[95]

CHAPTER 6 APPLICATION OF

TRANSMULTIPLEXERS IN OFDM ULTICARRIER modulations such as OFDM and DMT are efficient technologies

for the implementation of wireless and wire line communication systems. Due to several

advantageous features of MC systems, it has been adopted by many wireless communication standards

like IEEE802.11a/n, IEEE802.16, ADSL, VDSL, DAB and DVB-T. It is also proposed for the future

generation mobile communication system like 4G. A relatively simple implementation is possible for MC

systems. Low complexity is due to the use of fast DFT, avoiding complicated equalization algorithms.

Efficient performance of MC modulation is especially vivid in channels with frequency selective fading

and multipath [109].

6.1 MULTICARRIER MODULATION SYSTEMS

Multi-carrier (MC) modulation is an efficient technique for transmitting information over a

multipath fading channel. It is an attractive approach for high bit rate transmission over digital subscriber

line. The idea of MC modulation was proposed approximately 50 years ago [9 and 60]. However, these

ideas were not persuaded due to limitations of processing technology. Advances in the area of digital

signal processing have made this concept practically feasible and competitive with traditional single-

carrier system [1 and 9].

The basic concept behind MC transmission is to divide the available spectrum into number of

sub-channels, assigning a single carrier to each of them and distributing the information stream between

sub-carriers. Each carrier is modulated separately and the superposition of the modulated signals is

transmitted. Such a scheme has several benefits like, if the sub-carrier spacing is small enough, each sub-

channel exhibits a flat frequency response, thus making frequency-domain equalization easier. Each sub-

stream has a low bit rate, which means that the symbol has a considerable duration; this makes it less

sensitive to impulse noise. When the number of sub-carriers increases for properly chosen modulating

functions, the spectrum approaches a rectangular shape. The MC scheme shows a good modularity. For

instance, the sub-carriers are exhibiting a disadvantageous signal-to-noise ratio (SNR) which should be

minimized. Moreover, it is possible to choose the constellation size (bit loading) and energy for each sub-

carrier, thus approaching the theoretical capacity of the channel [57].

M

[96]

6.2 TRANSMULTIPLEXER BASED OFDM SYSTEM

The broadband wireless communication system is required to be operating in an environment

which is characterized by high carrier frequency, data transmission rate and mobility, altogether such an

environment can be modeled by a frequency selective fast time varying fading channel. It has been

studied and established that the MC data transmission techniques such as Multi Carrier Code Division

Multiple Access (MC-CDMA) and OFDM are best suited for such channels [108 and 109]. The OFDM is

a special case of MC modulation in which serial stream of data is divided in parallel and then modulated

by orthogonal sub-carriers with partial overlapping frequency bands.

The OFDM symbols have relatively long time duration as compared to single carrier modulation

with a narrow bandwidth. This increases the robustness against multipath deteriorations and results in less

complex equalizers which helps in performing the channel equalization easily in the frequency domain

through a bank of one-tap multipliers [109]. In a single-carrier system, a single fade or interferer can

cause the entire link to fail, but in a MC system, only a small percentage of the sub-carriers will be

affected. Error correction coding can then be used to correct for the few erroneous sub-carriers. One of

the major issues of OFDM system is the overlapping of OFDM symbols while transmission through

multipath fading channel which in turn generate ICI and ISI at the receiver [9 and 109].

In order to minimize these interferences, the OFDM system makes use of guard band, which

results in loss in spectral efficiency [18]. In addition, the DFT based modulation filters have side lobes of

the order of -13dB which causes the significant spectral overlap between the sub-carriers [79]. Many

researchers have been worked on this issue and suggested filter bank based-MC transmission systems,

such as the overlapped DMT, DWMT [47] and FMT [43]. These filter bank based-MC transmission

systems use filters of larger length than the rectangular filters of DMT system and results into

improvement in side lobes attenuation, lower level of ICI, ISI and greater robustness to narrowband

interference [1]. All the advantages of OFDM system are lies in the orthogonality of sub-carriers which is

also preserved by using DFT based digital filter bank. Therefore, the development in this technique is to

take place with the advancement in digital signal processing field. The DFT based OFDM system is

shown in Figure-6.2.1.

