1

CHAPTER 1

INTRODUCTION

1.1. Literature Review and Motivation

A 4G system is expected to provide a comprehensive and secure all possible solution where

facilities such as IP telephony, ultra-broadband internet access, gaming services and streamed

multimedia may be provide to users. There are various numbers of multiple access techniques

which are proposed for 4G system named as DS-CDMA (Direct Spread- Code Division Multiple

Access), MCCDMA (Multicarrier-CDMA), OFDMA (Orthogonal FDMA), IDMA (Interleave

Division Multiple Access) etc. IDMA (Interleave Division Multiple Access) is a new technology

that can remove the disadvantages of existing CDMA technique i.e. Multiple Access Interference

(MAI) and Inter-Symbol Interference (ISI). [6] [17]

In CDMA interleaver are used for coding gain while in IDMA, they are employed for user

separation. IDMA is a recently proposed scheme that employs chip- level interleavers for user

separation and the receiver employ a simple chip- level iterative multiuser detector (MUD). Such

a system is a logical development of the earlier research on introducing chip- level interleaving

as a means of mitigating burst impulsive noise disturbances, multiple access interference, as well

as Inter-Symbol Interference. The basic principle of IDMA is that two users are separated by an

interleaver (and the interleavers should be different for different users) while, OCDMA/IDMA,

which uses the orthogonal spreading code and interleaver to distinguish different users, increase

the receiver complexity of the user ends (UEs). [6]

1.2. Objectives

In IDMA the users are separated via independent and random interleavers. In the transmitter of

IDMA scheme, a chip-interleaver is followed by spreading process which is different from

conventional CDMA scheme. This method makes the sequences of low-correlation. Applying

the Central Limit Theorem, Multiple Access Interference is approximated as a Gaussian Random

Variable with mean and variance at the receiver. Consequently there is a limitation that the sum

of the users may have high correlation. After the interleavers are assigned to the users, they

2

become fixed or permanent, hence it becomes necessary to design an interleaver which is free

from this problem.

1.3. Major contribution of Thesis

The major contribution of thesis are summarized as follows:

Brief history of Access technologies and their introductions.

Understanding the major concept behind IDMA (Interleave Domain Multiple Access)

Technique.

Understanding the mechanism of Interleavers and codes used in IDMA.

Understanding the problems faced in current random interleavers and a solution is

provided that does solve the problem to a great extent.

1.4. Organization of Thesis

This thesis consists of six chapters. Chapter 2 consists of some old access technologies and

history of wireless communication is also discussed. Chapter 3 describes the IDMA concepts and

the transmitter and receiver principles, features, future implementation and application of IDMA.

Chapter 4 gives an insight about different codes and interleavers used in a typical IDMA system.

Chapter 5 discusses the problems encountered in IDMA systems and remedy for the problems is

also discusses, while an algorithm is also given. Chapter 6 discusses the simulation results and

the future work is also briefed.

3

CHAPTER 2

INTRODUCTION TO ACCESS TECHNIQUES

2.1. Background

With the advent of Internet and the advancement of technology, there has been an increased

interest in wireless connectivity. This trend began in the 1880s. The first successful wireless

transmission was achieved by the Italian Physicist whose name is Guglielmo Marconi. Marconi

created an equipment that achieved the wireless transmission of electrical signal through the air

which was the beginning of telegraphy or radio transmission, in September 1895. [1]

In the last 20 years, science has grown rapidly in the area of Digital Signal Processing in forward

error control coding and circuit designing which had a huge impact on wireless communication.

As time passed, wireless communication became more dominant, which gave rise to the need for

new applications such as video conferencing, online gaming, social network applications, and it

plays a huge role in military applications in encoding and encrypting important information to

provide security. [1]

2.2. Ages of Wireless Communication

In 1957, Clark Maxwell derived a theory based on electromagnetics which laid the basis for the

concept given by Guglielmo Marconi. This was a great achievement and a milestone for wireless

communication. However, it was unable to achieve reasonable data transmission rates for years

to come. [2]

The first prototypes for wireless telephony were introduced in the late 1940s in the US, and

1950s in the Europe. These early mobile phone were heavily constrained by limited mobility

and poor service. These devices were both heavy and expensive. The evolution of wireless

cellular communication is divided into several generations. The first and second generation

utilized analog communication, the third generation was revolutionary and the fourth generation

utilized broadband technology. [2]

4

In the 1970s, the first generation of mobile telephony was introduced to the commercial

markets. These systems were referred to as cellular systems, and the name was later shortened to

cell phones. Due to this, the signals were handed off to the towers. The signals for these cell

phones were based on analog signals. 1G devices were a little less expensive than earlier

prototype devices and were less heavy. The most important protocol in the 1st generation was

known as AMPS, TACS and NMT. The mobile phone market worldwide increased 30-50%

annually due to 1G networks and the number of subscribers globally reached to 20 million in

1990s. In the early 1990s, 2G technology was introduced which was known as GSM

technology and it was based on digital modulation techniques to improve quality of service, but

the networks offered limited data service in 2nd generation. [2]

As demand drove uptake of cellphones, 2G networks were further improved to improve the

coverage and transmission quality and offer additional services such paging, voice mail, faxes,

and text messages. The limited data services under 2G included WAP, HSCST and MLS. [2]

An intermediary stage, referred to as 2.5G, was introduced in late 1990s which introduced

GPRS standard. GPRS introduced packet-switched data capabilities to existing GSM networks,

which allowed users to send multimedia data as packets, and convolved the cellular networks

with the Internet. As time went on, the importance of packet-switching became paramount with

the rise of the Internet or IP. EDGE networks, which was a further advancement of the existing

GSM network, also comes under 2.5G technologies. What 3G revolution allowed the users to do,

was to use audio, graphics and video data with acceptable Quality of Service. It is possible in 3G

networks to stream videos and engage in video telephony, although such activities are severely

constraint by network bottlenecks and over-usage. [2]

The main objective behind 3G technology was to unify the various different standards with a

single Global Network Protocol, in Europe, the US and other regions. In 3G phones the speed of

2 Mbps was achieved under ideal conditions. Moving at higher speeds can drop 3G bandwidth to

a mere 145 kbps due to Doppler-shift fading. [2]

3G cellular services is also known as UMTS. To sustain higher data-rates and to open the way

for internet style applications, 3G technology supports both packet-switching and circuit-

5

switching data transmission and a single set of standards can be used worldwide with

compatibility over a variety of mobile devices. [2]

UMTS introduces 1st possibility of global roaming with potential access of internet from any

location. In the current generation of mobile telephony, 4G technology was deployed. The

purpose of 4G networks was to provide transmission rates up to 20 Mbps while simultaneously

accommodating QoS features. QoS allows users and telephone carries to prioritize traffic

according to the type of application and adjust between your different telephony needs at a

moments notice. [2]

Only now can we truly see the potential of 4G applications, which is expected to include high-

performance streaming of multimedia content. With the deployment of 4G technology, video

conferencing functionality is improved. 4G is also expected to provide wider bandwidth for high

speed mobile application within the network area. [2]

In 2008, the ITU-R organization specified the IMT-Advanced (International Mobile

Telecommunications Advanced) requirements for 4G standards, setting peak speed requirements

for 4G service at 100 Mbit/s for high mobility communication (such as from trains and cars) and

1Gbit /s for low mobility communication (such as pedestrians and stationary users). A 4G system

is expected to provide a comprehensive and secure all-IP based mobile broadband solution to

laptop computer wireless modems, smart phones, and other mobile devices. Facilities such as

ultra-broadband Internet access, IP telephony, gaming services, and streamed multimedia may be

provided to users. [22]

Pre-4G technologies such as mobile WiMAX and first-release 3G Long term evolution (LTE)

have been on the market since 2006 and 2009 respectively, and are often branded as 4G. The

approaching 4G (fourth generation) mobile communication systems are projected to solve still-

remaining problems of 3G (third generation) systems and to provide a wide variety of new

services, from high-quality voice to high-definition video to high-data-rate wireless channels.

