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We normalize the channel by letting.
The constant (sigma ^{2}_{h}) is chosen to normalize the channel power to one.
so as to normalize the channel coefficients to unit variance [14].
For the sake of fair comparisons, we normalize the channel covariance matrix such that the mean of the eigen values equals one (equal to the i.i.d. channel case ).
We therefore normalize the channel matrices obtained from the QUADRIGA channel model to satisfy (mathbb {E}left (left |mathbf {H}_{u}[n]right |^{2}right) = N_{r} N_{t}phantom {dot {i}!}).
The proof of Corollary 1 is presented in Appendix 2. In this paper, we assume that each user has the same transmit power and then normalize the channel response vectors of all users h1,…,h K, then the channel response matrix ({mathcal {H}}) will have unit-columns.
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All tested normalization methods are able to correct for the observed biases, where from a technical standpoint, normalization approaches that normalize channels together (VSN, LOWESS, Peng's method, quantile) equalize the data distributions to a larger extent than normalization approaches that normalize the channels separately (T-quantile, Tukey's biweight scaling).
In addition, these coefficients can normalize the channels ρ i h i 's to the same statistics with the same unit norm.
Since we have normalized the channel gain at d=0, the two groups of curves meet at this position.
The CDI is calculated by normalizing the channel matrix between transmitter i and receiver k using its Frobenius norm as (phantom {dot {i}!}bar {mathbf {H}}_{ki} = frac {mathbf {H}_{ki}}{left |mathbf {H}_{ki}right |_{F}}).
These improvements will be demonstrated with performance comparisons by computer simulations in Section 4. Consider an OFDM system with DFT size N = 64 operated over a frequency-selective channel of dispersion length v = 9 having an exponential power profile αe-πm/10, m = 0, 1, …, v - 1, with unit power, where α is used to normalized the channel power[30].
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