Free Essay

Antenna Design

In: Computers and Technology

Submitted By ramyakanna
Words 7933
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Figure 1.1-The comparison between conventional FDM and the OFDM. 7
Figure 1.2- Traditional view of receiving signals carrying modulation. 7
Figure 1.3- OFDM Spectrum. 7
Figure1.4- Discrete-time system model of OFDMA. 9
Figure 1.5- Blocked and interleaved OFDMA. 10
Figure 2- Feature of SSA. 12
Figure 4.1.1-Main flow chart. 19
Figure 4.1.2-Flow chart when 2 users fall in 3,5,8,14. 21
Figure 4.1.3-Flow chart when all 3 user fall in 3,5,8,14. 24 Figure 5.1-Block diagram for transmitting and receiving control frame. 28 Figure 5.2-Block diagram for data transmission. 29
Figure 5.3-Characteristics of white noise (a) PSD , (b) autocorrelation. 30
Figure 5.4-signal space diagram for coherent BPSK system. 31
Figure 5.5-Block diagram for Data reception 31
Figure 6.2 - Control frame 39
Figure 6.4-BER plot after matlab simulation. 42

LIST OF ACRONYMS * OFDM – Orthogonal Frequency Division Multiplexing * OFDMA- Orthogonal Frequency Division Multiple Access * FDM - Frequency Division Multiplexing * CATV - Community Access Television/ Cable Access Television * DVB-RCT- Digital Video Broadcasting – Return Channel Terrestrial * WiMAX- Worldwide interoperability for Microwave Access * LTE - Long Term Evolution * ADSL- Asymmetric Digital Subscribers Line * WLAN- Wireless Local Area Network * ETSI –European Telecommunications Standard Institute * FFT – Fast Fourier Transform * IFFT- Inverse Fast Fourier Transform * ISI – Inter Symbol Interference * TDD- Time Division Duplexing * FDD- Frequency Division Duplexing * CP- Cyclic Prefix * CIR- Channel Impulse Response * SSA- Static Sub-Carrier Allocation * DSA- Dynamic Sub-Carrier Allocation * S/P- Serial to Parallel * P/S- Parallel to Serial * BPSK- Binary Phase Shift Keying * AWGN- Additive White Gaussian Noise * BER- Bit Error Rate * IEEE-Institute of Electrical and Electronics Engineers * PSD- Power Spectral Density * SFN- Single Frequency Networks * MoCA -Multimedia over Coax Alliance * VDSL- Very High Bit Rate Digital Subscribers Line * BPL -Broadband over Power line


In modern communication system, due to the limitations on available bandwidth there is a need to utilize the available frequency spectrum to its best. To improve spectral efficiency in a wired or wireless system i.e., to accommodate as many users as possible with least possible degradation in the performance of the system , several multiple access schemes are devised. One of the upcoming and challenging scheme is Orthogonal Frequency Division Multiple Access (OFDMA).
The concept of OFDMA was first introduced by Sari and Karam, who investigated the application of OFDMA to send upstream information from subscriber premises to the cable head-end in CATV networks. This scheme was then adopted in the standard of digital terrestrial television (DVB-RCT) in the uplink of the interaction channel . OFDMA became popular in 2002, when it was adopted as the air interface for emerging IEEE 802.16e standards for wireless metropolitan area networks.
OFDMA is an extension of the OFDM into a multiuser environment. The main concept in OFDM is the orthogonality of the subcarriers because of which it is possible to arrange the carriers in an OFDM signal so that the sidebands of the individual carriers overlap and the signals are still received without adjacent carrier interference.

In a conventional serial data system, the symbols are transmitted sequentially, with the frequency spectrum of each data symbol allowed to occupy the entire available bandwidth. When the data rate is sufficiently high, several adjacent symbols may be completely distorted over frequency selective fading or multipath delay spread channel.

Figure 1.1 : The comparison between the conventional FDM and the OFDM.

The traditional frequency spectrum looks like as shown below

Figure 1.2 - Traditional view of receiving signals carrying modulation

The idea of OFDM technique was to use parallel data transfer and FDM with overlapping sub-channels to provide significant advantages in terms of simplified equalization, robustness to multipath distortion and increased spectral efficiency. The OFDM spectrum looks as shown below.

Figure 1.3- OFDM spectrum.

The main concept in OFDM is the orthogonality of the subcarriers because of which it is possible to arrange the carriers in an OFDM signal so that the sidebands of the individual carriers overlap and the signals are still received without adjacent carrier interference.

A baseband OFDM system model can be expressed in the following manner , where each sub carrier is of the form

Where n is a discrete time variable and fk is the carrier frequency for sub carrier k.The sub carriers frequency fk is defined as

where N is the number of sub carriers & T is the original sample time of the transmitted symbol . The baseband model of an OFDM system in discrete time is

where c(k) is the transmitted symbol on subcarrier k & x(n) is the OFDM symbol.

