5.5 Consider the seven-signal set shown in Figure 5.28. The signals are transmitted over the AWGN channel with power spectral den-

sity No/2, with equal a priori probabilities (♬; = 1/7) and equal energies (for the six nonzero signals).

(a) Determine (draw on the figure) the optimal decision regions.

203

(b) Determine an upper bound on the probability of error given signal 56(1) was transmitted.

(c) Determine an upper bound on the probability of error given signal so(t) was transmitted.

(d) Determine an upper bound on the average probability of error.

(-1/2, √3/2)

(-1,0)

$3(1)

Figure 5.28 Signal set for Problem 5.7.

$2(1)

(-1/2,-√3/2)

Figure 5.28

$4(1)

91(1)

(0,0)

$6(1)

(1/2, √3/2)

$1(t)

(1,0) 40(1)

So(t)

$5(1)

(1/2,-√3/2)