Reference no: EM132205100

Purpose of the assessment

(Unit's Learning Outcomes covered, ULO) ULO b: Apply and evaluate the principles used in the generation, transmission and reception of digitally modulated signals.
ULO c: Report on the characteristics of sampling and analogue to digital conversion and source coding.
ULO f: Apply the techniques of, and report on, digital communication applications using Matlab and hardware devices.

Assessment - Analyzing Digital Communications Principles & Systems Both Manually and Using MATLAB/Simulink

Purpose of the assessment

(Unit's Learning Outcomes covered, ULO) ULO b: Apply and evaluate the principles used in the generation, transmission and reception of digitally modulated signals.

ULO c: Report on the characteristics of sampling and analogue to digital conversion and source coding.

ULO f: Apply the techniques of, and report on, digital communication applications using Matlab and hardware devices.

Objectives of the assignment:

This assignment seeks to fulfill the unit's learning outcomes b-e stated on Page 1 of this document and found in the unit description. The assignment

Question 1: ISI and Design of Equalizers

Combating inter-symbol interference (ISI) is one of the challenges in digital communications systems. Assume that the impulse response of the transmission medium between the transmitter and the receiver is p(t). The sampled impulse response is p[n], where n=t/T and T is the sampling period (or symbol duration). Then, ISI-free transmission require that

p(t) = δ(t) = { 1, t=0

                  { 0, otherwise   δ(t)

where is referred to as dirac impulse function. In practical, situations the transmission medium is not ISI-free. This is the reason why we need equalizing filters. Assume that the sampled impulse response of the channel is

p[n]= δ [n] - 0.2δ [n -1] + 0.5δ [n - 2]

(a) Derive the expression for the transfer function of the 3-tap linear equalizer which forces the ISI caused by this transmission medium to zero.
(b) Derive the expression for the impulse response of the 3-tap ZF-LE designed in Part (a).
(c) Verify that the ZF-LE that you have designed in Parts (a) and (b) actually mitigates the ISI in the channel.
(d) Does the ZF-LE cancel the entire ISI in the system? If not, how can you improve the ability of the ZF-LE to suppress the ISI?

Question 2: Digitization of signals

Consider the analog signal s(t ) = 5sin(500t + Π/5)+ cos(200t + Π/4) to be transferred over a digital communications system.

(a) Compute the maximum allowable sampling period that the analog-to-digital converter (ADC) must use to ensure the perfect reconstruction of the signal at the receiver.

(b) What theorem governs the choice made in part (a)?
(c) How many samples of the analog signal do we need to store in order to reproduce 10Π seconds of it (i.e., the analog signal)?
(d) Use MATLAB code to verify whether or not the samples collected can be used to uniquely reproduce the analog signal.

Question 3: Digital Baseband Data Generation and Transmission

We seek to transmit the message ME502 Unit using baseband digital M-ary PAM signaling, where M=16. As the transmission system is not ideal, we need to protect the bits using just a single-bit odd parity encoding for error detection. The process is that we convert each of the characters in the message into its equivalent 8-bit ASCII code, then partition the bitstream into log2(16)-bit segments streams (called symbols), then use each symbol to modulate a pulse to form the M-PAM signal prior to transmission.

(a) Encode the message into a series of bits using 8-bit ASCII encoding (including the odd- parity bit). Counting from the left side, the eighth bit in each character is the parity coding bit.

(b) How many bits in total are in the message?

(c) Divide the bit string into m= log2(16)-bit segments. Each of the m-bit segment is a symbol of 16-PAM. How many symbols do you get altogether?

(d) Evaluate the gross bit rate (Rb) and symbol rate (RS) of the 16-PAM system if we transmit the entire error-protected message in 8 microseconds.

(e) Determine the effective bit rate (Rb) and symbol rate (RS) of the 16-PAM system if we transmit the entire error-protected message in 8 microseconds

(f) Draw the signal constellation diagram of the M-PAM system, using d as a parameter.