Instead of using the physical oscillating displacement, the problem is described in terms of a complex envelope, generated by an appropriate use of the Hilbert transform.
These laws are introduced in a finite element code, which predicts the stress and strain status of a complex envelope structure.
Considering the complex envelope x k = ρ k e j θ k of the HPA input at each branch where ρ k and θ k denote, respectively, the amplitude and the phase of x k, the complex envelope of a memoryless HPA output z k (n) can be modeled as follows: z k n = g x k n = A ρ k e j θ k + P ρ k = S ρ k e j θ k (6).
Finally, the main issues of this work are concluded in Section 7. The complex envelope of an OFDM symbol in discrete-time domain can be written as x[n] = frac{1}{sqrt{N}}sumlimits^{N-1}_{k=0}X_{k}e^{frac{j2pi nk}{N}}enspace, 0leq nleq N-1, (1).
At the transmitter (TX) side, an SRRC filter is adopted, with a roll-off factor ρ. The complex envelope of the signal can be written as: s ( t ) = ∑ n = − ∞ + ∞ a n p ( t − n T s ), (2).
It is well-known in fact that, if the power spectral density (PSD) of the disturbance is not symmetric around a central frequency, the autocorrelation function of the complex envelope of the data is complex valued and consequently also the scatter matrix (see, e.g., [25]).
where P ˜ i ( t ) is the time-varying received complex envelope of each arrival L at a specific angle θ i.
where C t) is the complex envelope of the modulated signal, n(t) is a band-limited noise, fc is the carrier frequency, α is the channel amplitude, φ is the phase offset, Δf is the carrier frequency offset, and Re denotes the real part.
It is shown that we can have excellent performances using only 4 bits to quantize the real and imaginary parts of the complex envelope of the received signal at the BS, with a performance close to the MFB, and although relatively simple, our analytical approach was shown to be quite accurate.
In contrast, the complex envelope of the oscillator signal can be shown to be a stationary process (with [1, the Lorentzian power spectrum]).
