There are some systems in which only real and positive values can be transmitted. in the following matlab example, we show 3 systems. system 1 is the ordinary ofdm system and no special constraint is applied. system 2 follows conjugate symmetry property to ensure real value ifft output. system 3 also follows conjugate symmetry property. in addition, all odd-index values of x3 are set to 0. the output of ifft, x3, are real but can be both positive and negative. the transmitter simply sets the negative part of x3 to be 0 so that x3 p is resulted. it is clear that x3_p is real and positive. however, can the receiver recover x3 from x3_p? how and why? complete theoretical derivation/proof and matlab code.