UNIT-V

MULTICARRIER MODULATION
INTRODUCTION:

The basic idea of multicarrier modulation is to divide the transmitted bit stream into many
different sub-streams and send these over many different sub channels. Typically the sub
channels are orthogonal under ideal propagation conditions. The data rate on each of the sub
channels is much less than the total data rate, and the corresponding sub channel bandwidth is
much less than the total system bandwidth. The number of sub streams is chosen to ensure that
each sub channel has a bandwidth less than the coherence bandwidth of the channel, so the sub
channels experience relatively flat fading. Thus, the inter symbol interference on each sub
channel is small. The sub channels in multicarrier modulation need not be contiguous, so a large
continuous block of spectrum is not needed for high rate multicarrier communications.
Moreover, multicarrier modulation is efficiently implemented digitally.

Data Transmission using multiple carriers:

The simplest form of multicarrier modulation divides the data stream into multiple sub streams
to be transmitted over different orthogonal sub channels centered at different subcarrier
frequencies. The number of sub streams is chosen to make the symbol time on each sub stream
much greater than the delay spread of the channel or, equivalently, to make the sub stream
bandwidth less than the channel coherence bandwidth. This ensures that the sub streams will not
experience significant ISI.

Consider a linearly modulated system with data rate R and bandwidth B. The coherence
bandwidth for the channel is assumed to be Bc < B, so the signal experiences frequency selective
fading. The basic premise of multicarrier modulation is to break this wideband system into N
linearly modulated subsystems in parallel, each with sub channel bandwidth BN = B/N and data
rate RN ≈ R/N. For N sufficiently large, the sub channel bandwidth BN = B/N < Bc, which
ensures relatively flat fading on each sub channel.

This can also be seen in the time domain: the symbol time TN of the modulated signal in each
sub channel is proportional to the sub channel bandwidth 1/BN. So BN « Bc implies that TN » Tm,
where Tm denotes the delay spread of the channel. Thus, if N is sufficiently large, the symbol
time is much greater than the delay spread, so each sub channel experiences little ISI
degradation.

Multicarrier transmitter:

The bit stream is divided into N substreams via a serial-to-parallel converter. The nth substream
is linearly modulated (typically via QAM or PSK) relative to the subcarrier frequency fn and
occupies bandwidth BN. We assume coherent demodulation of the subcarriers so the subcarrier
phase is neglected in our analysis. If we assume raised cosine pulses for g(t) we get a symbol
time TN = (1 + β)/BN for each sub stream, where β is the roll-off factor of the pulse shape.

The modulated signals associated with all the sub-channels are summed together to form the
transmitted signal, given as (1) where si is the complex symbol associated with the ith subcarrier
and Φi is the phase offset of the ith carrier. For non-overlapping sub-channels we set fi = f0 +
i(BN), i = 0,..., N -1. The sub-streams then occupy orthogonal sub-channels with bandwidth BN,
yielding a total bandwidth NBN = B and data rate NRN ≈ R. Thus, this form of multicarrier
modulation does not change the data rate or signal bandwidth relative to the original system, but
it almost completely eliminates ISI for BN « Bc.

The modulated signals associated with all the subchannels are summed together to form the
transmitted signal, given as

(1)

where si is the complex symbol associated with the ith subcarrier and Fi is the phase offset of the
ith carrier. For nonoverlapping subchannels we set fi = f0 + i(BN), i = 0,..., N -1. The sub-streams
then occupy orthogonal subchannels with bandwidth BN, yielding a total bandwidth NBN = B
and data rate NRN ≈ R.

Thus, this form of multicarrier modulation does not change the data rate or signal bandwidth
relative to the original system, but it almost completely eliminates ISI for BN « Bc
Receiver for this multicarrier modulation:

Each substream is passed through a narrowband filter (to remove the other substreams),
demodulated, and combined via a parallel-to- serial converter to form the original data stream.
Note that the ith subchannel will be affected by flat fading corresponding to a channel gain
ai = H(fi).

Although this simple type of multicarrier modulation is easy to understand, it has several
significant shortcomings. First, in a realistic implementation, sub-channels will occupy a larger
bandwidth than under ideal raised cosine pulse shaping because the pulse shape must be time
limited.

Let e/TN denote the additional bandwidth required due to time limiting of these pulse shapes.
The sub-channels must then be separated by (1 + b + e)/ TN, and since the multicarrier system
has N sub-channels, the bandwidth penalty for time limiting is eN/TN.

In particular, the total required bandwidth for non-overlapping sub-channels is

Thus, this form of multicarrier modulation can be spectrally inefficient. Additionally, nearideal
(and hence expensive) lowpass filters will be required to maintain the orthogonality of the
subcarriers at the receiver. Perhaps most importantly, this scheme requires N independent
modulators and demodulators, which entails significant expense, size, and power consumption.
It is possible a modulation method that allows subcarriers to overlap and removes the need for
tight filtering, and a discrete implementation of multicarrier modulation, which eliminates the
need for multiple modulators and demodulators.
Multi carrier Modulation with overlapping subchannels:
We can improve on the spectral efficiency of multicarrier modulation by overlapping the
subchannels. The subcarriers must still be orthogonal so that they can be separated out by the
demodulator in the receiver. The subcarriers

{cos(2p(f0 + i/TN )t + Fi), i = 0,1,2,...}

form a set of (approximately) orthogonal basis functions on the interval [0, TN] for any set of
subcarrier phase offsets {Fi}, since

where the approximation follows because the integral in the third line is approximately zero
for f0TN »1 . Moreover, it is easily shown that no set of subcarriers with a smaller frequency
separation forms an orthogonal set on [0, TN] for arbitrary subcarrier phase offsets.