The term 4G is used broadly to include several types of broadband wireless access

communication systems, not only cellular telephone systems. One of the terms used to describe

4G is MAGICMobile multimedia, anytime anywhere, Global mobility support, integrated

wireless solution, and customized personal service. As a promise for the future, 4G systems, that

6

is, cellular broadband wireless access systems have been attracting much interest in the mobile

communication arena. The 4G systems not only will support the next generation of mobile

service, but also will support the fixed wireless networks. This article presents an overall vision

of the 4G features, framework, and integration of mobile communication. [22]

2.3. Multiple Access Techniques

Multiple Access Techniques are used so that we can allow many different mobile users to share

the allocated radio spectrum in the most efficient way. We know that the spectrum is limited,

thus sharing is important to increase the capacity of the cell over a geographical area by allowing

the available bandwidth to be used in different areas. It is paramount to achieve this in such a

way that the quality of service doesnt degrade for the existing users. [19]

2.3.1. Frequency Division Multiple Access (FDMA)

FDMA is one of the earliest multiple access technologies for cellular systems in which a separate

pair of frequency bands is allocated to each different user for making and receiving calls. One of

the frequencies is allocated to uplink and one to downlink. The frequencies allocated to certain

users can only be allocated once per cell, or adjacent cell, during a call which reduces co-channel

and intra-channel interference. The spectrum cannot be reassigned as long as the call is in place.

Different users can use different frequencies within a cell, whether they transmit at the same time

or at different times. [19]

The features of FDMA are as follows: [19]

1. FDMA channel carries one phone circuit at one time. When the FDMA channel is not

being used, then it sits idle and no other uses it to increase shared capacity.

2. After voice channel assignment, BS and MS transmit the data simultaneously and

continuously.

3. FDMA bandwidth is generally narrow, i.e. FDMA is generally implemented in

narrowband systems.

4. The symbol time is large compared to the average delay spread.

5. Complexity of FDMA mobile system is lower than that of TDMA mobile system.

7

6. FDMA requires highly efficient filters at the receiver end to minimize the adjacent

channel interference.

Figure 2.1. FDMA R. Victor Jones, Harvard University

Source: http://people.seas.harvard.edu/~jones/cscie129/nu_lectures/lecture3%20/FDMA%2001.html

2.3.2. Time Division Multiple Access (TDMA)

There is no requirement for continuous transmission in digital systems because the users do not

use the allocated bandwidth at all time. In such cases, TDMA is a complementary access

technique to FDMA. Oftentimes they are used in conjunction such as in GSM which uses

TDMA/FDD. [19]

In TDMA, the entire bandwidth is available to the users but only for a finite period of time. In

most cases of TDMA, the available bandwidth is divided into fewer channels with compared to

FDMA and the users are allocated distinct timeslots because of which they have the entire

channel bandwidth at their disposal. TDMA requires careful time synchronization unlike FDMA

as long as the user shares the bandwidth and frequency domain. There are fewer number of

channels, and inter-channel interference is negligible.

When TDMA uses different timeslots for transmission and reception, this type of duplexing is

known as Time Division Duplexing (TDD). [19]

8

Figure 2.2. TDMA R. Victor Jones, Harvard University

Source: http://people.seas.harvard.edu/~jones/cscie129/nu_lectures/lecture3%20/TDMA01.html

2.3.3. Code Division Multiple Access (CDMA)

The basic principle in CDMA allows us to use the same frequency bandwidth for every user, as

each individual user is assigned a unique spreading code so that we may differentiate different

users. CDMA utilizes spread spectrum techniques, in which you one can use a spreading signal

(code that is uncorrelated to the signal and allows us to spread the message signal to a much

larger bandwidth) to spread the narrowband message signal. This technique is most commonly

used in CDMA systems. [19]

There are two main types of CDMA spreading techniques known as Direct Sequence Spread

Spectrum (DSSS) and Frequency Hopping Spread Spectrum (FHSS). In DSSS, the message

signal is directly multiplied with a pseudorandom noise code (PN Code). Every user is allocated

a unique PN code, which is orthogonal to all other codes in the sequence, so that the receiver can

determine which device or receiver the data is intended for. For orthogonality, we generally use

64 x 64 Walsh-Hadamard codes and an m-sequence. [19]

9

The near-far problem is a serious problem faced in CDMA systems. This problem arises when

the signal of interest is attenuated as the distance from receiver increases, because of which

regardless of how strong the transmitted signal is, it would be read as a weak signal. This

problem does not arise in TDMA and FDMA because the mutual interference is filtered out. In

CDMA, however, near-far effect combined with imperfect orthogonality between codes (e.g. due

to different time-shifts), leads to substantial interference. Accurate and fast power-control is

essential to reliable operation of multiuser DS-CDMA systems. [19]

Figure 2.3. Comparison between FDMA, TDMA and CDMA

2.3.4. Orthogonal Frequency Division Multiple Access (OFDMA)

OFDMA is also known as digital modulation technique and not a multi-user channel access

technique. It is used for transferring one bit stream over one communication channel using

OFDMA symbols. However, it can be mix with other multiple accesses using coding separation,

time or frequency of other users. [21]

OFDMA employs multiple closely spaced sub-carriers. The sub-carriers are divided among

group of sub-carriers. The sub-carrier that carriers should not be adjacent. OFDMA provides

multiplexing operation of data streams from multiple users onto the downlink sub-channels and

uplink multiple access by means of uplink sub-channels. [22]

10

This is achieved by assigning different OFDM sun-channels to different user. In this downlink, a

sub-channel may be intended for other receivers. In the uplink, a transmitter may be assigned one

or more channels [21]

Orthogonal Frequency Division Multiplexing (OFDM) not only provides clear advantages for

physical layer performance, but also a framework for improving layer 2 performance by

proposing an additional degree of free- dom. Using OFDM, it is possible to exploit the time

domain, the space domain, the frequency domain and even the code domain to optimize radio

channel usage. It ensures very robust transmission in multi-path environments with reduced

receiver complexity. [21] [22]

OFDM also provides a frequency diversity gain, improving the physical layer performance. It is

also compatible with other enhancement Technologies, such as smart Antennas and MIMO

