5.2 A communication system transmits 3 bits using one of eight equally likely signals in two dimensions, as shown in Figure 5.26. That is, the signals are so(t) = Apo(t) $₁(t) = A$(1) + A$1 (1) $₂(t) = A$1(1) $3(t) = −A$(1) + A$1 (1) $4(t) = -Apo(t) $5(t) = -A$(1) - A$1 (1) $6(1) = -A$1(1) $7(1) = A$(1) - A$1(1). The signals (1) and 1(1) are orthonormal. The received signal is the transmitted signal plus WGN. (a) Draw a block diagram of the optimal receiver. (b) Determine (draw) the optimal decision regions (to minimize the average error probability). (c) Determine the probability of error for signal s₁(t). (d) Determine a bound on the error probability for signal so(t). 281

Fig: 1