[97]

(a)

(b)

Figue-6.2.1: (a) OFDM system (b) TMUX

The DFT can be interpreted from the theory of multirate systems as an exponentially modulated

filter bank, where the prototype filter is an N-length window function [10], having N is the length of the

DFT (the number of sub-channels in MCM systems). Since each filter in the DFT bank is obtained from a

window function, the minimum sub-channel discrimination is on the order of 13.5 dB. Considering that

the dispersive channel destroys orthogonality between subcarriers, when IFFT / FFT is used for data

transmission, the system suffers from ICI and ISI.

M

M

M

H0(z)

H1(z)

HM-1(z)

.

.

.

C (z)

F0(z)

F1(z)

FM-1(z)

M

M

M

.

.

.

x0 [n]

x1 [n]

xM-1 [n]

X1 [n]

XM-1[n]

y [n]

x0 [n]

[98]

In addition to radio frequency interferences emerging from AM radio signals, other kinds of

narrow-band interferences sometimes lead to the major performance degradation, affecting a large

number of sub-carriers [109]. As a result, the performance of DFT-based multi-carrier modulation

systems in noisy environments, mainly with narrow-band noise, is far from being robust and reliable. In

order to solve these problems, researchers have been investigating the use of alternative filter banks with

a TMUX configuration [76]. Figure- 6.1(b) shows an example of an M-channel filter-bank based TMUX.

The delay has been introduced at the transmitter or at the receiver stage in order to obtain proper system.

The shaded blocks of OFDM system in Figure-6.2(a) are replaced with TMUX as shown in Figure-

6.2.1(b).

It is well-known that several maximally decimated filter banks can be efficiently implemented,

reducing the total computational cost. By using some of the fast algorithms, a significant group of filter

bank-based TMUX can be achieved, as shown in Figure- 6.1(b). The general block diagrams for the

transmitter and the receiver can be obtained from the synthesis and the analysis filter banks, respectively.

At the transmitter, there are the processes like (a) Matrix and transform operations; (b) poly-phase filters,

or lattice or butterfly structures; (c) parallel/serial (P/S) converter. At the receiver, the different operations

are (a) Serial/parallel converter; (b) poly-phase filters, or lattice or butterfly structures: (c) matrix and

transformation operations. For this system, the key point is that the last and the first stage of the

transmitter and the receiver are, respectively, a P/S and an S/P converter. Various building blocks of

OFDM system are explained below.

6.2.1 PSK/QAM Mapping and Demapping

In the transmitter side, the binary bit stream is generated by data generator as shown in Figure-

6.1(a) which will be mapped to the frequency domain (constellation mapping) when they are allocated on

each sub-carrier. The data stream is mapped using one or more digital modulation schemes, such as

Phase-Shift Keying , Quadrature Amplitude Modulation (QAM) [109] etc., which are represented by a

complex in-phase and quadrature-phase vector. At the receiver end, the constellation points are de-

mapped to obtain the time domain transmitted information bits.

6.2.2 Serial to Parallel/ Parallel to Serial Conversion

At the input of the OFDM system, data is arriving in the form of a serial data stream, therefore a

serial to parallel conversion block is needed to convert the input serial bit stream into the parallel data in

each OFDM symbol. The data allocated to each symbol depends on the modulation scheme used and the

number of sub-carriers, viz. for a sub-carrier modulation of 16-Quadrature Amplitude Modulation (QAM)

[99]

each subcarrier carries 4 bits of data, and for a transmission using 100 sub-carriers, the number of bits per

symbol would be 400. At the receiver, the parallel to serial conversion block is performed as an inverse

operation, converting the data in each OFDM symbol to the output serial bit stream [33].

6.2.3 IFFT/FFT

In the transmitter side, after serial data stream is converted to parallel blocks of size N, the IFFT

operation is used to convert modulated data on each sub-carrier from frequency domain to the time

domain, allowing it to be transmitted. Time domain samples are calculated as-

푥 (푛) = 푋(푘)푒 ⁄ ,

for 0 ≤ n ≤ N-1 (6.2.3.1)

where, X(k) is the symbol transmitted on the kth subcarrier and N is the number of sub-carriers. The

samples x(n) are interpreted as time domain signal. At the receiver side, the signal is transformed to the

frequency domain using FFT operation [34].

