Neural FIR adaptive Laguerre equalizer with a gradient adaptive amplitude for nonlinear channel in communication systems

To mitigate the linear and nonlinear distortions in communication systems, two novel nonlinear adaptive equalizers are proposed on the basis of the neural finite impulse response （FIR） filter, decision feedback architecture and the characteristic of the Laguerre filter. They are neural FIR adaptive decision feedback equalizer （SNNDFE） and neural FIR adaptive Laguerre equalizer （LSNN）. Of these two equalizers, the latter is simple and with characteristics of both infinite impulse response （IIR） and FIR filters; it can use shorter memory length to obtain better performance. As confirmed by theoretical analysis, the novel LSNN equalizer is stable （0 〈α〈1）. Furthermore, simulation results show that the SNNDFE can get better equalized performance than SNN equalizer, while the latter exhibits better performance than others in terms of convergence speed, mean square error （MSE） and bit error rate （BER）. Therefore, it can reduce the input dimension and eliminate linear and nonlinear interference effectively. In addition, it is very suitable for hardware implementation due to its simple structure.

Nonlinear and non-CP gates for Bloch vector amplification

Any state r=(x,y,z)of a qubit,written in the Pauli basis and initialized in the pure state r=(0,0,1),can be prepared by composing three quantum operations:two unitary rotation gates to reach a pure state r=(x^(2)+y^(2)+z^(2))-1/2×(x,y,z)on the Bloch sphere,followed by a depolarization gate to decrease|r|.Here we discuss the complementary state-preparation protocol for qubits initialized at the center of the Bloch ball,r=0,based on increasing or amplifying|r|to its desired value,then rotating.Bloch vector amplification increases purity and decreases entropy.Amplification can be achieved with a linear Markovian completely positive trace-preserving(CPTP)channel by placing the channel’s fixed point away from r=0,making it nonunital,but the resulting gate suffers from a critical slowing down as that fixed point is approached.Here we consider alternative designs based on linear and nonlinear Markovian PTP channels,which offer benefits relative to linear CPTP channels,namely fast Bloch vector amplification without deceleration.These gates simulate a reversal of the thermodynamic arrow of time for the qubit and would provide striking experimental demonstrations of non-CP dynamics.

An Improved Cancellation of Nonlinear Intersymbolinter ference for Voiceband Data Transmission

in this paper ,an imprcoed nonltnear cancellation techn,que is proposed for ,wnioving nonlin-ear intersyde interference for voicel,and data lransmiss,on over dtspersive no,ilinear channels. A newstrecture 'cancellation first ,match and egualization later' is adopled in lhe ,wceiver. A fractionally-spaced equalizer (FSE)behind the nonlinear canceller can perform the functions of both a maitched fil-ter and a linear equalizer,and maximize the oulput signal to noise ralio . so that a perforniance im-provement of 2～ 3 dB is obtained compared with Biglteri's system￣[5].The ftrst order Volterra kernelmeasurement and adaptive recursive algorithms are used for the nonlinear channel eslimulor whichadaptively follws parameters of dispersive nonlinear channels. This approach allews a simple. and ef-fective implementalton ,as less computations are required. Simulation results for 9. 6 kbil/s data trans-mission over dispersive nonlinear channels show thal the nonlinear cancellalion proposed in this papercan reduce the probalelity of btt error by three orders of magnitude for the 16 QAM syuem.

Examples of Boundary Layers Associated with the Incompressible Navier-Stokes Equations

The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated.All of them are associated with the incompressible Navier-Stokes equations for Newtonian fluids equipped with various Dirichlet boundary conditions(specified velocity).These examples include a family of(nonlinear 3D) plane parallel flows,a family of(nonlinear) parallel pipe flows,as well as flows with uniform injection and suction at the boundary.We also identify a key ingredient in establishing the validity of the Prandtl type theory,i.e.,a spectral constraint on the approximate solution to the Navier-Stokes system constructed by combining the inviscid solution and the solution to the Prandtl type system.This is an additional difficulty besides the wellknown issue related to the well-posedness of the Prandtl type system.It seems that the main obstruction to the verification of the spectral constraint condition is the possible separation of boundary layers.A common theme of these examples is the inhibition of separation of boundary layers either via suppressing the velocity normal to the boundary or by injection and suction at the boundary so that the spectral constraint can be verified.A meta theorem is then presented which covers all the cases considered here.