Equivalence of Time- and Frequency-domain Channel Estimation for Multicarrier Signal Reception

1. Introduction Ultra high-speed data transmission capability will be required in the next generation wireless communication systems in a severe frequency-selective fading channel [1]. In a mobile radio channel, the transmitted signal is reflected and diffracted by many obstacles and is received as a multipath signal with different time delays at a receiver, thus creating the frequency-selective fading. Recently, the multicarrier technique, e.g., orthogonal frequency division multiplexing (OFDM) and multi-carrier code division multiple access (MC-CDMA), has been attracting much attention [2], [3]. For achieving high-quality data transmissions, the use of coherent modulation rather than differential modulation is essential. So far, many channel estimation schemes in time-and frequency-domain have been proposed for coherent detection of multicarrier signals in a severe frequency-selective fading channel [4]-[6]. In this paper, time-domain representation of the frequency-domain channel estimation is presented and equivalence of time-and frequency-domain channel estimation is pointed out. Frequency-domain channel estimation using 2M+1-tap FIR filter is considered for OFDM and MC-CDMA with N c subcarriers. The filter structure is illustrated in Fig. 1. Channel estimation is carried out using the noisy instantaneous channel gains } 1-~ 0 ; ˆ { c k N k H = , which are obtained from received pilot symbols or reverse modulation to remove data-modulation from the received subcarriers, where k represents the subcarrier index. Using 2M+1 tap weights {W k ; k=-M~+M}, the channel gain k H ~ at the k-th subcarrier is estimated as { } ¦ ¦ − = − = − − = = 1 0) 2 exp() () (ˆ ˆ ~ c N c c M M m m m k k N k j w h N W H H τ τ π τ τ , (1) where) (ˆ τ h and w(τ) represent the channel impulse response corrupted by noise and the delay-time window, respectively. In the above, edge effect in the frequency-domain filtering is neglected. Eq. (1) implies that the frequency-domain filtering is equivalent to multiplying the noisy impulse response estimate by delay-time window. Therefore, the problem of finding the frequency-domain filter tap weights can be replaced by finding the good delay-time window. Once the delay-time window is found,) () (ˆ τ τ w h can be computed and then, using N c-point FFT, the channel gain at the k-th subcarrier is obtained. Fig. 1 Frequency-domain FIR filter structure. The multipath fading channel is assumed to have an L=8-path exponential …