- A mobile radio system receives a coherent FSK signal with an average SNR per bit of 18 dB. Compute the probability of a word error for a 12-bit word for each of the following cases:
a) no diversity or error-correcting coding
p=7.740917e-003 pem=8.903645e-002
b) 3-out-of-5 multiple transmission,
p1=4.584803e-006 pem=5.501625e-005
c) (17,12) Hamming code,
p=7.740917e-003 pem=7.543490e-003
d) (23,12) Golay code,
p=7.740917e-003 pem=2.826314e-005
e) two-branch spatial diversity with equal-gain combining.
p1=2.511886e-004 pem=3.010103e-003
- We want to use a (23,12) Golay code over a mobile channel where burst errors can have a duration of up to 6 symbol periods. Explain how interleaving can be used to get an acceptable BER.
Since this code can correct 3 errors per word and we need to correct bursts of six errors, we need to interleave at least two codewords, i.e. send the following two codewords column-by-column
- Consider three channels:
channel A: 940.1 MHz
channel B: 940.4 MHz
channel C: 940.7 MHz
A base station is transmitting these signals with equal power using a power combiner having an output voltage eO given by
eO = 2ei + 0.05 ei2 + 0.01 ei3
Compute the ratio of in-band IM distortion power to desired signal power for channel B. Assume a 25 kHz bandwidth and ignore terms that cause only amplitude distortion.
Since the three channels are equally-spaced we have from the course notes, the in-band undesired term is 3a3/2 ABC cos(a+g-b)
Desired term is a1B cos(b)
Worstcase is A=B=C
SI = (a1*B/(3/2* a3*A*B*C))2 = 4/9 (a1/ a3) 2 / A4
SI = 5.625000e-005 / A4 or SI = -42.498775 / A4 dB
Note that the A4 term implies that the signal to IM interference ratio gets worse as the power output increases. This is what we would expect.
- For a cell radius of 8 km, compute the minimum filter slope required to attain a carrier-to-interference ratio of 18 dB when there is a mobile 300 m from the base station. Assume a=4 and a channel separation of three channels.
NEFER=57.038749, Req'd Loss=75.038749 dB, K=28.929626 dB/oct