This implies that the minimum frequency separation required for subcarriers to remain
orthogonal over the symbol interval [0, TN] is 1/ TN. Since the carriers are orthogonal the set
of functions {g(t)cos(2p(f0 + i/TN )t + Fi), i = 0,1,2, .. N - 1} also form a set of (approximately)
orthonormal basis functions for appropriately chosen baseband pulse shapes g(t): the family of
raised cosine pulses are a common choice for this pulse shape. Given this orthonormal basis set,
even if the subchannels overlap, the modulated signals transmitted in each sub-channel can be
separated out in the receiver.

Consider a multicarrier system where each sub-channel is modulated using raised cosine pulse
shapes with roll-off factor b.

The bandwidth of each sub-channel is then BN = (1 + b)/TN.

The ith subcarrier frequency is set to (2p(f0 + i/TN ), i = 0,1,2, .. N - 1}, for some f0, so the
subcarriers are separated by 1/TN. However, the bandwidth of each subchannel is BN = (1 +
b)/TN > 1/TN for b > 0, so the sub-channels overlap. Excess bandwidth due to time windowing
will increase the subcarrier bandwidth by an additional e/TN.
However, b and e do not affect the total system bandwidth resulting from the sub-channel
overlap except in the first and last sub-channels. The total system bandwidth with overlapping
sub-channels is given by

where the approximation holds for N large. Thus, with N large, the impact of b and e on the total
system bandwidth is negligible, in contrast to the required bandwidth of B =N(1 + b + e)/TN
when the subchannels do not overlap. In order to separate out overlapping subcarriers, a different
receiver structure is needed.

In particular, overlapping subchannels are demodulated with this receiver structure, which
demodulates the appropriate symbol without interference from overlapping subchannels.

The advantage of multicarrier modulation is that each subchannel is relatively narrowband,

which mitigates the effect of delay spread. However, each subchannel experiences flat fading,
which can cause large bit error rates on some of the subchannels. In particular, if the transmit
power on subcarrier i is Pi and if the fading on that subcarrier is ai, then the received signal-to-
noise power ratio is gi = ai Pi/NoBN, where BN is the bandwidth of each subchannel. If ai is small
then the received SNR on the ith subchannel is low, which can lead to a high BER on that
subchannel. Moreover, in wireless channels ai will vary over time according to a given fading
distribution, resulting in the same performance degradation as is associated with flat fading for
single-carrier systems. Because flat fading can seriously degrade performance in each
subchannel, it is important to compensate for flat fading in the subchannels.
There are several techniques for doing this, including coding with interleaving over time and
frequency, frequency equalization, precoding, and adaptive loading.

Discrete Implementation of Multicarrier Modulation

Although multicarrier modulation was invented in the 1950s, its requirement for separate
modulators and demodulators on each subchannel was far too complex for most system
implementations at the time. However, the development of simple and cheap implementations
of the discrete Fourier transform and the inverse DFT twenty years later - combined with the
realization that multicarrier modulation could be implemented with these algorithms - ignited
its widespread use.

The DFT and Its Properties

Let x[n], 0 ≤ n ≤ N — 1, denote a discrete time sequence. The N- point DFT of x[n] is defined
as

The DFT is the discrete-time equivalent to the continuous-time Fourier transform, because X[i]
characterizes the frequency content of the time samples x[n] associated with the original signal
x(t). The sequence x[n] can be recovered from its DFT using the IDFT:

Orthogonal Frequency-Division Multiplexing (OFDM) :

The input data stream is modulated by a QAM modulator, resulting in a complex symbol stream
X[0],X[1], ...,X[N — 1]. This symbol stream is passed through a serial-to-parallel converter,
whose output is a set of N parallel QAM symbols X[0],..., X[N - 1] corresponding to the
symbols transmitted over each of the subcarriers. Thus, the N symbols output from the serial-to-
parallel converter are the discrete frequency components of the OFDM modulator output s(t). In
order to generate s(t), the frequency components are converted into time samples by performing
an inverse DFT on these N symbols, which is efficiently implemented using the IFFT
algorithm. The IFFT yields the OFDM symbol consisting of the sequence x[n] = x[0], ...,x[N —
1] of length N, where
This sequence corresponds to samples of the multicarrier signal: the multicarrier signal consists
of linearly modulated subchannels, and the right-hand side corresponds to samples of a sum of
QAM symbols X[i] each modulated by the carrier ej2pni/N, i= 0,...,N-1.

