.The data rate is R=log,M/T bits/s. Then 2b=R/W=p,which is the spectral efficiency of a modulation scheme(bits s/Hz).or p=是1g,M bits/2D The average energy of A per dimension is given by E=E/N If the Msignal points inA are assumed to be equiprobable,then f 2,fm2 To simplify performance assessment,we define a figure of merit (CFM)for a constellation as 5e山 (2.5) As we have stated in Chapter 1,from the signal space viewpoint,the data modulation can be viewed as a two-step process:a signal mapper followed by a simple waveform converter.A signal mapper performs the mapping of a binary vector of length logM into one of a const thethe siaon Mapping is not airary.clever shoices Iead to betcr lation ally,the binar vector performance over noisy channels. In some channels it is suitable to label points that are close in Euclidean distance to map to being close in Hamming distance.An example for such mapping is the Gray-mapping Fig 2.6 illustrates an example. 1 2-6 ⚫ The data rate is 2 R M T = log / bits/s. ⚫ Then 2 / b R W =   , which is the spectral efficiency of a modulation scheme (bits / s / Hz), or 2 2 log M N  = bits / 2D ⚫ The average energy of  per dimension is given by Ed = EN / N If the M signal points in  are assumed to be equiprobable, then 2 1 1 || || M N j j E M = =  a and 2 1 1 || || M d j j E MN = =  a ⚫ To simplify performance assessment, we define a figure of merit (CFM) for a constellation as 2 min ( ) 4 d d E   (2.5) As we have stated in Chapter 1, from the signal space viewpoint, the data modulation can be viewed as a two-step process: a signal mapper followed by a simple waveform converter. A signal mapper performs the mapping of a binary vector of length log2M into one of the signal points in a constellation of size M. Usually, the binary vector is referred to as the label of the signal point. Mapping is not arbitrary, clever choices lead to better performance over noisy channels. In some channels it is suitable to label points that are close in Euclidean distance to map to being close in Hamming distance. An example for such mapping is the Gray-mapping. Fig. 2.6 illustrates an example