Robust pilot-aided channel estimator for time-varying OFDM channels

Abstract

K-l h[m, l] = L 'Yi [m]gdl], i=O where 'Yi [m] is the complex amplitude of the i-th path, and gi[l] = g(lTs -ri), where Ts is the sample period and g(r) is the shaping filter impulse response that satisfies the Nyquist criterion. The WSS-US assumption imposes the restriction In our model, the received signal x [m, k] and transmitted symbol a [m, k] at the m-th OFDM symbol and k-th subcarrier, forNs -1, are related as x[m, k] = H[m, k]a[m, k] + u[m, k] + w[m, k], where H[m, k] is the subcarrier complex attenuation, and u[m, k] and w[m, k] are the inter-carrier interference (leI) and noise components, respectively. We consider that the symbols a[m, k] are uncorrelated for different m's and k's. The noise w[m, k] is supposed i.i.d. and independent of the remaining signals. Supposing that a[m, k] at the pilot positions are selected from a PSK constellation, the LS estimate of H[m, k] can be found simply back-rotating x[m, k], which results in H[m, k] = x[m, k]a*[m, k] = H[m, k] + z[m, k] where z[m, k] = (u[m, k] + w[m, k])a*[m, k]. Due to the uncorrelated assumption of a[m, k], we can write lE{z*[ml, k1]z[m2, k2]} = 0, for ml =I-m2 or kl =I-k2, lE{H*[ml, k1]z[m2, k2]} = 0, for any ml, m2, kl, k2, where lE{.} denotes the expectation operator. This simplifies significantly the design of a second-order estimator for H[m, k] (see [2]). We consider the pilot subcarriers are arranged in grid. The pilot subcarriers are allocated at positions m = nMt and k = lMf' for n E Nand 1 = 0, ... , N p -1, where N p is the number of pilot subcarriers per OFDM symbol. Let H[n], H[n] and z[n] be column vectors containing respectively H[nMt , lMf], H[nMt , lMf] and z[nMt , lMf]' for 1= 0, ... , N p -1. Then we can state Rj[ = lE{H[n]HH[n]} = RH + pI, where R H lE{H[n]HH [n]} and p is the variance of z [nMt, lMf]. We also consider a cyclic prefix with length N cp in order to avoid inter-symbol interference. The considered channel model is the WSS-US one with a constant number of paths. In this case, the base-band impulse response is given byTo achieve high data rates in orthogonal frequency division multiplexing (OFDM) [1] it is mandatory to employ multilevel modulation with nonconstant amplitude, such as 16-QAM. For efficient coherent demodulation, it is necessary an accurate channel estimation method capable to track the variations of the fading channel. Furthermore, the performance of many diversity decoding techniques depends heavily on good channel estimates, specially when the channel is time-varying in nature. In the works [2,3], it is derived a minimum mean-square error (MMSE) channel estimator based on pilot symbols using Wiener-type filters. The disadvantage of the optimum design of these filters is the required knowledge of the channel statistics, i.e. time and frequency channel correlations, which are usually unknown at the receiver and their estimation has a high computational burden.Based on the use of a comb pilot pattern arrangement, subspace projection and low-pass filtering, in [4] proposes an algorithm which does ...