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Exact(16)
where C is defined as the vector of transmitted pilot symbols with a length of | P |.
where the vector of transmitted signals S t) and the vector of received signals R t) have the dimensions NT and NR, respectively (see Section 4).
We can then write the error signal ϵ and the vector of transmitted signals u as ϵ = ϵ o + ϵ ϵ T = 1 c H R RLP - D s + ϵ 1 c HTs, u = u 0 + ϵ u T = 1 c R RLP s + ϵ 1 c Ts. (28).
where r is the received signal vector and Ψ ˜ ˜ is the system matrix and b is the vector of transmitted data symbols, and finally n is the vector of independently and identicallydistributed additive white Gaussian noise (AWGN) samples with zero-mean and variance ρ2.
white noise with zero mean and known variance, u k ∈ C N × 1 is the vector of transmitted signals and H k ∈ C M g × N is the channel matrix where H ij k is the complex channel gain from transmitter j to user i.
where R, an N p × 1 vector containing the samples of the received signals, A ( u ) = F -1 a ( u ), the vector of transmitted modulation symbols of user u after subcarrier mapping with F, the N p × N p DFT matrix, G ( u ), the N p × N p channel matrix that can be expressed as G ( u ) ¯ = H ( u ) ¯ F ¯ δ ( u ) ¯ F − 1 ¯ + ( δ − N p ( u ) − 1 ) F ¯ h Δ ( u ) ¯ δ ( u ) ¯ F − 1 ¯ (6).
Similar(44)
The vector of transmit symbols is mapped directly to the transmit antennas.
The vector of transmit symbols with power, where, is mapped to the transmit antennas as follows: (5). is the precoding matrix of size which is a function of the received CSI of the scheduled users, and is the beamforming vector corresponding to MS. Therefore with linear precoding, the th MS, where, receives (6).
where is the channel matrix, is the vector of signals transmitted, and is the complex additive white Gaussian noise (AWGN) vector with zero mean and identity covariance matrix.
where is the channel from the th parent base station to the relay, is the symbol transmitted by the th base station (intended for the th user being served by the shared relay), is the matrix of channel coefficients from interfering base stations, is the vector of symbols transmitted by the interferers, and is spatially white zero-mean additive white Gaussian noise at the relay.
where is the effective channel gain from the base stations to the th mobile after precoding, dirty paper coding, and waterfilling, is the transmitted symbol intended for the th mobile, is the vector channel from the interferers to the th mobile, is the vector of symbols transmitted by the interferers, and is the additive white Gaussian noise at the th mobile.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com