# notes7 - ECE 562 Fall 2011 Optimum Reception in AWGN ◦...

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Unformatted text preview: ECE 562 Fall 2011 September 20, 2011 Optimum Reception in AWGN ◦ Restricting to the case of memoryless modulation with no ISI (ideal AWGN channel), we can focus on one symbol interval [0 ,T s ] without loss of optimality. We will also assume perfect syn- chronization at the receiver to begin the analysis. The received signal model in AWGN is then r ( t ) = s ( t ) + w ( t ) ≤ t ≤ T s The signal s ( t ) ∈ { s 1 ( t ) ,...,s M ( t ) } , and the goal of the receiver is to determine which symbol m (equivalently, which signal s m ( t )) was sent on the channel. Without the additive noise, this is a trivial problem as long as the signals are different, i.e., d km 6 = 0, for k 6 = m . What do we do in the presence of noise? As we saw in class, the optimum receiver can be split into two steps: ◦ Step 1: Demodulation. Projection of r ( t ) on to basis functions f 1 ( t ) ,...,f L ( t ) of the signal space to form the vector of sufficient statistics : R = [ R 1 R 2 ...R L ] > , R ` = h r,f ` i ◦ Step 2: Detection. Decide which symbol was sent based on R ....
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notes7 - ECE 562 Fall 2011 Optimum Reception in AWGN ◦...

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