there is no single frequency to lock to. The liter- ature on estimation of multiple CFOs is rather sparse. Existing liter- ature on this topic focuses on pilot based CFO estimation. In [6], the multiple CFOs were estimated by using pilots that were uncorrelated between the different users. In [13], multiple CFOs were estimated via Maximum Likelihood based on specially designed pilots. To ac- count for multiple offsets, [8] proposed that multiple nodes transmit the same copy of the data with an artificial delay at each node. The resulting system was modeled as a convolutive single-input/single- output (SISO) system with time-varying system response caused by the multiple CFOs. A minimum mean-square error (MMSE) deci- sion feedback equalizer was used to track and equalize the channel and to recover the input data. Training symbols were required in order to obtain a channel estimate, which was used to initialize the equalizer. Here we propose an approach for blind identification of multi- ple CFOs and subsequent symbol recovery. The received base-band signal is over-sampled, and its polyphase components

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