02(p) 00(2p) 01(2p) 02(2p) , - 1 ON-1 1(Np-1) ZNp-1 (9-26) Alternatively using matrix notations the above equation can be rewritten as: (9-26a) The Least Square (LS) estimate of the coefficients are calculated by minimizing the squared distance between the actual channel vector Hand the estimated channel vector H as: (9-27) Where superscript denotes conjugate transpose operation, hence: (9-28) A number of different options exist while selecting the basic functions such as orthogonal poly- nomials, Fourier series, discrete cosine transform function, discrete sine transform series, etc. There are a number of reasons for using orthogonal polynomials, including ease of calculation of since becomes a diagonal matrix if matrix is orthogonal, resulting in ease of calculation of an's and the inverse matrix (-- with minimal computational complexity. The degree of orthogonal poly- nomials can be increased without changes in recursive calculation of an's. When applying the poly- nomial-based channel estimation, a sliding window is typically used to estimate the channel. This is done to avoid the use of high-order polynomials to estimate highly frequency-selective channels. The sliding window approach allows for local approximations to the channel transfer function using a window length larger than the polynomial order, providing a better estimate. In a special case where the OFDM channel estimation symbols are transmitted periodically and all sub-carriers over an OFDM symbol are used as pilots, the channel estimation algorithm is more simplified. In this case, the receiver uses the estimated channel transfer function to decode the received data within the block until the next pilot symbol arrives. If Yk = HkXk + Zk, k = 0, 1, 2, NFFT - denotes the received signal at kth sub-carrier (pilot sub-carrier), the LS estimate of the channel transfer function in this case is given as HLS = = YNFFT-1)H; Xk = 1, Ak (9-29) The channel transfer function at non-pilot sub-carriers can be estimated using interpolation in time. For convenie