We need to calculate the TGVP for a relatively large number of time-slots K to obtain a tight approximation.
The authors of [11] have obtained a tight lower bound of the outage probability for underlay cognitive relay networks.
When K−1 is a prime power, we obtain a tight frame with K2+1 vectors and when K is a prime power, with K2+K−1 vectors.
The construction here is based on the unitary extension principle, we make use of the pseudo splines of type II to obtain a tight frame.
Due to the nonlinear nature of the original formulation, a piece-wise linearization approach is applied to obtain a tight lower bound of the optimal solution.
In fact, a new optimization formulation can be proposed that can set a limit on maximum constellation extension in order to obtain a tight trade-off between PAPR reduction and BER performance degradation caused by constellation distortion.
Several authors have considered different methods to obtain a tight tolerance for amplitude and phase mismatches of the two loops [22 32], but the method presented here is based on genetic algorithms (GAs) and it requires a simple additional circuit to obtain the desired matching based on the measurement of the out-of-band interference, maintaining the output mean power [33].
For both MRC and SD schemes, we also obtain a tight and invertible bound on the BLEP, that enables us to analytically evaluate the quality of service expressed in terms of outage probability in channel affected by fading and shadowing and, as a consequence, the impact of multiple antennas on the system coverage.
Some fundamental and yet challenging problems are addressed : (1) How to obtain a tight quasi-synchronization error bound; (2) How many and which nodes should be controlled; (3) How to design the coupling strength, to select the pinned nodes and to determine the impulse intervals to optimize the error bound or to achieve quasi-synchronization within a prescribed error bound.
As such, we propose replacing the term (b_{i}^{(ell)}xi ^{(ell)}_{i}(mathbf {y}_{i},mathbf {x}_{i}^{(ell)})) (which is smaller than (b_{i}^{(ell)}mathbf {y}_{i})) in the denominator of (14) by (b_{i}^{(ell)}mathbf {y}_{i}) to obtain a tight lower bound for throughput.
