Research On The Richness Of Multipath Fields In Waveguides

The sound filed in a waveguide is a multipath field for the reason that most sound rays undergo one or more reflections from the surface and the bottom of the ocean.The multipath field contains rich spatial information,and it lead us to study the multipath field from the spatial perspective which help us with many topics,such as source localization.Hilbert space is an infinite-dimensional space and we regard it as a generalization of Euclidean space.We can represent the multipath field by using a set of orthonormal basis functions in Hilbert space.There are many common orthonormal basis functions,such as complex exponential functions,associated Legendre functions,and spherical harmonic functions.We often use spherical harmonic function expansion to represent the wavefield in 3-D physical space.We can use superposition of infinitely many weighted spherical harmonic functions to represent the multipath field in a 3-D waveguide.In fact,it is proved that finite number of spherical harmonic functions are enough for us to essentially build the field and we define the number as the dimensionality of the field.The results of numerical simulations prove the relationship between dimensionality and r,and they also show that reflecting coefficients of bottom and the depth of waveguide do not affect the dimensionality.When dealing with stochastic waveguide environment,detailed information about the surface and bottom of waveguide is difficult to achieve.Therefore,it is reasonable for us to regard the multipath field as a random process.Different environment of waveguide will lead to different multipath fields.The Karhunen-Loeve(K-L)expansion is used to obtain the optimal representation of multipath field which takes away the correlation of a random process and make sure the representation has the minimum number of uncorrelated terms.Then the richness is defined as the number of significant eigenvalues that account for 99%of the summation of total eigenvalues provided by K-L expansion.Different waveguide environments lead to multipath fields with different richness.We use results of numerical simulations to show more properties of richness.