The cyclic prefix is then added to the OFDM symbol, and the resulting time samples are ordered
by the parallel-to-serial converter and passed through a D/A converter, resulting in the baseband
OFDM signal x(t), which is then upconverted to frequency f0. The transmitted signal is filtered
by the channel impulse response and corrupted by additive noise, resulting in the received
signal r(t). This signal is downconverted to baseband and filtered to remove the high-frequency
components. The A/D converter samples the resulting signal to obtain y[n]. The prefix of y[n]
consisting of the first m samples is then removed. This results in N time samples whose DFT in
the absence of noise is Y[i] = H[i]X[i] (being h[n] the discrete-time equivalent lowpass impulse
response of the channel). These time samples are serial-to-parallel converted and passed
through an FFT. This results in scaled versions of the original symbols H[i]X[i], where H[i] =
H(fi) is the flat fading channel gain associated with the ith subchannel. The FFT output is
parallel-to-serial converted and passed through a QAM demodulator to recover the original data.

The OFDM system effectively decomposes the wideband channel into a set of narrowband
orthogonal subchannels with a different QAM symbol sent over each subchannel. Knowledge of
the channel gains H[i], i = 0,..., N — 1, is not needed for this decomposition, in the same way
that a continuous-time channel with frequency response H(f) can be divided into orthogonal
subchannels without knowledge of H(f) by splitting the total signal bandwidth into
nonoverlapping subbands. The demodulator can use the channel gains to recover the original
QAM symbols by dividing out these gains: X[i] = Y[i]/H[i]. This process is called frequency
equalization. However, as discussed for continuous-time OFDM, frequency equalization leads
to noise enhancement because the noise in the ith subchannel is also scaled by 1/H [i]. Hence,
while the effect of flat fading on X[i] is removed by this equalization, its received SNR is
unchanged.

Peak-to-average power ratio (PAR)

The peak-to-average power ratio (PAR) is an important attribute of a communication system. A

low PAR allows the transmit power amplifier to operate efficiently, whereas a high PAR forces
the transmit power amplifier to have a large back-off in order to ensure linear amplification of
the signal. Operation in the linear region of this response is generally required to avoid signal
distortion, so the peak value is constrained to be in this region. Clearly it would be desirable to
have the average and peak values be as close together as possible in order for the power
amplifier to operate at maximum efficiency. Additionally, a high PAR requires high resolution
for the receiver A/D converter, since the dynamic range of the signal is much larger for high-
PAR signals. High-resolution A/D conversion places a complexity and power burden on the
receiver front end.

It may be demonstrated that the maximum PAR is N for N subcarriers. In practice, full coherent
addition of all N symbols is highly improbable and so the observed PAR is typically less than N
– usually by many decibels. Nevertheless, PAR increases approximately linearly with the
number of subcarriers. So even though it is desirable to have N as large as possible in order to
keep the overhead associated with the cyclic prefix down, a large PAR is an important penalty
that must be paid for large N.

There are a number of ways to reduce or tolerate the PAR of OFDM signals, including clipping
the OFDM signal above some threshold, peak cancellation with a complementary signal,
allowing nonlinear distortion from the power amplifier (and correction for it), and special
coding techniques.

ADVANTAGES AND DRAWBACKS OF OFDM SYSTEM

As explored in previous section that the OFDM system has been adopted by many current
wireless standards and also proposed for future wireless communication systems due to its
several advantageous features.
The key advantages of OFDM system are as follows:
1. Less Implementation Complexity: For a given delay spread of multipath fading channel, the
implementation compexity is significantly lower than that of single carrier system with an
equalizer (single tap equalizer is required in OFDM system).
2. Robustness Against Narrowband Interference: OFDM is more robust against narrowband
interference because in a single carrier system, a single fade or interferer can cause the entire link
to fail, but in a multicarrier system (like in OFDM), only a small percentage of subcarriers will
be affected.
3. Immune to Frequency Selective Fading: OFDM is highly immune to frequency selective
fading because of parallel transmission (each sub-carrier has narrow bandwidth in comparison to
overall bandwidth of signal). It converts a frequency selective fading channel into several nearly
flat fading channels.
4. High Spectral Efficiency: Due to orthogonal nature of each sub-carrier, large number of
subcarriers can be accomadate in a very narrow spectral region thus increasing the spectral
efficiency. Efficient Modulation and demodulation of OFDM symbol are possible with the help
of IFFT and FFT.
Besides these advantageous features, the OFDM systems also have some major problems like:

Symbol Timing Offset (STO): OFMD is highly sensitive to STO. Due to the use of IFFT and
FFT for modulation and demodulation at transmitter and receiver respectively, correct timing
(start of FFT window) is required at the receiver otherwise one FFT window will take sample
from two transmitted OFDM symbol. This deteriorates the performance of OFDM system.

Carrier Frequency Offset (CFO): OFMD is highly sensitive to carrier frequency offset. Most of
the advantages of OFDM are due to the orthogonal nature of sub-carriers and this orthogonality
between sub carriers will be destroyed if frequency offset arises between them. The major cause
of CFO is Doppler shifts (due to relative motion between transmitter and channel)