(multiple-input and multiple-output) radar antenna .OFDM modulation can also be employed as

a multiple access technology (Orthogonal Frequency Division Multiple Access). In this case,

each OFDM symbol can transmit information o/from several users using a different set of sub

carriers (sub channels). This not only provides additional flexibility for resource allocation

(increasing the capacity), but also enables cross-layer optimization of radio link usage. [21] [22]

Figure 2.4. Comparison between OFDMA and SC-FDMA. Agilent Technologies

11

2.3.5. Single-Carrier Frequency Division Multiple Access (SC-FDMA)

SC-FDMA is a relatively new multiple access technique that utilizes single carrier modulation,

DFT-spread orthogonal frequency multiplexing, and frequency domain equalization. It has a

similar structure and performance as OFDM. SC-FDMA is currently adopted as the uplink

multiple access scheme for 3GPP LTE. [23]

SC-FDMA is the multiple access equivalent of Single-Carrier Frequency-Domain Equalization

(SC-FDE), which is similar to OFDM, in that they both perform channel estimation and

equalization in the frequency domain. Multiple access is achieved in frequency domain in SC-

FDMA. Thus to transition from SC-FDE to SC-FDMA requires division frequency amongst

frequencies.

2.4. Future of Development of Multiple Access Techniques

With the tremendous increment in the users count and introduction of new features including

web browsing. In the past few years, the request for bandwidth has started to surpass the

availability in wireless networks. Different techniques have been studied to improve the

bandwidth, efficiency and increase the number of users that can be accommodated within each

cell. [18]

The International Telecommunication Union (ITU) also defined recommendations for mobile

communication system for fourth generation (4G).In these recommendations, data rates up to

100 Mbps for high mobility and up to 1 Gbps for low mobility or local wireless are predicted.

Systems fulfilling these requirements are usually considered as fourth generation (4G) systems.

But 3G systems provide data rate of around 3.6-7.2 Mbps. [18]

Existing multiple access techniques used in 1G/2G/3G systems (such as FDMA/TDMA/CDMA

respectively) are basically suitable for voice communication only and unsuitable for high data

rate transmission and burst data traffic which would be the dominant portion of traffic load in 4G

system. There are various numbers of multiple access techniques which are proposed for 4G

system named as DS-CDMA (Direct Spread- Code Division Multiple Access), MC-CDMA

(Multicarrier-CDMA), OFDMA (Orthogonal FDMA), IDMA (Interleave Division Multiple

Access) etc. [18]

12

CHAPTER 3

IDMA SYSTEMS

3.1. Introduction

As we know that, CDMA (specifically DS-CDMA) is an effective transmission technique which

is used in second generation (IS-95 and CDMA 2000) and third generation (UMTS, TD-

SCDMA) systems. IDMA can be seen as a special case of DS-CDMA with a spreading gain of

one using very low rate code and user specific interleaver for user separation. The main

difference between IDMA and DS-CDMA is that in conventional DS-CDMA the data is

transferred through FEC, then Interleaver (d), then at the end Spreading is done by Spreader

whereas in IDMA the spreading is done before interleaver. [4]

Computer simulations are performed in various scenarios and the performance is analyzed by

BER as well as by the Extensive transfer information chart. The analysis revelers the advantages

of IDMA over DS-CDMA in terms of performance and complexity under practical

considerations, particularly in a highly user loaded scenarios. [4] [15]

In communication systems, interleaving is referred to be technique commonly used to overcome

correlated channel noise such as burst error or fading. In interleaving mechanism, the input data

rearranges itself, such that consecutive data bits are split among different blocks and is swapped

in a known pattern amongst them. At the receiver end, the interleaved data are arranged back into

the original sequence with the help of de-interleaver. As a result of interleaving, correlated noise

introduced in the transmission channel appears to be statistically independent of the receiver and

thus allows better error correction. [5] [16]

3.2. Advantages of IDMA

As the demand for high data rate services grows in wireless networks, various challenging

problems arise when the existing multiple access technologies are used. For orthogonal multiple

access (MA) technologies such as TDMA, FDMA and OFDMA, the major problems include

their sensitivity to inter-cell interference and frame synchronization requirement for maintaining

orthogonality. [6] [16]

13

For non-orthogonal MA technologies such as random waveform CDMA, although it mitigates

inter cell interference and supports asynchronous transmission, the challenge is to combat intra-

cell interference. So, there is a new technique known as IDMA (Interleave Division Multiple

Access) which seems to be the solution for these problems. [6]

The advantages of interleaving over scrambling seems very important for cell edge subscriber

stations to receive broadcast services such as common signaling broadcasting because some

advanced transmitting techniques for any casting cannot be used for broadcasting. Interleave-

division multiple accesses (IDMA) can be considered as a special case of direct-sequence code

division multiple accesses (DS-CDMA). [6]

In IDMA, data streams are separated by different interleavers rather than by different spreading

codes as employed in DS-CDMA. Each data stream is encoded by the same low-rate channel

encoder. The data rate can be adapted by superimposing many encoded and interleaved data

streams. In contrast to other system designs, channel coding is an integral part of the system

design. Separation of the data streams at the receiver can be done in an iterative, low complexity

way. These properties are advantageous for multi-user detection at the uplink and therefore make

IDMA an attractive candidate for the 4G uplink, but also for an evolution of existing DS-CDMA

systems. [6]

3.3. Comparison of IDMA and CDMA

Important features of all named multiple access are compared IDMA have been compared with

the existing MA technologies. With the existing CDMA, high data rates can be achieved by

reducing spreading factor or adopting multi-code CDMA, but the former leads to reduced

spreading gain against fading and interference, and the latter needs to overcome the interference

among spreading sequences. [24]

In contrast, high data rate transmission can be achieved in IDMA systems by assigning the FEC

codes with high coding rates. Neglecting intra-cell interference at low computational cost the

multiple access interference (MAI) is a major concern for both CDMA and IDMA cellular

networks. [24]

14

Figure 3.1. Difference between CDMA and IDMA. Source: [24]

The existing CDMA mitigates the MAI by multi-user detection (MUD). However, the high

computational Cost involved in MUD which limits the high number of user- application in

practical systems. In contrast to CDMA, IDMA uses the iterative chip-by-chip (CBC) detection

algorithm to combat intra-cell interference. The per-user computational complexity of the CBC

is independent of the number of users involved. It achieves multi-user gain in the case of each

user with a rate constraint. This means that given the same sum-rate, the more users in a system,

the less average transmitted sum-power is required. The features of IDMA distinguished from

the other MA techniques must be considered in MAC design for IDMA based networks. IDMA

involves dynamic power control to improve link capacity and guarantee QoS for users. [18]

3.4. IDMA Transmitter and Receiver

3.4.1. Transmitter

The upper part of Figure 3.1 demonstrates the transmitter structure of the IDMA scheme under

consideration with K simultaneous users. The input data sequence deck of user-k is encoded

based on a low-rate code C, generating a coded sequence: [5]

Where J is the frame length.

