66 467 recall our goal is to maximize from 466

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Unformatted text preview: develop the MLS receiver. Suppose we transmit a sequence of information bits with rate ½Ì ½ ÒÒ ¼ symbols per second and the transmission and channel ﬁlters are both causal. The re- ceived signal up to time ´Ã · ½µÌ , i.e., for Ø ´Ã · ½µÌ , is Ã Ö´Øµ Ò ¼ Ò Ú ´Ø ÒÌ µ · Ò´Øµ (4.59) This is simply a rewrite of (4.3) with the above assumptions applied. As mentioned above, we try to decide the sequence of transmitted symbols Ã ÒÒ ¼ based on our observation Ö´Øµ up to time ´Ã · ½µÌ 8. To do so, we treat the whole summation on the right hand side of (4.59) as our desired signal9. With this point of view, we are equivalently considering an AWGN channel with Å Å -ary communication system over the ¾Ã exhausting all the possible transmitted bit sequences. Each bit sequence is treated as an Å -ary “symbol”. This is the problem we have solved. Assuming all the bit sequences are equally probable, we can employ the ML receiver to minimize the probability of making an error when determining the transm...
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This note was uploaded on 12/13/2012 for the course EEL 6535 taught by Professor Shea during the Spring '08 term at University of Florida.

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