S. Khalili , O. Simeone , M. Haimovich

1. Code-Aided EM Algorithm for Joint Channel Tracking and Decoding for Sparse Fast-Fading Multipath Channels S. Khalili,O. Simeone, M. Haimovich CWCSPR, New Jersey Institute of Technology, Newark, NJ, USA Introduction Conventional Approach Code Aided-EM Method Wireless communication networks are expected to play an increasingly prominent role in vehicular networks [1] [2]. Wireless communication is currently being considered for use in railways services in order to provide control functionalities as well as passenger entertainment. • Channel estimation by utilizing the training OFDM symbol • The same channel estimate is used to perform coherent decoding of the subsequent N data OFDM symbols in the frame. • Conventional approach assumes that the channel is time-invariant. • Log Likelihood Ratios required for message passing • Effective noise variance to avoiding mismatch in the decoding metric Joint Channel Tracking and Decoding: • Maximum Likelihood (ML) detection • The ML detection problem is efficiently solved by using the EM algorithm, which converges to a local optimum by iterating between so called E- and M-steps [4]. A radio link subject to a fast-fading multipath channel within a train backbone network. Due to the high speed of the train, wireless links between backbone nodes are subject to highly time-varying channels. Common wireless standards such as IEEE 802.11p prescribe a number of pilots that is significantly smaller than the total number of parameters to be estimated or tracked. • The M-step in (16) is efficiently performed by using a message passing LDPC decoder. System Model Code Aided-EM Method • The transmitted frame contains OFDM symbols, each consisting of K subcarriers. • The first OFDM symbol contains only pilot subcarriers. • The following N OFDM symbols contain Kppilot subcarriers. Simulations Results • Most previous work that deals with channel tracking assumes that the number Kp of pilot subcarriers in each data OFDM symbol is at least as large as the number Kt of taps. • In the IEEE 802.11p standard the number Kp of pilot subcarriers is generally smaller than the number Kt of taps. • The proposed algorithm is based on the following ideas: • Sparsity: While the number Kt of taps is larger than Kp, the number Kmp of paths is often small and comparable to the number of pilot subcarriers Kp. • Long-term vs. short-term channel parameters: Distinction between the long-term parameters 􀀀 , and the short-term time-varying amplitude vectors . • Code-aided methods: Utilizing the error-correcting properties of the LDPC code within a decision-feedback loop. Proposed Algorithm BPSK modulation, K = 64, Kp= 4, Kcp = 16, carrier frequency equal to 5 GHz, 520 information bits, B = 20 MHz, = 350 km/h, Kmp = 3. • Baseband equivalent discrete-time system model: (a) transmitter; (b) receiver • Block diagram of the proposed algorithm QPSK modulation, K = 64, Kp = 4, Kcp = 16, carrier frequency equal to 5 GHz, 520 information bits, B = 20 MHz, = 350 km/h, Kmp = 3. Channel Model • The channel corresponding to the nth OFDM symbol is defined by Kttaps. • The channel taps are the result of the superposition of Kmp multipath components. • Each path is characterized by a delay, an average power and a complex amplitude that varies across the OFDM symbol. • Due to the speed of the train the complex amplitudes are time-varying. • The complex amplitudes follow the standard Jakes model. • The receiver and the transmitter move in the same direction and with the same known velocity. • The Doppler frequency spread of the direct path is zero. • The time-domain channel vector Estimation of Long-Term Channel Parameters: • The channel taps Hn[k]are estimated using the MMSE criterion References [1] G . Shafiullah, A. Gyasi-Agyei, and P. Wolfs, “Survey of wireless communications applications in the railway industry,” in Proc. Wireless Broadband and Ultra Wideband Communications (AusWireless 2007), pp. 65-65, Aug. 2007. [2] G. Acosta and M.-A. Ingram, “Model development for the wideband expressway vehicle-to-vehicle 2.4 GHz channel,” in Proc. IEEE WCNC, vol. 3, pp. 1283-1288, Las Vegas, NV, Apr. 2006. [3] C. Berger, Z. Wang, J. Huang, and S. Zhou, “Application of compressive sensing to sparse channel estimation,” IEEE Commun. Magazine,, vol. 48, no. 11, pp. 164–174, Nov. 2010. [4] G. J. McLachlan and T. Krishnan, The EM algorithm and Extensions. Wiley, 1997 • The long-term parameter in the ithiteration is estimated by calculating the empirical average of • The long-term matrix is estimated by using a CS-inspired method [3]. • The number of multipath components Kmp can be estimated by using the Minimum Description Length (MDL) or Akaike Information Criterion principle.