15

The elements are referred to as coded bits which are then permutated by an interleaver , thus,

producing:

Following the CDMA convention, the element in xk will be denoted as chips. Users are solely

distinguished by their interleavers, hence the name interleave division multiple access (IDMA)

scheme. [5]

The key principle of IDMA is that the interleavers {k}, opted for user separation and should be

orthogonal for all the users. It is assumed that the interleavers are generated independently and

randomly. The randomly generated interleavers disperse the coded sequences so that the adjacent

chips are approximately uncorrelated, facilitating the simple chip-by-chip detection scheme as

discussed below. [5]

Figure 3.2. IDMA Transmitter and Receiver structure

Assuming that the channel with no memory and after chip matched filtering, the received signal

from K users can be written as:

Where hk is the channel coefficient for user-k and {n (j)} are samples of an AWGN process with

zero mean and variance, assuming that the channel coefficient {hk} are known a

priori at the receiver. Due to the use of random interleaver {k}, the PSE operation can be carried

out in a chip-by-chip manner, with only one sample used at a time. [5]

16

3.4.1. Receiver

Adopting an iterative sub-optimal receiver structure, consisted of the primary signal estimator

(PSE) and K single user a posteriori probability (APP) decoders (DECs), the data is iterated for

pre-decided number iterations before finally taking hard decision on it. For single path

propagation, there is only one path for the transmission. The multiple access and coding

constraints are considered separately in the PSE and DECs. The outputs of the PSE and DECs

are extrinsic log-likelihood ratios (LLRs) about {xk(j)} defined below as;

Those LLRs are further distinguished by subscripts, i.e., ePSE (xk(j)) and eDEC (xk(j)), depending

on whether they are generated by the PSE or DECs.

For the PSE section, y in the above given equation denotes the received channel output while for

the DECs, y in the same equation is formed by the de-interleaved version of the outputs of the

primary signal estimator (PSE) block. A global turbo type iterative process is then applied to

process the LLRs generated by the PSE and DECs blocks. [5]

3.5. Features of IDMA

3.5.1. Flexible Rate adaptation

The multi-code technique can be used for a rate/power adaptation as proposed in. A large variety

of data rates can be supported. As opposed to conventional adaptive modulation/channel coding

techniques, the modulation scheme is fixed (and even binary) and the same channel code is used

for all layers. Power adaptation/savings are particularly useful for the uplink. [7]

3.5.2. Soft-information

The mentioned receiver inherently delivers reliable soft-output information, which is useful for

rate adaptation and cross-layer optimization. [7]

3.5.3. Resource allocation

Resource allocation is greatly simplified since the same interleaver set is used at all times. [7]

17

3.5.4. Low delay

Due to chip-by-chip interleaving, the block size can optionally be reduced compared to

conventional DSCDMA (which employs symbol-by-symbol interleaving), because the

interleaver length is increased by the spreading factor. [7]

3.5.5. Scalable Bandwidth

For reasons of scalability and ease of implementation we propose to divide the available

bandwidth. Since the frequency bins allocated to 4G systems are not known yet, we suppose to

divide the 40 MHz into multiples of 5 MHz. That could be 220 MHz but also an

inhomogeneous allocation. Following this proposal, the available frequency bins need not to be

contiguous. Even dynamic bandwidth allocation may be considered. [7]

3.5.6. Low Complexity Receiver

In conjunction with IDMA, a possible low-complexity receiver is the simplified version of the

Wang & Poor receiver. The task of this receiver is to cancel any type of interference (multilayer

interference, multiuser interference, multi-antenna interference, inter-symbol interference, etc.)

jointly. The receiver is based on the Gaussian assumption and turbo processing in conjunction

with the low-rate encoder. Its complexity is only linear with respect to the number of layers,

number of chips/layer, number of users, number of receive antennas, number of channel taps,

and the number of iterations. [7]

3.5.7. Quality of Service

The quality of service (QoS) is mainly defined by a maximum bit error rate, a minimum data

rate, and a maximum delay (especially for packet based services). These parameters are highly

dependent on the application, e.g. text message, voice transmission or video transmission.

IDMA-based systems can be made highly adaptive in order to guarantee a certain QoS level.

Hence, we do not seek quasi error-free transmission, but apply the mentioned soft link adaption

strategy to guarantee a certain bit error rate for a layer or group of layers allocated to a user or

application. On the other hand, we keep the transmission power as low as possible for longer

battery life and less emitted radiation. [7]

18

The bit error rate that can be tolerated is application-dependent, e.g. voice transmission

allows higher bit error rates than data transmission. Instead of using adaptive modulation

and/or channel coding, in IDMA the number of layers and the transmission power are

modified to meet this requirement. The number of layers used for transmission can be

reduced if the data rate is higher than needed or, if the data rate cannot be reduced for

QoS reasons, the transmit power can be increased until the target BER is achieved. [7]

The data rate is an essential QoS parameter, for example text messaging services need

much lower data rates than video transmission. The data rate is adapted in a similar way

as the target BER is. With a higher number of layers assigned to a user, its data rate is

higher. To ensure a certain BER the power can be adapted as well. [7]

In some applications, e.g. real-time speech transmission, a large delay is very

inconvenient, in other applications even critical, e.g. packet loss in TCP based networks.

To achieve small delays, the block length for IDMA transmission can be chosen to be

quite small. This is possible because the chip-by-chip interleaving is done. [7]

19

3.6. IDMA Uplink vs. Downlink

IDMA Uplink features numerous benefits such as security, low receiver cost, cross cell

interference mitigation, decentralized control, diversity against fading, high spectral efficiency,

high power efficiency, suitability for wide and narrowband transmission, and higher gain. The

general methods such as TDMA FDMA and CDMA cant provide all these features whereas

IDMA can fulfill all these necessities and it is somehow suitable for the newly developed

wireless systems in favor of uplink. [9]

On the other hand, while a downlink IDMA system is, in many respects, similar to the uplink

system, such as at the transmitter, the signals for different users are interleaved by user-specific

interleavers and transmitted over a common broadcast channel. However, unlike the uplink

where a common MUD is shared by all users, an individual MUD is required for each user in the

downlink. Therefore, the MUD cost can be a serious concern here. [9]

Nevertheless, significant multiuser gain is also achievable in the downlink. This can be proved

using the duality principle and has been confirmed by simulation. The gain is quite significant, it

may justify the use of MUD in the downlink even at the cost of increased complexity, at least for

a small K (for which the cost increase is moderate). [9]

Figure 3.3. Downlink structure of an IDMA/CDMA scheme [27]

20

3.7. Drawbacks of TDMA FDMA & CDMA:

3.7.1. FDMA

FDMA, or frequency division multiple access, allows users to access a single channel, through a

shared frequency; this system is advantageous as it is run through a satellite and offers users the

chance to share a channel easily without time delays. FDMA are strictly sub optimal in fading

environments and they can be seriously inferior in MIMO channel. The disadvantage of FDMA

is the expense of running the system, which requires costly, custom filters and other technical

equipment. [8]

3.7.2. TDMA

A disadvantage of TDMA systems is that they create interference at a frequency which is

directly connected to the time slot length. This is the buzz which can sometimes be heard if a

TDMA phone is left next to a radio or speakers. Another disadvantage is that the "dead time"

between time slots limits the potential bandwidth of a TDMA channel. These are implemented in

part because of the difficulty in ensuring that different terminals transmit at exactly the times

required.

