In Section 4, the approximate analytical expression of the ergodic sum rate is derived, followed by our

asymptotic analysis for impaired hardware and upper bound for ideal hardware.

Soto, "

Asymptotic analysis for Volterra difference equations,"

Asymptotic Analysis, vol.

The

asymptotic analysis [26, 27] of the instantaneous mass or the instantaneous decay rate is obtained from the results of Section 3 and from (4) or (5), respectively.

Estimation (2.5) is an analog of the well known in

asymptotic analysis N.N.

Mauss,

Asymptotic Analysis and Boundary Layers, Scientific Computation, Springer, Berlin, Germany, 2007

In contrast to the

asymptotic analysis for [[sigma].sup.2.sub.e] = 0, the asymptotic outage probability of EPRS for [[sigma].sup.2.sub.e] [not equal to] 0 is easily obtained by inserting [R.sub.t] [approximately equal to] ([2.sup.2R] - 1)[[sigma].sup.2.sub.e] in (8)-(11), (17), and (18).

Lim, "

Asymptotic analysis of axially accelerating viscoelastic strings," International Journal of Engineering Science, vol.

(iv)

Asymptotic analysis of the outage probability of the secondary relay system under different scenarios, which provides important insights into the behavior of the outage performance.

The

asymptotic analysis of the integral [F.sub.2] (x) in (2.1) is much simpler than that of [F.sub.1](x), since the phase function f (t) has no stationary points in the integration interval [b, [infinity]) and then we can just repeatedly integrate by parts to get an asymptotic expansion [14, Chap.

The approach will be based on combining analytical methods (suitable perturbation theory,

asymptotic analysis) and numerical ones (spectral methods in space and time).

An

asymptotic analysis of the symbol error rates of a selection AF network is presented and a comparison of it with the conventional all participate schemes is carried out in [14].

Glizer, "

Asymptotic analysis and solution of a finite-horizon [H.sub.[infinity]] control problem for singularly-perturbed linear systems with small state delay," Journal of Optimization Theory and Applications, vol.