COHERENT RECEPTION definition block diagram , what is correlator receiver in digital communication ?
THE CORRELATOR : COHERENT RECEPTION
(U.P. Tech. Sem. Exam; 2004-05) (10 marks)
In this article, we shall discuss a little different type of receiver which is known as corrector. Figure 6.42 shows the block diagram of this correlator.
In figure 6.42, f(t) represents input noisy signal,
i.e., f(t) = x(t) + n(t).
The signal f(t) is multiplied to the locally generated replica of input signal x(t). Then, result of multipli-cation f(t) . x(t) is integrated. The output of the integrator is sampled at t = T (i.e., end of one symbol period). Then based on this sampled value, decision is made. This is how the correlator works. It is known as correlator because it correlates the received signal f(t) with a stored replica of the know signal x(t). In the block diagram of figure 6.42, the product f(t) x(t) is integrated over one symbol period, i.e., T.
DIAGRAM
FIGURE 6.42 Block diagram of a correlator
Thus, output y(t) will be,
y(t) = dt
At t = T, this equation will become, output of correlator,
y(t) = dt …(6.98)
DIAGRAM
FIGURE 6.43 Block diagram of a matched filter receiver
Now consider the matched filter as shown in figure 6.43.
In this block diagram, it may be observed that the matched filter does not need locally generated replica of input signal x(t). The output of the matched filter is obtained by convolution of input f(t) and its impulse response h(t).
This means that
y(t) = f(t) Ä h(t) = . h(t – ) dr …(6.99)
We know that the impulse response h(t) of the matched filter is given by,
h(t) = x (T – t) …(6.100)
Therefore, h(t-) = = x (T – t + )
Substituting this value of h(t – ) in equation (6.99), we get
y(t) = x (T – t + ) d
Because the integration is performed over one bit period, therefore, we can change integration limits from 0 to T.
Hence, we write
y(t) = d
At t = T. the last equation becomes,
y(t) = d = d
Now, let us substitute = t just for convenience for notation, then we have output of matched filter
y(T) = d …(6.101)
NOTE This equation (i.e. 6.101) gives the output of matched filter. It may be observed that this equation and equation (6.98) (which gibes output of correlator) are identical. In equation (6.101) the constant is present which can be normalized to 1. The similarity between equation (6.98) and equation (6.101) shows that the matched filter and correlator provider; same output.
Therefore we can state as under:
The matched filter and correlator are two distinct, independent techniques which yield same result. Intact, these two techniques are used to synthesize the optimum filter.
6.25 INTERSYMBOL INTERFERENCE (ISI) (Important)
In a communication system, when the data is being transmitted in the form of pulses (i.e., bits), the output produced at the receiver due to other bits or symbols interferes with the output produced by the desired bit. This is known as intersymbol interference (ISI). The intersymbol interference will introduce errors in the detected signal. Let us consider figure 6.44 which shows the elements binary PAM system. The input signal consists of a binary data sequence {bk} with a bit duration of Tb seconds.
DIAGRAM
FIGURE 6.44 Baseband binary data transmission system.
This sequence is applied to a pulse generator to produce a discrete PAM signal which given by
x(t) = v(t-kTb) …(6.102)
where v(t) denotes the basic pulse, normalized such that v(0) = 1. The first block of the system i.e., pulse amplitude modulator converts this input sequence into polar form as under:
if bk = 1 then ak = 1
and bk = 0 then ak = – 1
(i) The PAM signal x(t) is then passed through a transmitting filter. The output of the transmitting filter is then transmitted over transmission channel. Let the impulse response of this channel be h(t).
(ii) A random noise is then added to the transmitted signal when it travels over the transmission channel. Thus, the signal received at the receiving end is contaminated with noise.
(iii) The channel output is passed through a receiving filter. This filter output is sampled synchronously with the transmitter. The sampling instants are determined by a clock or timing signal which is extracted from the receiving filter output.
(iv) The sequence of samples obtained at the output of receiving filter is used to reconstruct the original data sequence with the help of a decision making device.
(v) Each sample is compared to a threshold level in the decision making device. If the amplitude of the sample is higher than the threshold level then it is decided that a symbol 1 is received. On the other hand, if the signal has an amplitude lower than the threshold, then the decision is that a 0 is received.
The receiving filter output can be written as under:
y(t) = p(t – kTb) + n(t) …(6.102a)
where is a scaling factor and the noise n(t) is the noise at the output of the receiving filter due to the added noise. The term p(t – hTb) represents the combined impulse response of the receiving filer.
The receiving filter output y(t) is sampled at time ti – iTb with i taking on integer value:: to provide following expression:
y(ti) = p(iTb – kTb) + n(ti) …(6.103)
or y(ti) = ai + p(iTb – kTb) + n(ti) …(6.104)
This is the receiver output y(t) at instant t = ti.
Now, it may be noted that equation (6.104) has two terms.
(i) The first term ai is produced by the ith transmitted bit. Theoretically, only this term should be present, however, practically it is not so.
(ii) The second term represents the residual effect of all the transmitted bits, obtained at the time of sampling the ith bit. This residual effect is known as the intersymbol interference (ISI).
6.26 FACTORS RESPONSIBLE FOR INTERSYMOL INTERFERENCE (ISI)
- Definition
The intersymbol interference ISI arises due to the imperfections in the overall frequency response of the system. When, a short pulse of duration Tb seconds is transmitted through a bandlimited system, then the frequency components contained in the input pulse are differentially attenuated and more importantly differentially delayed by the system. Due to this, the pulse appearing at the output of the system will be dispersed over an interval which is longer than Tb seconds. Due to this dispersion, the symbols each of duration Tb will interfere with each other when transmitted over the communication channel. This will result in the intersymbol interference (ISI). The transmitted pulse of duration Tb seconds and the dispersed pulse of duration more than Tb seconds are shown in figure 6.45.
DIAGRAM
FIGURE 6.45 Cause of Intersymbol Interference (ISI).
- Effect of Intersymbol Interference (ISI)
Following are the effects of ISI:
(i) In the absence of ISI and noise, the transmitted bit can be decoded correctly at the receiver.
(ii) The presence of ISI will introduce errors in the decision at the receiver output.
(iii) Hence, the receiver can make an error in deciding whether it has received a logic 1 or a logic 0.
- Remedy to Reduce ISI
(i) It has been proved that the function which produces a zero intersymbol interference is a sinc function. Hence, instead of a rectangular pulse if we transmit a sinc pulse then the ISI can be reduced to zero.
(ii) This is known as Nyquist Pulse Shaping. The sinc pulse transmitted to have a zero ISI has been shown in figure 6.46 (a).
(iii) Further, we know that Fourier transform of a sinc pulse is a rectangular function. Hence, to preserve all the frequency components, the frequency response of the filter must be exactly flat in the pass band and zero in the attenuation band as shown in figure 6.46 (b).
DIAGRAM
FIGURE 6.46.
NOTE: However, type of filter is practically not present or not possible. Hence, in practice, the frequency response of the filter is modified as shown in figure 6.47 with different roll off factors a to obtain the achievable filter response curves.
DIAGRAM
FIGURE 6.47 Illustration of practical filter characteristics.