Multiple Access Techniques Using Superframes Radu Balan Siemens

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

Overview 1. 2. 3. 4. 5. Superframe – what is it? Multiplexing of Signals using Superframes Intermezzo – Band Limited Signals TDMA, FDMA within this framework FHMA as an extension on FDMA

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:

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

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

Definition. A collection of indexed sets of vectors called a superframe if the direct sum set is is a frame for Properties. 1. 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

2. Multiplexing with Superframes Channel

3. Intermezzo – Band Limited Signals

4. The TDMA and FDMA Superframes Note the following:

This suggests the use of the following frames:

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

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: