Analysis and Design of Wireless Ad Hoc Networks With Channel Estimation Errors

Dynamic power optimization of pilot and data for downlink OFDMA systems

“…According to MMSE estimator,Ĝ ij (τ ) andG ij (τ ) are uncorrelated mean-zero Gaussian random vectors with variances σ 2 Gij (τ ) = γt(τ ) 1+γt(τ ) and σ 2 Gij (τ ) = 1 1+γt(τ ) , respectively, where γ t (τ ) = Pt(τ ) (Li+1)N0 is the signal-to-noise ratio (SNR) for pilot transmission, and P t (τ ) is the pilot power which uniformly spreads in frequency domain. The data transmission rate in terms of estimation error is given by [16]:…”

“…t (τ ), P ij (τ ))  ≥ λ i + ϑ. (39)From (39) and (38) can be further simplified as(Q(τ )) − V E * t (τ ), P * ij (τ )) | Q(τ ) t (τ ), P ij (τ )) | Q(τ ) From (40), it is easily proved that there exist some finite positive constants C satisfying(Q(τ )) ≤ C.(41)Substituting(15) and(16) into above inequality and summing over τ ∈ {0, 1, • • •, T − 1}, we obtainE{Q i (T ) 2 } ≤ 2T C + 2E{L(Q(0))}. (42)From the variance formula D{Q i (T )} = E{Q 2 i (T )} − E 2 {Q i (T )}, we have E{Q 2 i (T )} ≥ E 2 {Q i (T )}, since D{Q i (T )} > 0.…”

Subcarrier and power allocation for multi‐user OFDMA wireless networks under imperfect channel state information

“…n ij is zero mean Gaussian noise with variance . Treating the channel estimation error as noise [28], the SNR can be expressed as where γ ij = P ij / B 0 n 0 . Then the corresponding data rate of user m i is written as Note that the second equality in (7) holds true, because arbitrary Gaussian random variance is normalised to a standard Gaussian random variable ν i with zero mean and unit variance by dividing by the standard deviation, that is, …”

Large-Scale Fluid Antenna Systems With Linear MMSE Channel Estimation

“…However, a limited number of prior works addresses the impact of channel estimation error on the network performance from a macroscopic pointof-view. The authors in [12], evaluated the impact of channel estimation in the context of point-to-point single-input singleoutput ad-hoc systems, by using linear minimum mean square error (LMMSE) channel estimation. The coverage probability and the impact of channel estimation on the performance of random networks have been studied in [13], capturing the dependence of the optimal training-pilot length on the ratio between the receiver and transmitter densities.…”