The sub-carriers spacing in an OFDM channel is given as: ∆f = K/Tu ( Hz) where , ∆f = subcarrier spacing K = positive integer ≈ 1 Tu = symbol duration(s)
For ‘N’ subcarriers total bandwidth is given by,
B =N.∆f ( Hz)

OFDMA is an extension of the OFDM into a multiuser environment . The principle of OFDMA is to divide the available subcarriers into several mutually exclusive groups (i.e., subbands) according to the subcarrier allocation strategies. Then each group of subcarriers is assigned to one user for simultaneous transmission. The OFDMA subcarrier structure can support a wide range of bandwidths, by adjusting FFT size to channel bandwidth while fixing the subcarrier spacing. [1]
In OFDMA systems, both time and/or frequency resources are used to separate the multiple user signals. Groups of OFDM symbols and/or groups of subcarriers are the units used to separate the transmissions to/from multiple users.
A general block diagram of this multiple access method can be seen in Figure 1.4. * Here user Data is modulated with a baseband modulated scheme * Baseband modulated symbols are assigned to sub-carriers,using the assignment map defined by the subcarrier allocation scheme ,then OFDM symbol is transmitted. * Data of Uth user can be received by knowledge of the subcarrier assignment * Cyclic prefix (CP) is added to combat Inter-Symbol Interference (ISI) and Inter-Channel Interference (ICI).

Figure1.4- Discrete-time system model of OFDMA

OFDMA can be employed in both, TDD(time division duplexing) and FDD (frequency division duplexing). In TDD , both downlink and uplink transmissions are made in same frequency band but in different time interval. In FDD, downlink and uplink transmissions are simultaneously done in different frequency bands.
A fraction of OFDM sub-carriers is assigned to a user in a contiguous or inter leaved manner:
Blocked OFDMA : Simple but possible throughput degradation due to channel fading.
Interleaved OFDMA: Attains channel diversity but there is need for “ stricter” synchronization.

Figure 1.5- Blocked and interleaved OFDMA The allocation of sub-carriers to the different users can be done in basically two different ways:
• Static Sub- carrier Allocation (SSA)
• Dynamic Sub- Carrier Allocation (DSA)
The use of OFDM/A as a modulation and multiple access scheme is growing for both indoor and outdoor applications. OFDM/A is being used in a number of wireless and wire-line applications including LTE, WLAN, Digital Audio and Video Broadcast, Fixed WiMAX, ADSL, and ADSL2+, Mobile WiMAX and LTE. It has been adopted in a wide range of systems, such as the IEEE 802.20 , which is supposed to be true mobile wireless technology with high capacity and high mobility, ETSI broadband radio access networks , multiuser satellite communications , and the fourth-generation cellular network .




In OFDMA , sub-carriers are grouped into sets (sub-channels) each of which is assigned to different user . In SSA each user can have a predetermined set of subcarriers for the duration of connection. The sub-channel allocation may depend on factors like incoming data rate, available bandwidth, limiting BER etc. Interleaved , randomized , or clustered sub-carrier assignment can be used.
The features of SSA include simple implementation, cost effectiveness & minimal signaling overhead . But no frequency diversity is achieved.

Figure 2.1- Feature of SSA

Consider a subcarrier OFDMA system supporting users on the uplink .Each user is allotted subcarriers (either in block or interleaved fashion), in such a away that each subcarrier is allotted to only one user. Let Su denote the set of subcarriers allotted to the uth user.

The sequence transmitted by uth user reaches the receiver through an independent multipath channel with CIR , hu. With perfect timing of the processing window and perfect carrier frequency synchronization, the signal at the input to the N-point DFT unit in the receiver is

With all the K users perfectly aligned in time and with no Carrier frequency offset, the overall input to the N-point DFT unit in the receiver is

The kth subcarrier output of the uth user at the output of DFT unit is

The Static subcarrier allocation uses fixed resource allocation scheme in which each user is allocated a predetermined number of subcarriers. Consequently the allocated subcarriers to the users are under -utilized.

Dynamic subcarrier allocation enables users to adapt parameters for the appropriate use and reuse of subcarriers to minimize interference and increase overall network performance. It allocates subcarriers according to the users need and quality.
Adaptivity is one of the key requirements of DSA. By combining gathered information with knowledge of current system capabilities and limitations , DSA can perform various tasks . DSA concept is the ability to measure, sense, learn ,and be aware of important operating conditions.
An OFDM-based system can adaptively change the modulation order, coding, and transmit power of each individual subcarrier based on user needs or the channel quality. This adaptive allocation can be optimized to achieve various goals such as increasing the system throughput, reducing bit error rate (BER), limiting interferences, increasing coverage, or to prolong unit battery life. In multiuser OFDM systems, subcarriers allocation to users can be done adaptively as well to achieve the same goals.
Dynamic resource allocation can fully exploit the advantages of OFDM. Dynamic (adaptive) resource allocation can improve the performance of OFDM systems. Adaptive resource allocation strategies allow available resources to be used efficiently, by taking account of the channel conditions, and allocate to each user a subset of subcarriers which experience good channel conditions for that user.

