rates independently in time and frequency domains. First, the CTF is estimated from the received short blocks. Second, time domain channel inter- polation is considered. For the simplicity of derivation of the channel estimation algorithm, the channel impulse response is considered constant over the duration of an OFDM symbol. 6.10.1 Frequency-Domain Channel Estimation For frequency-domain channel estimation, first an estimate of the CTF at the pilot subcarriers is obtained. Then the full channel transfer function is calculated using an interpolation method. 1. Estimate at pilot position: Let Pii=0,..., Np - 1 be a set of indexes contain- ing the subcarrier indexes that carry pilot symbols, where N is the indexes of pilot symbols in the short block. A least-squares (LS) estimate of the CTF at these pilot positions can be calculated as (6.17) where z[p;] and z[pi] are, respectively, the received short block after the FFT and the transmitted short block in the ith pilot subcarrier. hp is an Np long col- umn vector containing the LS estimates of the channel at pilot subcarriers. Wiener filtering interpolation: Wiener filtering is the optimum interpola- tion method in terms of MSE. Using the statistics of the channel and noise, it performs an MMSE interpolation of the estimates at pilot subcarriers, optimally reducing the effects of noise and channel distortion. The full CTF is obtained by (6.18) where Rhhp is the cross-correlation matrix of the true CTF and the true CTF at pilot subcarriers, Rhphp is the autocorrelation matrix of the true CTF at pilot subcarriers, 02 is the noise power, and INP is the N, X N, identity matrix. Note that the CTF coefficients are assumed to be uncor- related to the noise process. © 2009 by Taylor & Francis Group, LLC Single-Carrier Transmission for UTRA LTE Uplink 6.10.2 Time-Domain Channel Estimation A simple time-domain channel estimation based on linear interpolation is assumed. In a subframe, two short blocks are transmitted. The channel estimation for each subframe is a linear int