ronecker product C = A x B, also called matrix direct product, is an mp X nq matrix with elements defined by cab = ajkl where a = p(i - 1) + k and B = q(j - 1) + 1. The matrix direct product provides the matrix of the linear transformation induced by the vector space tensor product of the original vector spaces. More precisely, suppose that operators S:V1 -> W1 and T:V2 W2 are given by S(x) = Ax and T(y) = By, then S T:V1 x V2 W1 x W2 is determined by SQT(xy) = =(Ax)@(By)=(A@B)(xy). = New Radio Access Physical Layer Aspects (Part 1) 313 Table 3.3: gNB/UE correlation matrix [9]. Number of Antennas Entity RgNB 1 RUE = 1 Rue=(1-1) Table 3.4: Values of a and B for different antenna correlations [9]. Low Correlation Medium Correlation High Correlation cross-polarized antennas are present at the receiver, it is assumed that NRx/2 receive anten- nas have the same polarization, while the remaining NRx/2 receive antennas have orthogo- nal polarization. Likewise, if cross-polarized antennas are present at the transmitter, it is assumed that NTx/2 transmit antennas have the same polarization, while the remaining NTx/2 transmit antennas have orthogonal polarization. It is further assumed that the antenna arrays are composed of pairs of co-located antennas with orthogonal polarization. Under these assumptions, the per-tap channel correlation is determined as Rn = RgNB,n X T X RUE,n where RUE,n is an NRX X NRX matrix, if all receive antennas have the same polarization, or an NRx/2 X NRx/2 matrix, if the receive antennas are cross- polarized. Likewise, RgNB,n is an NTX X NTX matrix, if all transmit antennas have the same polarization, or a NTX/2XXTX/2 matrix, if the transmit antennas are cross-polarized. Matrix T is a cross-polarization matrix based on the cross-polarization defined in the cluster-delay-line models. Matrix T is a 2X2 matrix, if cross-polarized antennas are used at the transmitter or at the receiver. It is a 4 X 4 matrix if cross-polarized antennas are used at both the transmitter and the receiver [9]. Table 3.3