Praise for Fundamentals of WiMAX

188 Chapter 5 • Multiple-Antenna Techniques5.7.2.2 Frequency-Domain Channel EstimationChannel estimation is simpler in the frequency domain than in the time domain. For preamblebasedfrequency-domain channel estimation, the received symbol of the lth subcarrier in the frequencydomain isYl ()= HlXl () () + Nl ().(5.71)Since Xl () is known a priori by the receiver, the channel frequency response of each subcarriercan easily be estimated. For example, lth frequency-domain estimated channel using LS is−1Ĥl ()= Xl () Yl ().(5.72)Similarly, for pilot-based channel estimation, the received symbols for the pilot tones arethe same as Equation (5.71). To determine the complex channel gains for the data-bearing subcarriers,interpolation is required.Least-squares channel estimation is often not very robust in high-interference or noisy environments,since these effects are ignored. This situation can be improved by averaging the LSestimates over numerous symbols or by using MMSE estimation. MMSE estimation is usuallymore reliable, since it forms a more conservative channel estimate based on the strength of thenoise and statistics on the channel covariance matrix. The MMSE channel estimate in the frequencydomain isĤ= AY,(5.73)where H and Y here are the L point DFT of H and the received signal on each output subcarrier,and the estimation matrix A is computed as2 * 1 1 1A= R ( R σ ( X X) ) X ,H H + − − −(5.74)*and Ris the channel covariance matrix, and it is assumed that the noise/interferenceon each subcarrier is uncorrelated and has variance σ 2 . It can be seen by setting σ 2 = 0 thatH= E[ HH ]if noise is neglected, the MMSE and LS estimators are the same.One of the drawbacks of conventional Linear MMSE frequency-domain channel estimation isthat it requires knowledge of the channel covariance matrix in both the frequency and timedomains. Since the receiver usually does not possess this information a priori, it also needs to beestimated, which can be performed based on past channel estimates. However, in mobile applications,the channel characteristics change rapidly, making it difficult to estimate and track the channelcovariance matrix. In such cases, partial information about the channel covariance matrix maybe the only possibility. For example, if only the maximum delay and the Doppler spread of thechannel are known, bounds on the actual channel covariance matrix can be derived. Surprisingly,the LMMSE estimator with only partial information often results in performance that is comparableto the conventional LMMSE estimator with full channel covariance information. The performanceof these channel-estimation and tracking schemes for WiMAX are provided in Chapter 11.