Question

An 8-ary PSK (phase shift keying) signal is transmitted over an additive, zero mean, band-limited Gaussian noise channel.The channel output is r(t)-s(t)+n(t), st<T, where s(tAcos 2rft+0) for ie 10,123,4,5,6,7) were,+8 16 8 The noise n(t) is narrowband, zero mean, bandpass Gaussian noise with power spectral density Sn (f) is shown in Figure 3, where B is the bandwidth of the noise S, (f) (Watts/Hz) 2 cf (Hz) Figure 3 T herefore, 2 2 2 0 elsewhere (i) What is the transmitted symbol rate, R,, in symbols per second as a function of T? (ii) What is the transmitted bit rate, R,, in bits per second as a function of T? () What is the power of s(t), P, as a function of A? (iv) What is the transmitted energy per bit, E,, in Joules as a function of A and T?

Answer 1

gt) Gven hat Srenbals Teansmit Fiter 8-PSK damel bit ncr 4SI +n (t) be st) Noise n twill be

ale оссаpies Symbol T sec Ts mbalcc Eymbol dc R = )bit ale it corrie 29us & Pst modellated Sym bal 3 bits bitec 3 bits Bit Pate R6 Sec

YC) SCtht) + 16 Caft+) A Cos Sa'aYenkt«0)dc Ese ( Cos Est A Esa) dt fett20 dt Ese) Psc EsT) T 'c|d (1

A T Escu 2. EncrPer mbol AT Esu) 6 Engyfs bit 3