6.2.4 Equalization

The aim of equalization is to find an inverse filter that compensates for the ISI so that all the

multipath signals become shifted and aligned in time, rather than being spread out. In the OFDM systems,

the bandwidth of the sub-carriers is much narrower than the entire frequency selective fading channel;

this makes the frequency response over the bandwidth of each sub-carrier effectively flat. As a result,

only simple frequency domain equalization is required, in the simulation zero-forcing equalization

algorithm is used [86].

6.2.5 Cyclic Prefix and Zero Padding

Cyclic prefix (CP) and zero padding (ZP) are two common guard intervals in the OFDM system

to combat the effect of multipath. The low transmission power is one of the most important characteristics

of ultra wideband (UWB) communication systems. For this consideration, MB-OFDM (Multiband

Orthogonal Frequency Division Multiplexing) UWB system adopts the ZP-OFDM scheme to decrease

the transmission power (ZP part does not occupy any energy). ZP-OFDM scheme also has another

advantage compared to CP-OFDM, it guarantees the symbol recovery and assures the equalization of FIR

channels regardless of the channel zero locations [109].

[100]

However, the ZP-OFDM scheme increases the receiver complexity. In CP-OFDM symbol, the

basic idea is to replicate part of the OFDM time-domain symbol from back to the front to create a guard

period. Time domain OFDM signal is cyclically extended to mitigate the effect of multipath [86].

6.3 PERFORMANCE PARAMETERS OF OFDM SYSTEM BY USING

OPTIMIZATION TECHNIQUES

The performance of the OFDM system can estimate on the basis of variation in BER with respect to

change in SNR.

6.3.1 Multiband -OFDM System

In the year 2005, the ECMA-368 was chosen as the physical layer of high data rate wireless

specifications for high speed Wireless USB, Bluetooth 3.0 and Wireless High-Definition Media Interface.

The MB-OFDM systems consist of 14 bands with a bandwidth of 528 MHz for each band. These bands

are then grouped into five band groups. The information transmitted on each 528 MHz band is modulated

using OFDM. OFDM distributes the data over 122 useful subcarriers with 4.125 MHz subcarrier spacing.

Frequency-domain spreading, time-domain spreading and forward error correction coding are

used to vary the data rates. The supporting data rates are 53.3, 80, 106.7, 160, 200, 320, 400 and 480

Mb /s. The MB-OFDM UWB system has two modes of operation: Time Frequency Interleaved (TFI) and

Fixed Frequency Interleaved (FFI). In the TFI mode, the signal hops over two or three bands within a

band group. The hopping pattern is called a time frequency code (TFC) and has a period of six hops. In

each hop, one OFDM symbol is transmitted. For each band group, a TFC is defined. In the FFI mode the

system does not hop and only uses one of the 528 MHz bands. In this study an IFFT block of OFDM

system has been replaced by TMUX block. Figure-6.2 clearly illustrates that IFFT block of OFDM

system can be replaced by TMUX because graph between bit error rate and signal to noise ratio is same

for OFDM with IFFT as well as TMUX [34].

6.3.2 Narrow-band Interference Models in MB-OFDM UWB System

Narrow-band interference (NBI) can be generated due to the transmission signals or harmonics

(caused by the nonlinearity characteristic of the power amplifier) generated from other services. These

signals (or harmonics) may occupy the same frequency band with the MB-OFDM UWB system, hence

introduce the interference to the system. In this analysis, one limits the cases where NBI problem is due to

the harmonics generated by GSM interferer and WLAN interferer. Further, investigation has limited to

[101]

two extreme cases: second harmonic of GSM signal and third harmonic of WLAN signal. These two

cases represent the minimum/maximal bandwidth, corresponding to maximal/ minimum power spectral

density for the same SIR [109].