3.7.3. CDMA

CDMA is also known as code division multiple access, and it allows users to share a frequency

through a special technique known as spread spectrum. The disadvantage of CDMA is that the

codes assigned to each user can only be utilized by those people. As the number of users

increases, the overall quality of service decreases Self-jamming Near- Far- problem arises [8]

3.8. Applications of IDMA

3.8.1. Ultra Wideband (UWB) and Sensor Systems

Ultra-Wideband (UWB) is a technology for transmitting information spread over a large

bandwidth that should, in theory and under the right circumstances, be able to share spectrum

with other users. Federal Communications Commission (FCC) authorizes the unlicensed use of

UWB in 3.110.6 GHz. Ultra Wideband was traditionally accepted as impulse radio, but the

21

FCC and ITU-R now define UWB in terms of a transmission from an antenna for which the

emitted signal bandwidth exceeds the lesser of 500 MHz or 20% bandwidth. [9]

Each pulse in a pulse-based UWB system occupies the entire UWB bandwidth, thus reaping the

benefits of relative immunity to multipath fading (but not to inter-symbol interference), unlike

carrier-based systems that are subject to both deep fades and inter-symbol interference. A

significant difference between traditional radio transmissions and UWB radio transmissions is

that traditional transmissions transmit information by varying the power/frequency/and or phase

in distinct and controlled frequencies while UWB transmissions transmit information by

generating radio energy at specific times with a broad frequency range. [9]

Due to the extremely low emission levels, UWB systems tend to be short-range. However, due to

the short duration of the UWB pulses, extremely high data rates are possible, and data rate can be

readily traded for range by simply scaling the number of pulses per data bit. However, simple

and effective techniques for combating frequency-selective fading and MAI still need to be

developed. [9]

3.8.2. Relay and Ad Hoc Networks

An interesting concept related to IDMA is described in to separate different replicas of a

common signal that arrive at a destination through different relays. Suppose that the signal from

a transmitter is randomly delayed before transmission and its replicas experience different delay

factors through different transmission paths. If the delay difference among these paths is

relatively small, then Rayleigh fading may result. [9]

However, if the delay difference is sufficiently large, these replicas may look as if they are

produced using different interleavers. (Note: The delayed version of a random interleaver is

almost random to itself.) Using this principle, it is shown in that random delay can be

deliberately introduced at the relay nodes to avoid Rayleigh fading and to facilitate IDMA-type

detection at the destination. [9]

This provides an efficient way to exploit the diversity provided by different transmission paths.

If IDMA is used in ad hoc networks, not all receivers will probably afford the full complexity of

MUD. Furthermore, not all signals, which are simultaneously transmitted, are necessary to be

22

detected. Then, in addition to desired signals, only a few strong interferers may be important to

be detected and canceled. In such scenarios, our strategy may be found useful since, as we will

see, the complexity can be signicantly reduced while achieving graceful performance

degradation. [9]

3.8.2. Optical Networks

Interleave Division Multiple Access (IDMA) is a recently proposed multiple access scheme

which relies on an iterative multiuser detection. With the increasing number of users it is

required to get the higher transmission capacity to support the projected growth in traffic levels,

and the exponential use of the Internet together with an increase in the number and range of new

services. [9]

All optical fiber networking is considered to be the central solution for higher capacity. The huge

inherent bandwidth of single mode optical fiber has already been one of the major transmission

media for long distance Telecommunication with very low losses. To fully utilize the single

mode optical fiber bandwidth, optical multiplexing techniques have been deployed. There are

three multiplexing alternatives: wavelength division multiple access (WDMA), optical time

division multiple access (OTDMA) and optical code division multiple access (OCDMA). [9]

The need of faster and more reliable communication systems has been felt these last years and

the sharing of the huge optical bandwidth between users need appropriate access techniques. In

order to meet these requirements, Optical IDMA (OIDMA) presents an attractive solution. This

scheme inherits many advantages such as flexibility of asynchronous and decentralized

networking, potentially secure and uncongested high-rate data transmission, total bandwidth

utilization by all network users, both high rate and low rate transmission achieved, reduced

multiple access interference (MAI), better bit error rate (BER). [9]

23

CHAPTER 4

CODES & INTERLEAVERS

4.1. Orthogonal Codes

4.1.1. Walsh Codes

The Walsh matrix was proposed by Joseph L Walsh in 1923. Each row of a Walsh matrix

corresponds to a Walsh function. Walsh codes have the advantage to be orthogonal, in this way

we should get rid of any interference under perfect synchronization. Orthogonal codes are easily

generated by starting with a seed of 0, repeating the 0 horizontally and vertically, and then

complementing the 1 diagonally. This process is to be continued with the newly generated block

until the desired codes with the proper length are generated. Sequences created in this manner are

referred as Walsh code. [26]

The Walsh code is used to differentiate the user in the forward CDMA link. In any given sector,

each forward code channel is assigned a distinct Walsh code. In mathematics, a Walsh matrix is

a specific square matrix, with dimension a power of 2, the entries of which are +1 or -1, and the

property that the dot product of any two distinct rows is zero. [26]

4.1.2. Orthogonal Variable Spreading Factor (OVSF):

With the advancement in the cellular technology and convergence of wireless technologies, now

it is the need to combine two messages having different data rates in an orthogonal manner. Take

an example, the date rate of user 1 is r1 and of user 2 is r2 and we have to spread the user 1

message by spreading factor s1 and that of user 2 by s2, so that we can produce and overall chip

rate of . We can use Walsh-Hadamard sequences if the spreading factors are powers of 2. The

result so obtained is referred to as Orthogonal Variable Spreading factor. For OVSF the

orthogonality requirement can be stated mathematically as:

24

That is, code 1 of duration T1 is orthogonal to all subsequences of code 2, of the same length, and

offset by a multiple of T1, the length of code 1. [20]

4.1.3. Importance of Orthogonality:

Orthogonal codes and orthogonal signals are used frequently today in the communications

industry. They range from a simple sine/cosine quadrature signals to multiple signals whose

inner product is equal to zero. Orthogonal signals can be used for many other applications.

Quadrature signals can be used to transmit and reception of separate information channels on

each orthogonal signal with minute interference between them. [25]

Orthogonality can also be used and can be applicable to polarization in an antenna system. Two

signals can be sent on separate polarizations or two parallel channels can be used with the same

frequency for better data rates. Orthogonal principles are also used to differentiate desired signals

from jammers using a Gram Schmidt Orthogonalizer (GSO). Another application for orthogonal

signals is to prevent adjacent channel interference. [25]

4.2. Channel Codes:

Channel coding deals with error control techniques. If the data at the output of a communications

system has errors that are too frequent for the desired use, the errors can often be reduced by the

use of a number of techniques. Coding permits an increased pace of information transfer at a fixed

error rate, or a reduced error rate for a fixed transfer rate. The two primary methods of error control

are: Automatic Repeat Request (ARQ) when a receiver circuit detects errors in a block of data, it

requests that the data is retransmitted. Forward Error Correction (FEC) the transmitted data is

encoded so that the data can correct as well as detect errors caused by channel noise. [10]

4.2.1. Convolutional Coding:

Convolutional Codes the coded sequence of n bits depends not only on the present k information

bits, but also on the previous information bits. The primary objective of coding is that the

decoder can determine if the received word is a valid code word, or if it is a code word which has

been corrupted by noise (i.e. detect one or more errors). Ideally the decoder should be able to

25

decide which code word was sent even if the transmitted code word was corrupted by noise (i.e.

error correction). [11]

If a convolutional code that produces r parity bits per window and slides the window forward by

one bit at a time, its rate (when calculated over long messages) is 1/r. The greater the value of r,

the higher the resilience of bit errors, but the trade-off is that a proportionally higher amount of

communication bandwidth is devoted to coding overhead. In practice, we would like to pick r

and the constraint length to be as low as possible. [11]

Figure 4.1. Rate 1/3 non-recursive, non-systematic convolutional encoder

with constraint length 3. (Public domain image.)