The adaptivity in OFDMA systems can be performed either at algorithm level or at parameter level. In classical wireless systems, usually algorithm parameters, e.g. coding rate, have been adapted in order to optimize the transmission. In DSA throughput is optimized but signaling is overhead compared to SSA. DSA can be complex especially when there are large number of subcarriers present in DFT window.

Depending upon the incoming data packets and the available buffer size we allocate the sub-carriers among three users . We assume that maximum of 256 buffers are available for each user. Each buffer acts as a register of length 256 bits. A total of 256x256 bits can be transmitted and received by each user on the allocated number of sub-carriers. This dynamic sub-carrier allocation scheme for 3 users will be explained in the chapter 4.
The total number of sub-carriers considered are 64 in number. We assume the wired environment to be an AWGN channel. For example, if 3 users need to send data via co-axial cables( fixed available Band width) then they have to wait until the channel is sensed to be free. By extending the concept of wireless OFDMA to wired one we want to enable simultaneous transmission of data from the 3 users in their allocated sub-carriers.
The sub-carriers allocation will change each time we read the filled buffer size. The allocated number of sub-carriers will be sent to the respective receivers in the first time slot and this is followed by the data transmission and reception. This is explained in chapter 5.



Our idea of subcarrier allocation among 3 users in an OFDMA system in a wired environment is shown graphically in the flowchart. Initially we have divided the maximum buffer size (256) into different ranges. Accordingly some numbers are assigned to each range so that it is useful for computation and initial subcarriers are assigned to each user so that even for a worst case scenario the sum of all initial subcarriers assigned will not exceed maximum number of sub-carriers(64) to be allocated. The remaining subcarriers are allocated using dynamic subcarrier allocation algorithm designed. The algorithm is divided into 3 steps. First step is when all the 3 users fall in any range from 0-255(buffer size),second step is when 2 users fall in the range numbered 3,5,8 and 14 and third step is when all 3 users fall in the range numbered 3,5,8 and 14.Based on this subcarriers are allocated accordingly.

The input to each user is of random length. Hence the buffer size is also random. Maximum buffer length of 256 is assigned to each user. Initially, the buffer size for each user is found. The length of the buffer is divided into ranges i.e 0-15,16-31,32-63,64-127,128-191,192-255.The numbers 1,2,3,5,8,14 and initial subcarriers 4,8,12,15,18,21 are assigned to the users in the particular range as shown in the flowchart. The total number of subcarriers to be assigned in our algorithm is 64.Next ,the remaining number of subcarriers(X) is found by subtracting the sum of initial subcarriers assigned from the total number of subcarriers. Now, this remaining number of subcarriers are to be allocated dynamically to different users. This is done as follows- case 1: If all 3 users fall in the range numbered 1,2 which has less data to be transmitted, X/3 number of subcarriers are assigned to each user. case 2: If 2 users fall in the range numbered 1,2 then, X is assigned to the third user because it has large data to be transmitted and hence requires more number of subcarriers. case 3: If 1 user falls in the range numbered 1,2 then, assign X between other 2 users. case 4: If all 3 users fall in the range numbered 3,5,8,14 then, assign X among 3 users. case 3 and case 4 is considered in detail in step2 and step 3 respectively.
After initial and dynamic allocation of subcarriers, the sum of all the allocated subcarriers is found and checked if it is equal to 64.If this condition satisfies stop the main algorithm and if not satisfied , assign (sum-X) subcarriers to the third user.

Find the buffer size for each user

0-15 Nos assigned for computation Initial sub-carriers
1 Y



3 Y



8 Y

14 Y

Find the remaining number of sub-carriers to be assigned(X)


If 3 users fall in 1,2
Assign X/3 to all three users Y

If 2 users fall in 1,2

Assign X to the 3rd user


Assign X between other two users

If 1 user fall in 1,2


Assign X between 3 users

Sum of sub-carriers is 64 ?

Assign (Sum-X) to the 3rd user



Figure 4.1.1: Main flow chart

The users falling in this range has large data to be transmitted and hence requires larger number of subcarriers. The other user is neglected and only initial subcarriers are assigned to that user. In this step, the difference between the numbers assigned to different ranges is found and depending on the difference the number of subcarriers to be allocated to different users is decided. First, the difference between the numbers assigned to 2 users is found and the following cases are checked- case 5: If diff =2,3,6; assign 0.55X to user1 and 0.45X to user2. case 6: If diff =-2,-3,-6; assign 0.45X to user1 and 0.55X to user2. case 7: If diff =5,9; assign 0.65X to user1 and 0.35X to user2. case 8: If diff =-5,-9; assign 0.35X to user1 and 0.65X to user2. case 9: If diff =11 ;assign 0.75X to user1 and 0.25X to user2. case 10: If diff=-11 ;assign 0.25X to user1 and 0.75X to user2.