6.3.3 Additive White Gaussian Noise (AWGN) Channel

The AWGN channel is the simplest channel model used in most communication systems. The

thermal noise in the receivers can be characterized as an additive white Gaussian process. AWGN has a

uniform spectral density (making it white) and a Gaussian probability distribution. This model does not

account for the phenomena of fading, frequency selectivity, interference, nonlinearity or dispersion [110].

6.3.4 Mathematical Derivation of Spectrum Leakage

A model with single frequency component is used to demonstrate the principle of the spectrum

leakage. This interference can be regarded as a NBI with extreme small bandwidth.

퐼(푛) = 푒 . (6.3.4.1)

where, I(n) is the discrete sampling points of the time-domain interference with single frequency

component fc, n is the time index having the range n =1, 2....m. m is the number of samples of time

domain OFDM signal by assuming one sample per bit. In OFDM modulation, the subcarrier frequency fn

is given as-

푓 = 푛훻푓.

(6.3.4.2)

훻푓 =푓푁

.

(6.3.4.3)

Here, fs is the entire bandwidth and N is the number of subcarriers. Suppose the interference with single

frequency component fc is located in the middle of sub-carrier 81 and sub-carrier 82 then cut-off

frequency is given as-

푓 = . 푓 = . .

(6.3.4.4)

[102]

Interference can be written as-

퐼(푛) = 푒 = 푒.

.

(6.3.4.5)

After taking FFT of I(n), the frequency-domain interference samples can be written as-

퐼(푘) = 퐼(푛) 푒 .퐼(푘) = 푒 푒

(6.3.4.6)

After putting the values of cut-off frequency fc as shown in (6.3.4.4)

= 푒 ( . ),

for k = 0, 1, 2,3………………. N-1 (6.3.4.7)

By using the summation formula of geometric progression

퐼(푘) = 푒 ( . ) =1 − 푒 ( . )

1 − 푒 ( . ).

(6.3.4.8)

In this case, narrow band interference has been introduced at different level of noise power in an

OFDM system with IFFT and TMUX. The performance of OFDM with TMUX is compared with the

OFDM with IFFT on the parameter bit error rate by varying signal to noise ratio (Eb/N0) and results

obtained are shown in Figure-6.3.1 which clearly illustrates that whenever the noise power of narrowband

interference has been increased TMUX based OFDM system provides better results as compared to

conventional OFDM with IFFT. The BER performance of an OFDM system using TMUX [in place of

FFT and IFFT blocks of Figure-6.2.1(a)] with narrow band interference has been shown in Figure- 6.3.2.

This clearly depicts that the BER of OFDM system using TMUX is found lower as compared to

conventional OFDM system.

[103]

The TMUX designed with various windows using bi-section algorithm for an OFDM system

performs differently. The proposed window provides better performance in terms of BER as visible from

Figure- 6.3.3 by which a conclusion can be drawn that at 12 dB SNR the BER is better than Kaiser, PC4

and PC6 window function.

Figure- 6.3.1: OFDM system with IFFT and TMUX

Figure- 6.3.2: OFDM system with TMUX at different value of narrow band interference

[104]

Figure- 6.3.3: OFDM system with TMUX designed with various windows using bi-section algorithm

Figure- 6.3.4: OFDM system with TMUX designed with various windows using LM algorithm

[105]

In this case, OFDM system with TMUX designed with the help of various windows and LM

algorithm are compared on the basis of BER pattern, as shown in Figure-6.3.4. This also shows that the

proposed window provides better results as compare to other existing combinational window functions.

6.4 COMPARATIVE STUDY AND FINDINGS

In this study, the proposed window family along with Kaiser, PC4 and PC6 are used to design a

TMUX for an OFDM system to analyze the performance based on parameter BER. The performance

comparison of OFDM system with several variable and combinational window functions is determined. It

is found that the BER of proposed window is better than Kaiser, PC4 and PC6 window functions. In

OFDM system, TMUX use prototype filter which consist of optimum value of filter coefficients that are

obtained by different optimization techniques such as bi-section and LM algorithms. Bi-section algorithm

provides better results in OFDM system as compared to other algorithm.

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