6.37 Information communication problems  (Page 3/8)

A novel communication system

A clever system designer claims that the depicted transmitter has, despite its complexity, advantages over the usual amplitude modulation system.The message signal $m(t)$ is bandlimited to $W$ Hz, and the carrier frequency $\gg (f_c, W)$ . The channel attenuates the transmitted signal $x(t)$ and adds white noise of spectral height $\frac{N_0}{2}$ .

The transfer function $H(f)$ is given by $H(f)=\begin{cases}i & \text{if $f< 0$}\\ -i & \text{if $f> 0$}\end{cases}$

1. Find an expression for the spectrum of $x(t)$ . Sketch your answer.
2. Show that the usual coherent receiver demodulates this signal.
3. Find the signal-to-noise ratio that results when this receiver is used.
4. Find a superior receiver (one that yields a better signal-to-noise ratio), and analyze itsperformance.

Multi-tone digital communication

In a so-called multi-tone system, several bits are gathered together and transmitted simultaneously ondifferent carrier frequencies during a $T$ second interval. For example, $B$ bits would be transmitted according to

1. Find a receiver for this transmission scheme.
2. An ELEC 241 almuni likes digital systems so much that he decides to produce a discrete-time version. Hesamples the received signal (sampling interval $T_s=\frac{T}{N}$ ). How should $N$ be related to $B$ , the number of simultaneously transmitted bits?
3. The alumni wants to find a simple form for the receiver so that his software implementation runs as efficiently as possible. How would you recommend he implement thereceiver?

City radio channels

In addition to additive white noise, metropolitan cellular radio channels also contain multipath: theattenuated signal and a delayed, further attenuated signal are received superimposed. As shown in [link] , multipath occurs because the buildings reflect the signal and thereflected path length between transmitter and receiver is longer than the direct path.

1. Assume that the length of the direct path is $d$ meters and the reflected path is 1.5 times as long. What is themodel for the channel, including the multipath and the additive noise?
2. Assume $d$ is 1 km. Find and sketch the magnitude of the transfer functionfor the multipath component of the channel. How would you characterize this transfer function?
3. Would the multipath affect AM radio? If not, why not; if so, how so? Would analog cellular telephone,which operates at much higher carrier frequencies (800 MHz vs. 1 MHz for radio), be affected or not? Analogcellular telephone uses amplitude modulation to transmit voice.
4. How would the usual AM receiver be modified tominimize multipath effects? Express your modified receiver as a block diagram.

Downlink signal sets

In digital cellular telephone systems, the base station (transmitter) needs to relay different voice signals toseveral telephones at the same time. Rather than send signals at different frequencies, a clever Rice engineersuggests using a different signal set for each data stream. For example, for two simultaneous data streams,she suggests BPSK signal sets that have the depicted basic signals .