If 1 of the above cases is satisfied, the subcarriers are assigned as shown above. This is as shown in Figure 4.1.2.


Calculate the difference of numbers assigned to the 2 users 3 5 8 14 2 3 6
If difference is 2,3,6

If difference is -2,-3,-6

Assign 0.55(X) to user1, Assign 0.45(X) to user2


Assign 0.45(X) to user1, Assign 0.55(X) to user2

If difference is 5,9


Assign 0.65(X) to user1, Assign 0.35(X) to user2

If difference is 11

If difference is -5,-9

Assign 0.35(X) to user1, Assign 0.65(X) to user2


Assign 0.75(X) to user1, Assign 0.25(X) to user2

Assign 0.25(X) to user1, Assign 0.75(X) to user2

Figure 4.1.2: Flowchart when 2 users fall in 3,5,8,14.

In this step, first find the difference of numbers assigned to each user .If difference is 0 for all users, it means all users fall in the same range. So, assign X/3 to each user. If this condition is not satisfied then the following conditions are checked-
Case 11: If any 2 user fall under the range numbered 14 then ,assign X/2 to each of the 2 user and neglect the 3rd user.
Case 12: If 1 user fall under the range numbered 14 then, assign X/2 to that user in 14 and X/4 to the other 2 users.
Case 13: If 2 users fall under the range numbered 8 then, assign X/2 to each of the 2 user and neglect the lower range user.
Case 14: If 2 users fall under the range numbered 5 then, check the difference between the numbers assigned to those 2 users. If the difference is 3, assign X/2 to each of the 2 users. If the difference is not 3 then, assign X/4 to each of the 2 users.
Case 15: If 2 users fall under the range numbered 3 then, assign X/4 to each of the 2 users.
Case 16: If 1 user fall under the range numbered 8 then, assign X/2 to that user and X/4 to each of the other 2 users.
If none of the cases from 11-16 is satisfied then, it means all 3 users fall under the range numbered 3 or 5.So assign X/3 to each user.
In this way subcarriers are utilized efficiently and the data is transmitted at high speed.
This is as shown in Figure 4.1.3.


Find the difference of no assigned to each user & using the numbers 3,5,8,14(we have as follows)

If all users fall in same range assign X/3 to each
Difference is 0 for all users

If any 2 user fall under 14 No
X/2 to each user neglect third user

Y NoIf 1 user fall under 14

Assign X/2 to that user in 14 and (X/4) to other two users

Y No
Assign X/2, X/2 to two users in 8 , Neglecting the lower range user
If 2 user fall in 8

Y No
Assign X/2, X/2 to the two users
Diff b/w the user in 5 & other is 2
If 2 user fall in 5

Y Y Assign X/4, X/4 No No


If 2 users fall are in 3

YAssign X/4, X/4

No YAssign X/4, X/4 to other users

Assign X/2 to that user

If 1 user in 8

This shows all 3 users are in 3 or 5 so assign X/3 to each user No

Figure 4.1.3: Flow chart when all 3 user fall in 3,5,8,14. 4.2 Algorithm * STEP 1- Find the buffer size of each user. Maximum buffer size for each 3 users =256. * STEP 2- Depending upon the size of data occupied in their respective buffers , assign numbers for further computation. Such that the difference of number assigned to each user should not be same. * STEP 3- Depending upon the range of data of each user, assign the predefined number of sub-carriers. Ex: 4,8,12,15,18,21. * STEP 4- After initial assignment of sub-carriers, find the remaining number of sub- carriers left for dynamically assigning in later part.