4.3. Introduction to Interleaving

Interleaving has been frequently employed in digital communication and storage systems to

improve the performance of forward error correcting codes. Many communication channels

which are not memory less in nature, errors typically occur in bursts rather than independently. If

the number of errors within a code word exceeds the error-correcting code's capability, it fails to

26

regain the original code word. Interleaving ameliorates this problem by shuffling source symbols

across several code words, thereby producing a more uniform distribution of errors. [5]

The user-specific interleavers play vital role in the efficiency of IDMA system. It not only

provides de-correlation between adjacent bit sequences as provided in the case of orthodox turbo

coding and decoding, but also facilitates a means for de-correlating various users. The

correlation between interleavers should measure how strongly signals from other users affects

the decoding process of a specific user. The better the interleaver de-correlation, the lesser the

iterations, required for detection in multiuser detection (MUD) mechanism. The de-correlation

between the user- specific interleavers provides a mean to reduce the multiple access interference

(MAI) from other users thus helping in the intersection of the detection process. [5] [15]

A set of interleaved is considered to be practical if it is easy to generate, and no two interleaved

in the set collide. The sender and receiver need not store or communicate many bits in order to

agree upon an interleaving sequence. It may be shown that a properly defined correlation

between interleavers can be used to develop a collision criterion, where zero cross-correlation

(i.e., Orthogonality) implies no collision. [5]

In case of IDMA systems, the transmitter is required to transmit the interleave matrix consisting

of the interleaving pattern along with spread data related to users, to the receiver. So, greater the

size of the interleaver, the more bandwidth and resources are consumed during transmission.

Also, it is worth to be mentioned that greater the size of interleaver, more the orthogonality is

achieved amongst interleave. [5]

For better understanding of interleaving mechanism, in the next section, interleaving process will

be discussed. [5]

4.3.1. Types of Interleavers:

1. Block interleavers

2. Random Interleavers

3. S- Interleavers

4. Pseudorandom Interleavers

5. Takeshita-Costello interleavers

27

6. Block random interleavers

7. Optimal interleavers

4.3.1.1. Block Interleavers:

In communication system block interleavers are the most commonly used interleavers. It write in

column wise from top to bottom and left to right and reads out row wise from left to right and top

to bottom. [3]

4.3.1.2. Random Interleavers:

The Random Interleaver rearranges the elements of its input vector using a random permutation.

The incoming data is rearranged using a series of generated permuter indices. A permuter is

essentially a device that generates pseudo-random permutation of given memory addresses. The

data is arranged according to the pseudo-random order of memory addresses. [12]

Figure 4.2. Random interleaving [12]

The de-interleaver must know the permuter-indices exactly in the same order as that of the

interleaver. The de-interleaver arranges the interleaved data back to the original state by knowing

the permuter-indices. The length input sequence assumed to be L. [12]

28

4.3.1.3. S - Interleavers:

The S interleaver is a random type interleaver. However the design of this interleaver is difficult

because of the complex computations. And unlike the pure random interleaver, by construction a

minimum interleaving distance equal with S is forced. [3]

4.3.1.4. Optimal Interleaver:

The interleaver that produces the fewest output coded sequences with low weights is known as

optimal interleavers. The design of optimal interleaver is tedious and exhaustive. [3]

4.3.1.5. Takeshita-Costello Interleavers:

The Takeshita-Costello interleaver takes the block length to be a power of 2.

4.3.1.6. Pseudo-Random Interleavers:

The pseudo random interleaver has a controlled spreading of bits. This is the high performance

interleaver which combines the advantages of random and block interleavers, i-e it presents a good

spreading at large minimum distances. [3]

4.3.1.7. Block Random Interleavers:

This interleaver is an alternative to S-Interleaver and aims to continue the qualities of the block

interleavers and random interleavers. [3]

29

CHAPTER 5

ORTHOGONAL INTERLEAVERS

5.1. Problem Statement

In the IDMA scheme, we use a spreading code to encode the data, followed by chip-level

interleavers to differentiate between different users. This data can be decoded relatively easily at

the receiver end with the help of an iterative chip-by-chip decoder. Interleaving allows the data

to be sent over a multiple access channel such that different users can gain access to their

intended receiver, as well as providing forward error correction which allows the channel

capacity to be increased. However, these random interleavers may have high correlation, thus it

is necessary to design an interleaving scheme that prevents this from occurring. [9] [13] [14]

5.2. Proposed Solution

We propose a solution to this problem by introducing an alternative scheme for interleaving that

has lower correlation and high spectral efficiency. This alternative scheme is based on the

concept of orthogonality, by having random interleavers maintain orthogonality between each

other as it is the most commonly used interleaving scheme. Random interleavers also provide a

higher level of security. This orthogonality is achieved by having the interleavers be based on

Walsh Codes matrices, which are also the most commonly used orthogonal codes.

5.3. Algorithm

We term this alternative interleaving scheme Orthogonal Interleaving. We interleave the data

(from the Encoder), such that it resembles the orthogonal Walsh codes and get a random

permutations code for the bit positions. This code allows us to de-interleave the data at the

receiving end. This allows for little to zero correlation between the interleaver codes.

We can change the size of the interleavers by changing the size of the Walsh matrix. For

instance, if we take a 128 by 128 Walsh matrix, we can accommodate 127 users by allocating a

Walsh sequence to each user. (Note: we ignore the first row of the Walsh Matrix as it is an all-

zero sequence.)

30

We describe the algorithm as follows:

Generate a Walsh Matrix for the interleaving sequences. (In this case, we take a 128 x

128 matrix).

We estimate the number of 1s and number of 0s in the input data sequence we get from

the Encoder.

Each bit in the data sequence is compared with a given Walsh sequence from left-to-

right, such that the first position in the Walsh sequence that equals the input data is

allocated to that position.

The allocated positions are saved in a separate matrix called Scramble Rule.

If the number of 1s in the input sequence exceed that of the Walsh matrix, we allocate the

remaining ones to the extra 0s after all the 0 data bits have been allocated.

If the number of 0s in the input sequence exceed that of the Walsh matrix, we allocate the

remaining zeros to the extra 1s, after all the 1 data bits have been allocated.

This process is repeated for every user.

