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Necessary Density Conditions for MIMO Sampling
| Content Provider | CiteSeerX |
|---|---|
| Author | Venkataramani, Raman |
| Abstract | Abstract- We consider a sampling scheme where a set of multiband input signals is passed through a MIMO channel and the outputs are sampled nonuni-formly. MIMO sampling is a general scheme that en-compasses various other schemes, including Papoulis’ generalized sampling and nonuniform sampling as special cases. We present necessary density conditions for stable nonuniform MIMO sampling and consistent reconstruction of the multiband inputs. I. PROBLEM DESCRIPTION Let a set of multiband signals x T ( t) , r = 1,..., R with spectral supports Fr W be passed through a MIMO channel consisting of linear time-invariant filters to produce outputs y p ( t) , p = 1,..., P given by y p ( t) = E,“=, g p r * zr ( t) where * denotes convolution and g p r ( t) E L2(R) are the channel fd-ter impulse responses. The outputs y p ( t) are subsequently sampled on nonuniform sets A, = { A n p : n E Z}. This gen-eral scheme, called MIMO sampling, subsumes various other schemes including Papoulis ’ generalized sampling [l] as spe-cial cases. We address the following questions: (a) what are necessary conditions on {A,} for stable reconstruction of the inputs z r ( t) from the MIMO output samples {yp(Xnp)}? (b) what are necessary conditions on {A,} for consistent recon-struction, i.e., 3zr(t) such that yp(X,,) = cnp for any sequence {cnp: n E Z, p = 1,..., P} E 1’. Our results, expressed in terms of sampling densities, use ideas from [2] to generalize Landau’s classical results [3]. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Mimo Sampling Necessary Density Condition Various Scheme Necessary Condition Spectral Support Fr Linear Time-invariant Filter Nonuniform Sampling Sequence Cnp Special Case Spe-cial Case Stable Reconstruction Consistent Recon-struction Problem Description Mimo Output Sample Stable Nonuniform Mimo Sampling Gen-eral Scheme Nonuniform Set Mimo Channel Mimo Channel Consisting General Scheme Consistent Reconstruction Channel Fd-ter Impulse Response Landau Classical Result Following Question Sampling Scheme Present Necessary Density Condition Multiband Input Signal Multiband Signal |
| Content Type | Text |
| Resource Type | Article |