* STEP 5- By using the numbers assigned to users, find in which category they come in our algorithm: X= Remaining number of sub-carriers. a) If 3 users fall in 1,2 . Assign X/3 to all three users. b) If 2 users fall in 1,2 . Assign X to the 3rd user. c) If 1 user fall in 1,2 . Assign X between other two users based on flow chart from “B which are explained in steps 5.1 to 5.5. * STEP 6- If all users do not come in 1,2, assign X based on flow chart from “C” further explained in steps 6.1 to 6.10 * STEP 7- After final assignment determine sum of sub-carriers=64, if not assign the remained sub-carrier to last user. * STEP 8- Stop
The algorithm from steps 5.1 to 5.5 are given below. * STEP 5.1- Find the difference of numbers assigned to the 2 users. The differences can be + ( 2 ,3,6,5,9,11.) * STEP 5.2- If the difference is 2, 3,6 . Assign 0.55(X) to user1. Assign 0.45(X) to user2.
If difference is -2,-3,-6. Assign 0.45(X) to user1, Assign 0.55(X) to user2. * STEP 5.3- Similarly If the difference is 5, 9. Assign 0.65(X) to user1, Assign 0.35(X) to user2.
Or if the difference is -5,- 9. Assign 0.35(X) to user1, Assign 0.65(X) to user2. * STEP 5.4- If difference is 11, Assign 0.75(X) to user1, Assign 0.25(X) to user2.
Or if difference is -11, Assign 0.25(X) to user1, Assign 0.75(X) to user2 * STEP 5.5- Return to main algorithm i.e to STEP 7 The algorithm from steps 6.1 to 6.10 are given below. * STEP 6.1- If all users do not come in 1,2. Find the difference of no assigned to each user & using the numbers 3,5,8,14. * STEP 6.2- If difference of all user is 0, i.e all the users fall in same range, then assign X/3 to each * STEP 6.3- If any 2 user fall under 14. Assign X/2 to each user neglect third user, because 3rd user data is less than comparing to these twos. * STEP 6.4- Now if 1 user fall under 14 , Assign X/2 to this user and (X/4) to other two users * STEP 6.5- Now If 2 user fall in 8, Assign X/2, X/2 to two users in 8 , Neglecting the lower range user * STEP 6.6- If not above case then now check whether If 2 user fall in 5, if so then now calculate difference between the user in 5 and user in other.
If the difference is 2, then assign X/2, X/2 to each user
If the difference is other than 2, then assign X/4, X/4 to each * STEP 6.7- Now check if two user come under 3, then assign them X/4,X/4 to each. * STEP 6.8- Next case if 1 user in 8, then Assign X/2 to that user and X/4, X/4 to other users * STEP 6.9- Finally the last case if above all cases not satisfied, This shows all 3 users are in 3 or 5 so assign X/3 to each user * STEP 6.10 - Return to main flow algorithm i.e to STEP 7


In the first time slot the control information i.e, the number of sub-carriers allocated to each user determined as per the DSA algorithm is sent. The Block diagram for this is as shown.

Figure 5.1 : Block diagram for transmitting and receiving control frame. Here S/P is Serial to Parallel Converter ,IFFT stands for Inverse Fast Fourier Transform ,P/S is parallel to serial converter , FFT Stands for Fast Fourier Transform. We use Binary Phase Shift Keying (BPSK) to modulate each control bit. Here 0 is mapped to -1 and 1 is mapped to 1. Hence it is also called as symbol mapping. The serial to parallel converter (S/P) converts the input data from a serial stream to parallel sets. The output of S/P converter is fed to an IFFT block. Inverse Fast Fourier Transform (IFFT) converts the frequency domain data set into samples of corresponding time domain representation. Specially, IFFT is useful for OFDMA because it generates samples of waveform with orthogonal frequency components. At receiver , DFT and symbol demapping is performed and the control information is decoded and stored.
Data and control information are time multiplexed and transmitted over the Gaussian channel. The block diagram for data transmission is as shown in figure 5.2.

Figure 5.2 : Block diagram for data transmission
The sub-carrier allocation block stands for implementing the DSA algorithm. Depending on the number of sub-carriers allocated finally , the data for the remaining number of sub-carriers should be zero padded for each user . Finally the output of the 3 IFFT Blocks are added and sent over the AWGN channel.
The white noise is characterized by a constant power spectral density i.e., power spectral density(PSD) is independent of the operating frequency. We express the PSD of white noise, with sampled function w(t) as

where the dimensions of N0 are in watts per Hertz. The autocorrelation function is given as

Figure 5.3 Characteristics of white noise (a) PSD , (b) autocorrelation.
The random variable Y is said to be Gaussian distribution if the Probability Density Function (PDF) is of the form

Where is the mean and is the variance of Y. We assume zero mean and variance of 1.Hence Y is said to be normalised.
The IFFT equation is given by where x(n) is the data bits mapped using BPSK.
The signal space diagram of BPSK can be shown as below. Here Eb is the average transmitted energy per bit.

Decision boundary

Region Z 2 Region Z1

- Eb + Eb Message point 2 Message point 1

Figure 5.4 : signal space diagram for coherent BPSK system.

The decision rule is that 1 was transmitted if the received point falls in the region Z1 and 0 was transmitted if the received point falls in the region Z2.

Figure 5.5: Block diagram for Data reception The data transmitted is subjected to white Gaussian noise. The serially received data is converted to parallel before giving it to the FFT block. Fast Fourier Transform (FFT) is a method to convert time domain sequence into frequency domain sequence. This is given by the equation below.

From the knowledge of the sub-carrier allocation and the decoded control frame, the receiver for each user de-maps the corresponding data and utilizes it.
Note : Data is fed parallely to IFFT and DFT blocks for speed and accuracy.


MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment where problems and solutions are expressed in familiar mathematical notation. Typical uses include:
• Math and computation
• Algorithm development
• Modeling, simulation, and prototyping
• Data analysis, exploration, and visualization
• Scientific and engineering graphics
• Application development, including graphical user interface building.

MATLAB is an interactive system whose basic data element is an array that does not require dimensioning. This allows you to solve many technical computing problems, especially those with matrix and vector formulations, in a fraction of the time it would take to write a program in a scalar non-interactive language such as C or Fortran.

