Inter symbol Interference in Baseband
Communication
If we transmit digital data which demands more bandwidth which exceeds channel
bandwidth, spreading will occur and cause signal pulses to overlap. This overlapping is
called Inter Symbol Interference. In short it is called ISI
ISI causes degradations of signal if left uncontrolled. This problem of ISI exists
strongly in Telephone channels like coaxial cables and optical fibers.
BASEBAND TRANSMISSION
PAM signal transmitted is given by
V(t) is basic pulse, normalized so that V(0) = 1,
x(t) represents realization of random process X(t) and ak is
sample value ofrandom
variable ak which depends on type of line codes.
The receiving filter output
The output pulse μ P(t) is obtained because input signal ak .V(t) is passed through
series of systems with transfer functions HT(f), HC(f), HR(f).
Therefore μ P(f) = V(f). HT(f).HC(f).HR(f)
The receiving filter output y(t) is sampled at ti = iTb. where i takes intervals i = ±1,
±2 . .
Nyquist Pulse Shaping Criterion
In detection process received pulse stream is detected by sampling at intervals ±KTb,
then in detection process we will get desired output. This demands sample of ith
transmitted pulse in pulse stream at Kth sampling interval should be
If received pulse P(t) satisfy this condition in time domain,
then y(ti) = μai
Ideal Solution
Ideal Nyquist filter that achieves best spectral efficiency and avoids ISI is designed to have bandwidth as
suggested
B0 = 1/2Tb (Nyquist bandwidth) = Rb/2
ISI is minimized by controlling P(t) in time domain or P(f) to be rectangular
function in frequency domain.
Practical solution
To design raised cosine filter which has transfer function consists of a flat portion and a
roll off portion which is of sinusoidal form.
Bandwidth Bo=1/2Tb is an adjustable value between Bo and 2Bo.
The frequency f1 and bandwidth Bo are related by
Transmission bandwidth required can be obtained from the relation
B = 2Bo- f1
Correlative coding
By adding ISI to the transmitted signal in a controlled manner, it is possible to achieve
a bit rate of 2Bo bits per second in a channel of bandwidth Bo Hz. Such a scheme is
correlative coding or partial- response signaling scheme.
Duobinary scheme
It is an extension of the duo-binary signaling. The modified duo binary technique
involves a correlation span of two binary digits. Two-bit delay causes the ISI to spread
over two symbols. This is achieved by subtracting input binary digits spaced 2Tb secs
apart.
Generalized form of correlative coding
scheme
Base band Transmission of M-ary data
In base band M-ary PAM, output of the pulse generator may take on any one of the Mpossible amplitude
levels with M>2 for each symbol
The blocks of n- message bits are represented by M-level waveforms with
T= 2Tb is termed symbol duration .
In general symbol duration T = Tb log 2M.