At the receiving end, the reverse process is applied to estimate the input data sequence

with the help of a chip-by-chip (CBC) iterative detector or elementary signal estimator

(ESE).

This is followed by the Decoder (DEC) which despreads the data, and sends an

estimation back to the ESE to estimate the original data signal.

Figure 5.1. Orthogonal Interleaving

31

5.4. Advantages

1. The algorithm for establishing such an interleaving scheme is relatively simple to design.

2. Such an algorithm does not require large memory spaces to store the data.

3. This sort of algorithm is fast and simple as it is cost-effective.

5.5. Drawbacks

The one major drawback of this technique is that the number of users supported by the Walsh

matrix is limited. However, as in CDMA schemes, we can reuse the allocated codes in different

cells to increase spectral efficiency.

32

CHAPTER 6

Simulation Results

6.1. Simulation

These simulation have been executed on MATLAB R2009a ver. 7.8.0.347 software. We have

simulated two systems, one using random interleavers and one using our proposed orthogonal

interleavers and calculated both their correlation and BER. The results are shown below:

6.2. Results

6.2.1. Random Interleavers

The autocorrelation of the first random interleaver in a randomly interleaved IDMA system can

be seen below:

Figure 6.1. Autocorrelation of the first random interleaver

33

The next result is shown in Figure 6.2. of the first five random interleavers being cross-correlated

with the first random interleaver.

Figure 6.2. Correlation of 1st random interleaver with the first five interleavers

If we focus on the colored lines, we can see that there is some extent of correlation that exists in

the random interleavers. The graph on the next page shows the BER of the randomly interleaved

system:

34

Figure 6.3. BER of the system implementing random interleavers

35

6.2.2. Orthogonal Interleavers

Here we introduce orthogonal interleavers into the system in order to lower the correlation

between the users. The simulation results of the auto-correlation of the orthogonal interleavers

are shown below:

Figure 6.4. Autocorrelation of the 1st orthogonal interleaver

36

Figure 6.4. Correlation of the 1st orthogonal interleaver with the first five interleavers

37

Figure 6.6. BER of the system implementing orthogonal interleavers

6.3. Conclusions

IDMA conventionally utilizes fixed random permutations to interleave the data. This creates a

higher correlation among the users. In our thesis, we proposed an interleaver that has reduced

correlation and simulated the results.

The results obtained showed that the correlation is reduced significantly. The values of the

random interleaver correlation are very high. Comparatively, a reduction is observed with the use

of the algorithm for orthogonal interleavers.

6.4. Future Work

Further work is intended to reduce this minimum correlation to zero as is standard for orthogonal

codes and sequences. Further changes can be made in the Walsh matrix size and the number of

interleavers used in the process.

38

References

[1] Michael San Filippo, Marconi: Grandfather of Wireless. [Online]

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February 2014]

[2] Jefe Nubarrn, Evolution Of Mobile Technology: A Brief History of 1G, 2G, 3G and 4G

Mobile Phones [Online] Available from:

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22 Jan 2014]

[3] John M. Cioffi, Code Concatenation and Advanced Codes, Digital Communications.

Department of Electrical Engineering, Stanford University. p.258 275

[4] KusumeK, IDMA vs. CDMA: Analysis and Comparison of Two Multiple Access Schemes [Online] Available from: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6092790&url=http%3A%2F%2Fi

eeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D6092790 [Accessed on: 24 Jan 2014]

[5] Manoj Kumar Shukla. Performance Evaluation of IDMA Scheme in Wireless

Communication. Partial Ph.D. Thesis Department of Electronics & Communication

Engineering Motilal Nehru National Institute of Technology, Allahabad (India),

November 2010.

[6] Kuldeep choudhary, P S Sharma. Interleavers for IDMA Technology: A Comparison

Survey. Department of Electronics &Communications Department of Electronics & communication Tulas Institute, Dehradun-248001, India1 , Dehradun Institute of

Technology, Dehradun 248001, India

[7] Hendrik Schoeneich, Justus Christian Fricke, and Peter Adam Hoeher. Adaptive 4G

Uplink Proposal Based on Interleave-Division Multiple Access Faculty of Engineering,

University of Kiel

39

[8] Lou Frenzel, Fundamentals of Communications Access Technologies: FDMA, TDMA,

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technologies-fdma-tdma-cdma-ofdma-and-sdma [Accessed on 21 Jan 2014]

[9] Li Ping and Peng Wang and Xiaodong Wang Recent Progress in Interleave-Division

Multiple-Access (IDMA) Department of Electronic Engineering City University of Hong

Kong, Hong Kong SAR and Department of Electronic Engineering Columbia University,

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[10] Dr. Aoife Moloney, Channel Coding [Online]. Available from:

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[Accessed 20 Jan 2014]

[11] MIT, lecture notes on Convolutional Coding. [Online] Available from:

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[13] Li Ping, Lihai Liu, K. Y. Wu, and W. K. Leung Interleave-Division Multiple-Access

(IDMA) Communications. Department of Electronic Engineering City University of Hong

Kong, Hong Kong.

[14] Li Ping, Lihai Liu, and W. K. Leung A Simple Approach to Near-Optimal Multiuser

Detection: Interleave-Division Multiple-Access Department of Electronic Engineering

City University of Hong Kong, Hong Kong.

[15] P. Niroopan, Yeon-ho Chung A User-Spread Interleave Division Multiple Access System.

Department of Information and Communications Engineering, Pukyong National

University, Busan, South Korea.

40

[16] Performance Evaluation of IDMA Scheme in Wireless Communication, Thesis Submitted

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Electronics & Communication Engineering by Manoj Kumar Shukla.

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for the 4G Uplink Based on Interleave-division Multiple Access Faculty of Engineering,

University of Kiel Kaiserstr. 2, 24143 Kiel, Germany.

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(4G) Communication: A Comparison Survey. Member IEEE GLA University Mathura,

India and GLA University Mathura, India

[19] Book: Mobile Wireless Communications by Mischa Schwartz. pp.137 140.

[20] Dynamic Assignment of Orthogonal Variable-Spreading-Factor Codes in W-CDMA, Thit

Minn and Kai-Yeung Siu, Member, IEEE

[21] Deepak Sharma, OFDMA Basics, RF Engineer at Lepton Software on Apr 05, 2010.

[22] Subrat Suman, 4G Mobile Communication System, A Seminar Report.

[23] White Paper on Single Carrier FDMA in LTE, IXIA, Nov 2009.

[24] Peter Adam Hoeher and Hendrik Schoeneich, Interleave Division Multiple Access from a

Multiuser Theory Point of View. University of Kiel, Kaiserstr, Germany.

[25] Scott R. Bullock, Application and Uses for Orthogonal Signals. In: Broadband

Communications and Home Networking. Illustrated, Pennsylvania State University,

Noble Publishing Corporation, 2001.

[26] Mangat Parsad Soren, Spread Spectrum Analysis For CDMA Systems. B.Tech Thesis,

National Institute of Technology, 2010.

