0.8 Stuff happens  (Page 11/14)

Multipath interference

The next impairment is interference caused by a multipath channel, which occurs whenever there is more than one route between thetransmitter and the receiver. Because these paths experience different delays and attenuations, multipath interference canbe modelled as a linear filter. Since filters can have complicated frequency responses, some frequencies may be attenuatedmore than others, and so this is called frequency-selective fading .

The “mild” multipath interference in impsys.m has three (nonzero) paths between the transmitter and the receiver. Its frequency response has numerousdips and bumps that vary in magnitude from about $+$ 2 to $-4$  dB. (Verify this using freqz .) A plot of the soft decisions is shownin [link] (from plot([1:length(z)],z,'.') ), which should be compared with the ideal constellationdiagram in [link] . The effect of the mild multipath interference is tosmear the lines into stripes. As long as the stripes remain separated, the quantizer is able torecover the symbols, and hence the message, without errors.

The “harsh” multipath channel in impsys.m also has three paths between the transmitter and receiver, but the later reflections are largerthan in the mild case. The frequency response of this channel has peaks up toabout $+$ 4 dB and down to about $-$ 8 dB, so its effects are considerably more severe. The effect of this channel can be seen directly by looking at theconstellation diagram of the soft decisions in [link] . The constellation diagram is smeared, and it is no longer possible to visuallydistinguish the four stripes that represent the four symbol values. It is no surprise that the message becomes garbled.As the output shows, there are about 10% symbol errors, and a majority of the recovered characters are wrong.

Carrier phase offset

For the receiver in [link] , the difference between the phase of the modulating sinusoidat the transmitter and the phase of the demodulating sinusoid at the receiver is the carrier phase offset.The effect of a nonzero offset is to scale the received signal by a factor equal to the cosine of the offset,as was shown in [link] of [link] . Once the phase offset is large enough,the demodulated signal contracts so that its maximum magnitude is less than 2. When this happens,the quantizer always produces a $\pm 1$ . Symbol errors abound.