The MATLAB system consists of five main parts:

Development Environment: This is the set of tools and facilities that help you use MATLAB functions and files. Many of these tools are graphical user interfaces. It includes the MATLAB desktop and Command Window, a command history, and browsers for viewing help, the workspace, files, and the search path.
The MATLAB Mathematical Function Library: This is a vast collection of computational algorithms ranging from elementary functions like sum, sine, cosine, and complex arithmetic, to more sophisticated functions like matrix inverse, matrix eigenvalues, Bessel functions, and fast Fourier transforms.

The MATLAB language: This is a high-level matrix/array language with control flow statements, functions, data structures, input/output, and object-oriented programming features. It allows both "programming in the small" to rapidly create quick and dirty throw-away programs, and "programming in the large" to create complete large and complex application programs.
Handle Graphics ®: This is the MATLAB graphics system. It includes high-level commands for two-dimensional and three-dimensional data visualization, image processing, animation, and presentation graphics. It also includes low-level commands that allow you to fully customize the appearance of graphics as well as to build complete graphical user interfaces on your
MATLAB applications:
The MATLAB Application Program Interface (API). This is a library that allows you to write C and Fortran programs that interact with MATLAB. It include facilities for calling routines from MATLAB (dynamic linking), calling MATLAB as a computational engine, and for reading and writing MAT-files.
6.1.1 INSTRUCTIONS USED IN CODE 1) RANDI : Pseudorandom integers from a uniform discrete distribution. R = RANDI([IMIN,IMAX],...) : returns an array containing integer values drawn from the discrete uniform distribution on IMIN:IMAX.

2) RANDN : Normally distributed pseudorandom numbers.
R = RANDN(N) returns an N-by-N matrix containing pseudorandom values drawn from the standard normal distribution. RANDN(M,N) or RANDN([M,N]) returns an M-by-N matrix. RANDN(M,N,P,...) or RANDN([M,N,P,...]) returns an M-by-N-by-P-by-... array. RANDN returns a scalar. RANDN(SIZE(A)) returns an array the same size as A.
Note: The size inputs M, N, P, ... should be nonnegative integers. Negative integers are treated as 0.

3) LENGTH : Length of vector.
LENGTH(X) returns the length of vector X. It is equivalent to MAX(SIZE(X)) for non-empty arrays and 0 for empty ones.

4) FLOOR : Round towards minus infinity. FLOOR(X) rounds the elements of X to the nearest integers towards minus infinity.

5) CEIL : Round towards plus infinity.
CEIL(X) rounds the elements of X to the nearest integers towards infinity.

6) DE2BI: Convert decimal numbers to binary numbers.
B = DE2BI(D) converts a nonnegative integer decimal vector D to a binary matrix B. Each row of the binary matrix B corresponds to one element of D. The default orientation of the binary output is Right-MSB; the first element in B represents the lowest bit. 7) AWGN: Add white Gaussian noise to a signal. Y = AWGN(X ,SNR) adds white Gaussian noise to X. The SNR is in dB. The power of X is assumed to be 0 dBW. If X is complex, then AWGN adds complex noise.

8) WGN :Generate white Gaussian noise. Y = WGN(M,N,P) generates an M-by-N matrix of white Gaussian noise.
P specifies the power of the output noise in dBW.

9) RESHAPE(X,...,[],...) : (acts as a serial to parallel converter block) calculates the length of the dimension represented by [], such that the product of the dimensions equals PROD(SIZE(X)). PROD(SIZE(X)) must be evenly divisible by the product of the known dimensions. You can use only one occurrence of []. Note : RESHAPE(X,...,,...[]) : performs parallel to serial conversion. 10) IFFT : Inverse discrete Fourier transform.
IFFT(X) is the inverse discrete Fourier transform of X.

11) FFT : Discrete Fourier transform. FFT(X) is the discrete Fourier transform (DFT) of vector X. For matrices, the FFT operation is applied to each column. For N-D arrays, the FFT operation operates on the first non-singleton dimension.

For length N input vector x, the DFT is a length N vector X, with elements N X(k) = sum x(n)*exp(-j*2*pi*(k-1)*(n-1)/N), 1 <= k <= N. n=1 The inverse DFT (computed by IFFT) is given by N x(n) = (1/N) sum X(k)*exp( j*2*pi*(k-1)*(n-1)/N), 1 <= n <= N. k=1

12) PADARRAY : Pad array.
B = PADARRAY(A,PADSIZE,PADVAL,DIRECTION) pads A in the direction specified by the string DIRECTION. DIRECTION can be one of the following strings. String values for DIRECTION
'pre' Pads before the first array element along each dimension .
'post' Pads after the last array element along each dimension.

