6.37 Information communication problems  (Page 4/8)

Thus, bits are represented in data stream 1 by $s_1(t)$ and $-s_1(t)$ and in data stream 2 by $s_2(t)$ and $-s_2(t)$ , each of which are modulated by 900 MHz carrier. The transmitter sends the two data streams sothat their bit intervals align. Each receiver uses a matched filter for its receiver. The requirement isthat each receiver not receive the other's bit stream.

1. What is the block diagram describing the proposed system?
2. What is the transmission bandwidth required by the proposed system?
3. Will the proposal work? Does the fact that the two data streams are transmitted in the samebandwidth at the same time mean that each receiver's performance is affected? Can each bit stream bereceived without interference from the other?

Mixed analog and digital transmission

A signal $m(t)$ is transmitted using amplitude modulation in the usual way. The signal has bandwidth $W$ Hz, and the carrier frequency is $f_c$ . In addition to sending this analog signal, the transmitter also wants to send ASCII text in an auxiliary band that lies slightly above the analog transmission band. Using an 8-bit representationof the characters and a simple baseband BPSK signal set (the constant signal +1 corresponds to a 0, the constant-1 to a 1), the data signal $d(t)$ representing the text is transmitted as the same time as the analog signal $m(t)$ . The transmission signal spectrum is as shown , and has a total bandwidth $B$ .

1. Write an expression for the time-domain version of the transmitted signal in terms of $m(t)$ and the digital signal $d(t)$ .
2. What is the maximum datarate the scheme can provide in terms of the available bandwidth?
3. Find a receiver that yields both the analog signal and the bit stream.

Digital stereo

Just as with analog communication, it should be possible to send two signals simultaneously over a digitalchannel. Assume you have two CD-quality signals (each sampled at 44.1 kHz with 16 bits/sample). Onesuggested transmission scheme is to use a quadrature BPSK scheme. If $b^{\left(1\right)}(n)$ and $b^{\left(2\right)}(n)$ each represent a bit stream, the transmitted signal has the form $$x(t)=A\sum b^{\left(1\right)}(n)\sin (2\pi f_c(t-nT))p(t-nT)+b^{\left(2\right)}(n)\cos (2\pi f_c(t-nT))p(t-nT)$$ where $p(t)$ is a unit-amplitude pulse having duration $T$ and $b^{\left(1\right)}(n)$ , $b^{\left(2\right)}(n)$ equal either +1 or -1 according to the bit being transmitted for each signal. The channel adds whitenoise and attenuates the transmitted signal.

1. What value would you choose for the carrier frequency $f_c$ ?
2. What is the transmission bandwidth?
3. What receiver would you design that would yield both bit streams?

Digital and analog speech communication

Suppose we transmit speech signals over comparable digital and analog channels. We want to compare theresulting quality of the received signals. Assume the transmitters use the same power, and the channelsintroduce the same attenuation and additive white noise. Assume the speech signal has a 4 kHz bandwidth and, inthe digital case, is sampled at an 8 kHz rate with eight-bit A/D conversion. Assume simple binary sourcecoding and a modulated BPSK transmission scheme.

1. What is the transmission bandwidth of the analog (AM) and digital schemes?
2. Assume the speech signal's amplitude has a magnitude less than one. What is maximum amplitudequantization error introduced by the A/D converter?
3. In the digital case, each bit in quantized speech sample is received in error with probability $p_e$ that depends on signal-to-noise ratio $\frac{E_b}{N_0}$ . However, errors in each bit have a different impact on the error in the reconstructedspeech sample. Find the mean-squared error between the transmitted and received amplitude.
4. In the digital case, the recovered speech signal can be considered to have two noise sources added to eachsample's true value: One is the A/D amplitude quantization noise and the second is due to channel errors. Becausethese are separate, the total noise power equals the sum of these two. What is the signal-to-noise ratio of thereceived speech signal as a function of $p_e$ ?
5. Compute and plot the received signal's signal-to-noise ratio for the two transmissionschemes as a function of channel signal-to-noise ratio.
6. Compare and evaluate these systems.