4.27 Consider a baseband M-ary system using M discrete a mplitude levels. The receiver mofiﬂl is as shown in Figure P4.27, the operation of which is governed by the following assumptions: Problems 305 (a) The signal component in the received wave is x £ m(t) = ; a, smc(T n) where 1/T is the signaling rate in bauds. (b) The amplitude levels are a, = *A/2, +34/2, ..., =(M — 1)A/2 if M is even, and 4, =0, *4,...,=(M— 1)A/2if Mis odd, * (c) The M levels ate equiprobable, and the symbols tranismitted in adjacent time slots are statistically independent. (d) The channel noise w(t) is white and Gaussian with zero mean and power spectral density No/2. () The low-pass filter is ideal with bandwidth B = 1/2T. (f) The threshold levels used in the decision device are 0, A4, ..., (M — 2)A/2 if M is even, and *4/2, *3A/2, ..., (M — 2)A/2 if M is odd. The average probability of symbol error in this system is defined by where o is the standard deviation of the noise at the input of the decision device. Dem- onstrate the validity of this general formula by derermining P, for the following three cases: M = 2, 3, 4. Low-pass il filter Output wli) 4.27 Consider a baseband M-ary system using M discrete amplitude levels. The receiver modelis as shown in Figure P4.27, the operation of which is governed by the followingassumptions:Problems305(a) The signal component in the received wave ism(t) = 2 a, sinc - nwhere 1/T is the signaling rate in bauds.(b) The amplitude levels are a, = ±A/2, ±3A/2,...,an = 0, ±A, ..., ±(M- 1)A/2 if M is odd.(c) The M levels are equiprobable, and the symbols transmitted in adjacent time slots arestatistically independent.(d) The channel noise w(t) is white and Gaussian with zero mean and power spectraldensity No/2.(e) The low-pass filter is ideal with bandwidth B = 1/2T.(f) The threshold levels used in the decision device are 0, ±A,..., ±(M- 2)A/2 if Mis even, and ±A/2, +3A/2, ..., ±(M 2)A/2 if M is odd.The average probability of symbol error in this system is defined by+(M1)A/2 if M is even, andAerfc2V20)P, =1where o is the standárd deviation of the noise at the input of the decision device. Dem-onstrate the validity of this general formula by determining P, for the following threecases: M = 2, 3, 4.ΣLaw-passfilterDecision-devicem(e)Outputw(1)Throrhald

a Polar signalling M=2In this case, we have mt=∑n an sinctT-nwhere, an=±A2Digits 0 and 1 are thus…

Answered: Consider a baseband M-ary system using…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Related questions

Concept explainers

Question

4.27 Consider a baseband M-ary system using M discrete a mplitude levels. The receiver mofiﬂl is as shown in Figure P4.27, the operation of which is governed by the following assumptions: Problems 305 (a) The signal component in the received wave is x £ m(t) = ; a, smc(T n) where 1/T is the signaling rate in bauds. (b) The amplitude levels are a, = *A/2, +34/2, ..., =(M — 1)A/2 if M is even, and 4, =0, *4,...,=(M— 1)A/2if Mis odd, * (c) The M levels ate equiprobable, and the symbols tranismitted in adjacent time slots are statistically independent. (d) The channel noise w(t) is white and Gaussian with zero mean and power spectral density No/2. () The low-pass filter is ideal with bandwidth B = 1/2T. (f) The threshold levels used in the decision device are 0, A4, ..., (M — 2)A/2 if M is even, and *4/2, *3A/2, ..., (M — 2)A/2 if M is odd. The average probability of symbol error in this system is defined by where o is the standard deviation of the noise at the input of the decision device. Dem- onstrate the validity of this general formula by derermining P, for the following three cases: M = 2, 3, 4. Low-pass il filter Output wli)

4.27 Consider a baseband M-ary system using M discrete amplitude levels. The receiver model
is as shown in Figure P4.27, the operation of which is governed by the following
assumptions:
Problems
305
(a) The signal component in the received wave is
m(t) = 2 a, sinc - n
where 1/T is the signaling rate in bauds.
(b) The amplitude levels are a, = ±A/2, ±3A/2,...,
an = 0, ±A, ..., ±(M- 1)A/2 if M is odd.
(c) The M levels are equiprobable, and the symbols transmitted in adjacent time slots are
statistically independent.
(d) The channel noise w(t) is white and Gaussian with zero mean and power spectral
density No/2.
(e) The low-pass filter is ideal with bandwidth B = 1/2T.
(f) The threshold levels used in the decision device are 0, ±A,..., ±(M- 2)A/2 if M
is even, and ±A/2, +3A/2, ..., ±(M 2)A/2 if M is odd.
The average probability of symbol error in this system is defined by
+(M
1)A/2 if M is even, and
A
erfc
2V20)
P, =
1
where o is the standárd deviation of the noise at the input of the decision device. Dem-
onstrate the validity of this general formula by determining P, for the following three
cases: M = 2, 3, 4.
Σ
Law-pass
filter
Decision-
device
m(e)
Output
w(1)
Throrhald

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Similar questions