Several factors of error in digital receivers are discussed.
When we incorporate additive noise into our channel model, so
that
, errors can creep in. If the transmitter sent bit
0 using a
BPSK
signal set , the integrators' outputs in the
matched filter
receiver would be:
It is the quantities containing the noise terms that cause
errors in the receiver's decision-making process. Because theyinvolve noise, the values of these integrals are random
quantities drawn from some probability distribution that varyerratically from bit interval to bit interval. Because the noise
has zero average value and has an equal amount of power in allfrequency bands, the values of the integrals will hover about
zero. What is important is how much they vary. If the noise issuch that its integral term is more negative than
, then the receiver will make an error, deciding that
the transmitted zero-valued bit was indeed a one. Theprobability that this situation occurs depends on three factors:
Signal Set Choice — The difference
between the signal-dependent terms in the integrators'outputs
(equations
[link] ) defines how
large the noise term must be for an incorrect receiverdecision to result. What affects the probability of such
errors occurring is the energy in the difference of the received signals incomparison to the noise term's variability. The signal-difference energy equals
For our BPSK baseband signal set, the difference-signal-energy term is
.
Variability of the Noise Term — We
quantify variability by the spectral height of the white noise
added by the channel.
Probability Distribution of the Noise
Term — The value of the noise terms relative
to the signal terms and the probability of their occurrencedirectly affect the likelihood that a receiver error will
occur. For the white noise we have been considering, theunderlying distributions are Gaussian. Deriving the following expression for the probability the
receiver makes an error on any bit transmission is complicated but can be found at
[link] and
[link] .
Here
is the integral
.This integral has no closed form expression, but it can be
accurately computed. As
[link] illustrates,
is a decreasing, very nonlinear function.
The term
equals the energy expended by the transmitter in sending the
bit; we label this term
. We arrive at a concise expression for the
probability the matched filter receiver makes a bit-receptionerror.
[link] shows how the receiver's
error rate varies with the signal-to-noise ratio
.
Derive the probability of error expression for the modulated
BPSK signal set, and show that its performance identicallyequals that of the baseband BPSK signal set.
The noise-free integrator outputs differ by
, the factor of two smaller value than in the
baseband case arising because the sinusoidal signals haveless energy for the same amplitude. Stated in terms of
, the difference equals
just as in the baseband case.
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
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ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
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