13) PLOT : Linear plot. PLOT(X,Y) plots vector Y versus vector X. If X or Y is a matrix, then the vector is plotted versus the rows or columns of the matrix, whichever line up. If X is a scalar and Y is a vector, disconnected line objects are created and plotted as discrete points vertically at X. PLOT(Y) plots the columns of Y versus their index. If Y is complex, PLOT(Y) is equivalent to PLOT(real(Y),imag(Y)). In all other uses of PLOT, the imaginary part is ignored. Various line types, plot symbols and colors may be obtained with PLOT(X,Y,S) where S is a character string made from one element from any or all the following 3 columns: b blue . point - solid g green o circle : dotted r red x x-mark -. dashdot c cyan + plus -- dashed m magenta * star (none) no line y yellow s square k black d diamond w white v triangle (down) ^ triangle (up) < triangle (left) > triangle (right) p pentagram h hexagram 14) XLABEL : X-axis label, YLABEL: Y-axis label. XLABEL('text') adds text beside the X-axis on the current axis. YLABEL('text') adds text beside the Y-axis on the current axis. 15) LEGEND(string1,string2,string3, ...) puts a legend on the current plot using the specified strings as labels. LEGEND works on line graphs, bar graphs, pie graphs, ribbon plots, etc. You can label any solid-colored patch or surface object. The fontsize and fontname for the legend strings matches the axes fontsize and fontname.

This block generates a control frame based on the information from the sub-carrier allocation block, which contains the buffer length and number of subcarriers allocated to each user. This information is needed by the receiver to know which sub-carriers contains which users data so that it can decode appropriately.
For example: Figure 6.2 – Control frame.
L=buffer length
U=no. of sub-carriers allocated
Sample result :
After matlab simulations of the flow chart given in chapter 4, the following results were obtained for a particular case. Here initially assigned sub-carriers for user1,2 and 3 are 12, 21 and 15. According to the algorithm 16/4=4 is added to the initially assigned sub-carriers for user1 and 3. To user1 which has relatively more data 16/2=8 sub-carriers are added.
The length of data buffers for user1 is 59
The length of data buffers for user2 is 216
The length of data buffers for user3 is 85
The initial no of sub-carriers assigned for user1 is 12
The initial no of sub-carriers assigned for user2 is 21
The initial no of sub-carriers assigned for user3 is 15
The remaining no of subcarriers to be allocated 16
The final assignment for user1 is 16
The final assignment for user2 is 29
The final assignment for user3 is 19
The control frame generation and reception outputs are as follows:
The control frame is 59 16 216 29 85 19
The binary form of control frame is 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1

The total no of subcarriers assigned for data reception incase of user 1 is 16
The total no of subcarriers assigned for data reception incase of user 2 is 29
The total no of subcarriers assigned for data reception incase of user 3 is 19
The bufsiz is a variable which has the size of each register. Here it 256. The data generated is so divided that at a particular time only the corresponding subcarriers for each user transmits and receives data. The variables rp1,rp2 and rp3 are used to determine the number of times the loop for transmission and reception is run since BPSK maps only 1 bit into corresponding symbol. Data is generated using randn function (inbuilt ) in matlab. Zero padding is done wherever necessary using the ‘padarray’ instruction.
To determine the performance of the system, the bit error rate is calculated simultaneously for varying Eb/N0 values. The calculation is discussed in chapter 6.4.
The additive white Gaussian complex noise is added to the channel using function wgn (inbuilt). The practical BER values is calculated for the user which has the most data to be transmitted. 6.4 BER CALCULATION AND RESULTS
In digital transmission, the number of bit errors is the number of received bits of a data stream over a communication channel that have been altered due to noise, interference, distortion or bit synchronization errors. The bit error rate (BER) is the number of bit errors divided by the total number of transferred bits during a studied time interval. BER is a unitless performance measure, often expressed as a percentage.

The probability of error for a coherent BPSK is given by

As we increase the transmitted signal energy per bit Eb, for a specified noise spectral density No, the message points corresponding to symbols 1 and 0 move farther apart , and the average probability of error is correspondingly reduced in accordance to the above equation which is intuitively satisfying
The derivation of the probability of error formula mentioned above for BPSK is further discussed in Appendix- A.
The BER plot obtained for an example is as shown

Figure 6.4 : BER plot after matlab simulation.


7.1 ADVANTAGES: * For large bandwidth solutions, OFDMA allows simpler receivers such as in optical communication, which could lead to lower cost devices. * Good performance under delay spread / frequency selective fading conditions. * Efficient digital signal processor based generation/ detection techniques. * Can easily adapt to severe channel conditions without complex time-domain equalization. * Robust against narrow-band co-channel interference. * Robust against Inter-symbol interference(ISI) * High spectral efficiency as compared to conventional modulation schemes, spread spectrum, etc. * Efficient implementation using Fast Fourier Transform (FFT). * Low sensitivity to time synchronization errors. * Tuned sub-channel receiver filters are not required (unlike conventional FDM). * Facilitates single frequency networks (SFNs). * Dynamic sub-carrier allocation (DSA) improves signal quality and system capacity of OFDMA system. * DSA has low signaling overhead and low complexity of multiuser receiver. * DSA can achieve higher throughput compared to static assignment schemes. * Good performance under delay spread/ frequency selective fading conditions due to the orthogonality of the sub carriers.

