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Multiple Access Techniques Using Superframes

Explore the concept of superframes for multiplexing signals using TDMA, FDMA, and FHMA within a framework. Learn about single access encoding-decoding schemes and the properties and benefits of superframes.

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Multiple Access Techniques Using Superframes

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  1. Multiple Access Techniques Using Superframes Radu Balan Siemens Corporate Research Princeton , NJ 08540 rvbalan@scr.siemens.com SPIE Conference, San Diego August 2000

  2. Overview • Superframe – what is it? • Multiplexing of Signals using Superframes • Intermezzo – Band Limited Signals • TDMA, FDMA within this framework • FHMA as an extension on FDMA

  3. 1. Superframes - Introduction Let H be a Hilbert space (e.g. , the space of -band limited signals) embedded in K (e.g. with ). Let I be a countable index set. A subset of K is a frame for H with bounds A,B>0 if: Property. There is a dual frame such that:

  4. Single Access Encoding – Decoding Scheme Channel Encoder Decoder Formal Embedding in the Coefficients Space

  5. The signals can be reconstructed from provided: Or, equivalently:

  6. Definition. A collection of indexed sets of vectors is called a superframe if the direct sum set is a frame for • Properties. • Geometric Picture: Equivalent conditions in term of component • sets (frames and transversal intersection of coeffs ranges); • 2. Duality: The existence of dual superframe -> Reconstruction • formula

  7. 2. Multiplexing with Superframes Channel

  8. 3. Intermezzo – Band Limited Signals

  9. 4. The TDMA and FDMA Superframes Note the following:

  10. This suggests the use of the following frames:

  11. In the Frequency-Division Multiple Access (FDMA) case, the encoding scheme has the following structure:

  12. 5. FHMA as an Extension of FDMA The Frequency-Hoping Multiple Access is a variation of FDMA. The Encoding scheme uses the following relation: and the associated frames are:

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