70 to update and store and the that maximizes it

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Unformatted text preview: 4.16: Maximum likelihood sequence receiver that gives the largest metric. Hence its complexity increases exponentially with time. This is clearly impractical and this is why the relatively simple equalization techniques described in the previous section are more popular in practice. ¼ for Ò When ÜÒ is of finite-support10, i.e., ÜÒ Ä, a significant simplification can be applied to the calculation of the maximum metric rendering the MLS receiver practical. First, we can update the metric in the following way: ¼ ô õ à ½ ´ à ½ µ · à Ýà à ½ Ò Ã Ä ½ Ò ÜÒ Ã Ã Ü¼ ¾ ½ (4.64) We are going to make use of two important observations from (4.64) to simplify the maximization of the metric. The first observation is that the updating part (the second term on the right hand side) depends only on ×à If we decompose à into à à ô õ à ½ à ¾ ×à à ½ ´×à ¼ à ×à µ (4.65) Ã Ä ½ , (4.64) can be rewritten as where Ô´ÝÃ Ã Ä Ã Ã Ä ½ µ · Ô´Ýà Ýà à ½ Ò Ã Ä Ã ×à µ ½ Ò ÜÒ Ã Ã Ü¼ ¾ (4.66) ½ (4.67) Recall our goal is to maximize à ´ à µ. From (4.66) Ñ Ü Ã´ õ à ÑÜ Ã ½ ´×Ã Ñ ×Ü Ñà ´×à µ · Ô´Ýà à ×Ã Ã Ä ½ Ãà 10 Ã Ä ½ µ · Ô´Ýà à ×à µ à ×à µ (4.68) This is generally not true for a channel with a bandlimited response unless some form of transmission pulse design is applied. However, even when ÜÒ is not strictly of finite-support, the simplification here can sti...
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