Extending our algorithm to N users is a challenge. The limitations on channel bandwidth and the distance between the users is a concern. The maximum distance over which the signal can be transmitted without considerable attenuation can be area of concern. There should be proper synchronization (timing and channel) between the transmitter and receiver. The control frame should not be corrupted to an extent where its contents cannot be decoded. * It has a relatively high sensitivity to frequency offsets as this degrades the orthogonality between the carriers * It is sensitive to phase noise on the oscillators as this degrades the orthogonaility between the carriers. * Requires complex electronics to run the software - DSP including FFT algorithms needed for the forward error correction. This is always active regardless of data rate, although when no data is being transmitted the system can hibernate. However power consumption can be an issue. * If only a few carriers are assigned to each user the resistance to selective fading will be degraded or lost. * The adaptive sub-carrier assignment is more complex than CDMA.


8.1 APPLICATIONS: 1. Favourable in broadcasting networks like Ethernet LAN , Token bus, etc., with 3 users operating at the same time . 2. OFDMA is used in Asymmetric digital subscriber line (ADSL) and Very-high-bit-rate digital subscriber line (VDSL or VHDSL) broadband access via Plain old telephone service (POTS) copper wiring. 3. Used in PLC ( Power line communication) as well as in BPL (Broadband over Power line): OFDMA is used by many powerline devices to extend Ethernet connections to other rooms in a home through its power wiring. 4. Allows single frequency networks to be used, particularly important for broadcasters where this facility gives a significant improvement in spectral usage. 5. Multimedia over Coax Alliance ( MoCA) home networking: It is a trade group promoting a standard that uses coaxial cables to connect consumer electronics and home networking devices in homes. It allows both data communication and the transfer of audio and video streams. 6. OFDMA is being used in a number of wireless and wire-line applications including LTE (Long term evolution), Wireless LAN, Digital Audio and Video Broadcast, Fixed WiMAX, ADSL and ADSL2+.


In this project report, an algorithm to allocate subcarriers dynamically for a random input data rate in an OFDMA-based wired network is given. The complexity of the resource allocation problem increases exponentially with the number of subcarriers, the possible number of bits per subcarrier and the number of users. The flexibility of adaptive resource allocation (DSA), combined with the ability to deal with ISI, makes OFDMA very suitable to support high-data-rate services. With the spectrum becoming more and more fragmented especially for systems such as ADSL, DVB-RCT, LTE etc our idea to improve data rate provides flexibility of deployment across a variety of frequency bands with little need for modifications. Data transmissions with a higher rate can be achieved with the use of digital signal processing techniques and simpler receiver designs. The technique can be extended to many other applications. Hence this technique can be of paramount importance in the near future.


In coherent BPSK system, the pair of signals, s1(t) and s2(t) , used to represent binary symbols 1 and 0, respectively are defined by

Where , and Eb is the transmitted signal energy per bit. There is only 1 basis function of unit energy given by

We write the transmitted signal , s1(t) and s2(t) in terms of we get

The signal space diagram is as shown in Figure 5.4. The coordinates of the message points equals

To calculate probability of error, from figure 5.4 we have, the decision region associated with the symbol 1 or signal s1(t) is described by

where x1 is the observation scalar :

where x(t) is the received signal. We deduce that the likelihood function, when symbol 0 or s2(t) is transmitted is defined by

The conditional probability of the receiver deciding in favour of symbol1 , given that 0 was transmitted , is therefore


And changing the variable of integration from x1 to z , we may re-write above equation in the form

Where erfc(*) is complementary error function. Similarly the conditional probability of the receiver deciding in favour of symbol 0, given that 1 was transmitted , also has the same values as the above equation. Thus , averaging the conditional probabilities, we find that the average probability of symbol error equals. [2]


The references [1] amd [2] used in the report are

1. OFDMA Fundamentals and Applications by Tao Jiang, Lingyang Song and Yan Zhang. 2. The derivation for probability of error for BPSK as mentioned in Appendix –A is taken from Digital Communications by Simon Haykin.
The other references used are * 3GPP Long-Term Evolution Uplink Friday December 4, 2009 EE359 Project by Nima Soltani Comparison of Single-Carrier FDMA vs. OFDMA * Signal Processing for Communications EPFL Winter Semester 2006/2007 by Prof. Suhas Diggavi * Uplink Resource Scheduling in Dynamic OFDMA Systems by Farshad Naghibi * Wimax general info about 802.16 by Rohde & Schwarz * Multi-Carrier Digital Communications: Theory and Applications of OFDM Ahmad R. S. Bahai and Burton R. Saltzberg * Wireless networks and communications by Dr Van Zhang, Series Editor Simula Research Laboratory, Norway * OFDM-based Communication Systems: Lecture Notes by Dr. Doron Ezri, Dr. Michael Erlihson…...

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