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Small cell networks promise good quality of service (QoS) even for cell edge users, however pose challenges to cater to the high-speed users. The major difficulty being that of frequent handovers and the corresponding handover losses, which significantly depend upon the speed of the user. It was shown previously that the optimal cell size increases with speed. Thus, in scenarios with diverse users (speeds spanning over large ranges), it would be inefficient to serve all users using common cell radius and it is practically infeasible to design different cell sizes for different speeds. Alternatively, we propose to allocate power to a user based on its speed, e.g., higher power virtually increases the cell size. We solve well known Hamiltonian Jacobi equations under certain assumptions to obtain a power law, optimal for load factor and busy probability, for any given average power constraint and cell size. The optimal power control turns out to be linear in speed. We build a system level simulator for small cell network, using elaborate Monte-Carlo simulations, and show that the performance of the system improves significantly with linear power law. The power law is tested even for the cases, for which the system does not satisfy the assumptions required by the theory. For example, the linear power law has significant improvement in comparison with the 'equal power' system, even in presence of time varying and random interference. We observe good improvement in almost all cases with improvements up to 89\% for certain configurations.

Photoacoustic sensing and imaging techniques have been studied widely to explore optical absorption contrast based on nanosecond laser illumination. In this paper, we report a long laser pulse induced dual photoacoustic (LDPA) nonlinear effect, which originates from unsatisfied stress and thermal confinements. Being different from conventional short laser pulse illumination, the proposed method utilizes a long square-profile laser pulse to induce dual photoacoustic signals. Without satisfying the stress confinement, the dual photoacoustic signals are generated following the positive and negative edges of the long laser pulse. More interestingly, the first expansion-induced photoacoustic signal exhibits positive waveform due to the initial sharp rising of temperature. On the contrary, the second contraction-induced photoacoustic signal exhibits exactly negative waveform due to the falling of temperature, as well as pulse-width-dependent signal amplitude which is caused by the concurrent heat accumulation and thermal diffusion during the long laser illumination. An analytical model is derived to describe the generation of the dual photoacoustic pulses, incorporating Gruneisen saturation and thermal diffusion effect, which is experimentally proved. Lastly, an alternate of LDPA technique using quasi-CW laser excitation is also introduced and demonstrated for both super-contrast in vitro and in vivo imaging. Compared with existing nonlinear PA techniques, the proposed LDPA nonlinear effect could enable a much broader range of potential applications., Comment: 23 pages, 6 figures