Question

Question 4: a) Given the following received signal z vAS b+w where w is the white zero-mean Gaussian noise with variance of σ,a No/2 and b is the data symbol (b E {-1, + 1). Assume that No 0.5 and that the two symbols +1 are equally likely. Assuming that the maximum likelihood (ML) decision rule is used, determine Eb to achieve the bit error probability of P 0.01 (the Q-function table is given at the end of this examination paper.) 7 marks)] b) Wireless digital communication systems usually have to operate in multipath propagation environments. Explain what is meant by the "coherence bandwidth" of a wireless channel. Describe flat fading" and frequency selective fading." 9 marks) c) It is well known that constraints like the transmission power and the available bandwidth determine the choice of modulation scheme to be used in digital communication systems. If the system is bandwidth limited briefly describe which modulation scheme would be recom- mended for bandwidth efficiency and which would be suitable for power efficiency 9 marks

Answer 1

b)

coherence bandwidth:

Coherence bandwidth is a statistical measurement of the range of frequencies over which the channel can be considered "flat", or in other words the approximate maximum bandwidth or frequency interval over which two frequencies of a signal are likely to experience comparable or correlated amplitude fading. If the multipath time delay spread equals Dseconds, then the coherence bandwidth in rad/s is given approximately by the equation:

"b) coherence bandwidth: Coherence bandwidth is a statistical measurement of the range of frequencies over which the channel can be considered ""flat"", or in other words the approximate maximum bandwidth or frequency interval over which two frequencies of a signal are likely to experience comparable or correlated amplitude fading. If the multipath time delay spread equals Dseconds, then the coherence bandwidth W_c in rad/s is given approximately by the equation: W_c almostequalto 2 pi/D flat fading: In flat fading, the coherence bandwidth of the channel is larger than the bandwidth of the signal. Therefore, all frequency components of the signal will experience the same magnitude of fading. In frequency-selective fading, the coherence bandwidth of the channel is smaller than the bandwidth of the signal. frequency selective fading: Selective fading or frequency selective fading is a radio propagation anomaly caused by partial cancellation of a radio signal by itself - the signal arrives at the receiver by by two different"

$W_{c}\approx {2\pi \over \ D}$

flat fading:

In flat fading, the coherence bandwidth of the channel is larger than the bandwidth of the signal. Therefore, all frequency components of the signal will experience the same magnitude of fading. In frequency-selective fading, the coherence bandwidth of the channel is smaller than the bandwidth of the signal.

frequency selective fading:

Selective fading or frequency selective fading is a radio propagation anomaly caused by partial cancellation of a radio signal by itself — the signal arrives at the receiver by two different paths, and at least one of the paths is changing (lengthening or shortening).