Quantization Codes Comprising Multiple Orthonormal Bases Alexei Ashikhmin Bell Labs MIMO Broadcast Transmission Quantizers Q(m) for MIMO Broadcast Systems • transmission to mobiles with orthogonal channel vectors • transmission to mobiles with almost orthogonal channel vectors Simulation Results Algebraic Constructions of Q(m)
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Quantization Codes Comprising Multiple Orthonormal Bases Alexei Ashikhmin Bell Labs MIMO Broadcast Transmission Quantizers Q(m) for MIMO Broadcast.
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Quantization Codes Comprising
Multiple Orthonormal Bases Alexei Ashikhmin
Bell Labs MIMO Broadcast Transmission
Quantizers Q(m) for MIMO Broadcast Systems • transmission to mobiles with orthogonal channel vectors • transmission to mobiles with almost orthogonal channel vectors
Simulation Results
Algebraic Constructions of Q(m)
MIMO Broadcast Transmission
Base
Station
is a quantization code
The Base Station (BS):
• chooses some mobiles, for example mobiles 1,2,3
• forms and using computes a precoding matrix
• transmits to mobiles 1,2,3 using the precoding matrix
Requirements for a quantization code
• should provide good quantization (for given size )
• should afford a simple decoding
• should have many sets of M orthogonal codewords (bases of )
BS
is the channel vector of
is the channel vector of
If are pairwise orthogonal then signals sent to do
not interfere with each other
is the channel vector of
• Mobiles quantize:
• Base Station strategy – among find orthogonal codewords, say , and transmit to the corresponding mobiles 1,3,5
• The channel vectors of these mobiles will be almost orthogonal
Base
Station
If a channel vector is quantized into we say that is occupied
and mark by
• If the number of mobiles (channel vectors) is large, e.g. , then
with a high probability all codewords will be occupied
• In this case even if we have only a few sets of orthogonal codewords, we easily find a set of occupied orthogonal codewords
Let us have a quantization code
orthogonal codewords
• Let and the number of mobiles is small, say
• Let
• If are many sets of orthogonal code vectors there is a chance to find occupied orthogonal codewords