Signal and channel models Clausole campione

Signal and channel models. − We consider a network of L time-synchronized1 spectrum sharing operators (for ease of exposition one can set L=2), with full spectrum reuse. Estimation of (block- fading) channels in the uplink is considered,2 and all the SPs are equipped with M antennas each. To simplify the notations, we assume the 1st SP is the target SP, unless otherwise notified. We assume the pilots, of length τ , used by single- antenna users in the same SP area are mutually orthogonal. As a result, intra-cell interference is negligible in the channel estimation phase. However, non-orthogonal (possibly identical) pilots are reused from SP area to SP area, resulting in pilot contamination from L 1 interfering SPs. For ease of exposition, we consider the case where a single user per operator transmits its pilot sequence to its serving SP. The pilot sequence used in the l-th SP is denoted by: | | · · · | | sl = [ sl1 sl2 · · · slτ ]T . (3.14) The powers of pilot sequences are assumed equal such that sl1 2 + + slτ 2 = τ, l = 1, 2, . . . , L. × The channel vector between the l-th SP area’s user and the target SP is hl. Thus, h1 is the desired channel while hl, l > 1 are interference channels. All channel vectors are assumed to be M 1 complex Gaussian, undergoing correlation due to the finite multipath angle spread at the SP side [16]: hl = R1/2hW , l = 1, 2, . . . , L, (3.15) where hWl ∼ CN(0, IM ) is the spatially white M × 1 SIMO channel, and CN(0, IM ) denotes zero-mean complex Gaussian distribution with covariance matrix IM . In 1Note that assuming synchronization between uplink pilots provides a worst case scenario from a pilot contamination point of view, since any lack of synchronization will tend to statistically decorrelate the pilots. 2Similar ideas would be applicable for downlink channel estimation, provided the UT is equipped with multiple antennas as well, in which case the estimation would help resolve interferences originating from neighboring SPs. this scenario, we make the assumption that the covariance matrix Rl ¾ E{hlhH} can be obtained separately from the desired and interference channels. During the pilot phase, the M × τ signal received at the target SP is ΣY = h s + N, (3.16)l l=1 ∈ where N CM×τ is the spatially and temporally white additive Gaussian noise (AWGN) with zero-mean and element-wise variance σ2. Conventional channel estimation relies on correlating the received signal with the known pilot sequence (referred here as Least Squares (LS) estimate for exa...