41

[27] Xingzhong Xiong, Jianhao Hu, Feng Yang, Xiang Ling, (2010) "Analysis and

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Engineering, Vol. 29 Iss: 2, pp.431 444

42

Appendix: Simulation Code

clear all; close all;

%% Initialization

clc; %clear screen N = 8; %length of data User_num = 5; %number of users SF = 16; %spreading factor A = 1; ChipLen = N*SF; %length of chip D_num = 5; % SNR = -20:5:20; Num = length(SNR); h = ones(1,User_num); count = 100; %error accuracy iterations Blocklength = ChipLen; m_length = Blocklength; interleaver_num = 1; spread_seq = ones(1,ChipLen);

b = zeros(User_num,N); l_ESE = zeros(User_num,ChipLen); E_rj = zeros(1,ChipLen); Var_rj = zeros(1,ChipLen); ScrambleRule = zeros(User_num,Blocklength); d = zeros(User_num,N); dd = zeros(User_num,N); a = zeros(SF,N); c = zeros(User_num,Blocklength); x = zeros(User_num,Blocklength); rnd_noise = zeros(User_num,Blocklength); E_Xkj = zeros(User_num,Blocklength); Var_Xkj = zeros(User_num,Blocklength);

%% Generation of spreading sequence for i=1:ChipLen if (mod(i,2))==0 spread_seq(i)=-spread_seq(i); end end

for i=1:SF spread_seq_temp(i)=spread_seq(i); end

%% Simulation for interleaver=1:interleaver_num

for x_num=1:Num var1=SNR(x_num);

43

snr=(10^(var1/10))/SF N0=A*A/(2*snr); sigma=sqrt(N0); var=sigma*sigma;

%Error error_total=0; for j=1:count d=sign(randn(User_num,N)); dd=(d+A)/2;

%% Spreading for o = 1:User_num c(o,:) = spread(dd(o,:),SF); end

cc = xor(1,c) - c;

%% Interleaving for o = 1:User_num [x(o,:),ScrambleRule(o,:)]=intrlv3(c(o,:),(o*2)); end

x = xor(x,1) - x; c = cc;

%% Noise noise=randn(1,ChipLen); rnd_noise=sigma*noise;

%% Multiple Access Channel r=zeros(1,ChipLen); for i=1:User_num r=r+x(i,:); end r=r+rnd_noise;

%% ESE

for i=1:ChipLen TotalMean(i)=0; TotalVar(i)=var; end

for nuser=1:User_num for i=1:ChipLen Mean(nuser,i)=0; Var(nuser,i)=1; TotalVar(i)= TotalVar(i)+1; end end

for it=1:D_num for nuser=1:User_num

44

% LLR values for the de-interleaved chip sequence for i=1:ChipLen TotalMean(i)=TotalMean(i)-Mean(nuser,i); TotalVar(i)=TotalVar(i)-Var(nuser,i); e_ESE_Xkj(nuser,ScrambleRule(nuser,i))=2*(r(i)-

TotalMean(i))/ TotalVar(i);

end

%Decoder (DEC) for l=1:N L_bkj(nuser,l)=0; for k=1+(l-1)*SF:SF*l

L_bkj(nuser,l)=L_bkj(nuser,l)+e_ESE_Xkj(nuser,k)*spread_seq(k); end end

L_bkj_=spread_seq_temp'*L_bkj(nuser,:); a1=L_bkj_(:); L_bkj_back(nuser,:)=a1';

e_dec_ckj=L_bkj_back-e_ESE_Xkj;

for i=1:Blocklength

l_ESE(nuser,i)=e_dec_ckj(nuser,ScrambleRule(nuser,i)); end

for i=1:ChipLen Mean(nuser,i)=tanh(l_ESE(nuser,i)/2); Var(nuser,i)=1-Mean(nuser,i)*Mean(nuser,i); TotalMean(i)=TotalMean(i)+Mean(nuser,i); TotalVar(i)= TotalVar(i)+Var(nuser,i); end end end

L_bkj = L_bkj*(-1); b=(1+sign(L_bkj))/2;

error=xor(b,dd); error=error'; error_num=sum(error); error_num=error_num'; error_num=sum(error_num); error_total=error_total+error_num; end error_percentage(interleaver,x_num)=error_total; end

x = (x + 1)/2;

45

for o = 1:User_num [check(o,:),lags(o,:)] = xcorr(x(1,:),x(o,:)); end

figure(1),plot(lags(1,:),check(1,:),lags(2,:),check(2,:),lags(3,:),check(3,:)

,lags(4,:),check(4,:),lags(5,:),check(5,:)),grid; legend('1st Interleaver', '2nd Interleaver', '3rd Interleaver', '4th

Interleaver', '5th Interleaver');

end

%% BER error_percentage=error_percentage/(N*User_num*count);

figure(2) semilogy(SNR,error_percentage(1,:),'-db') axis([-20 6 0 1]) grid on xlabel('Eb/No /dB'); ylabel('BER'); title('BER OF the SYSTEM using Orthogonal Interleavers');

Additional user-defined functions:

1. intrlv3.m:

function [interleave,key,offset] = intrlv3(hopped_sig,n)

m = length(hopped_sig);

w = walsh(m); interleave = w(n,:); key = zeros(1,length(interleave)); inv_hopped_sig = xor(hopped_sig,1); marker_0 = 0; marker_1 = 0; marker_1_off = 0; marker_0_off = 0; off_m = 0;

offset = sum(hopped_sig)-(length(hopped_sig)/2); n1 = (length(hopped_sig)/2) + offset; n0 = -((length(hopped_sig)/2) - offset);

for k=1:length(interleave) if hopped_sig(1,k) == 0 if offset 0 marker = offmarker(interleave,n0,n1,offset,marker_1,1,off_m); else

46

marker = marker_1_off; end

off_m = marker; h = inv_hopped_sig(1,k);

else marker = marker_0; h = hopped_sig(1,k); end else if offset >= n1 if n0 < 0 marker = offmarker(interleave,n1,n0,offset,marker_0,0,off_m); else marker = marker_0_off; end

off_m = marker; h = inv_hopped_sig(1,k); else marker = marker_1; h = hopped_sig(1,k); end end

for j=marker+1:length(interleave) if h == interleave(1,j); key(1,k) = j;

if h == 0 if hopped_sig(1,k) == 0 marker_0 = j; n0 = n0 + 1;

if n1>=offset && n0==0 marker_0_off = j; off_m = j; % end else marker_0_off = j; off_m = j; % n1 = n1 - 1; end else if hopped_sig(1,k) == 1 marker_1 = j; n1 = n1 - 1;

if n0

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off_m = j; % n0 = n0 + 1; end end break

else continue end end end end

2. offmarker.m

function [m] = offmarker(interleave,n0,n1,offset,marker_1,n,off_m)

count = 0;

if offset == n0 off_m = marker_1; end

for l = off_m+1:length(interleave) if offset == n0 if interleave(1,l) == n count = count + 1;

if count == abs(n1) m = l; break end end else m = off_m; end end end

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3. spread.m

function [spread_sig]=spread(hopped_sig,s)

m = length(hopped_sig); spread_sig = zeros(m,s); spread_seq = zeros(1,s);

for k=1:s if mod(k,2) == 1 spread_seq(k) = 0; else spread_seq(k) = 1; end end

for i = 1:m spread_sig(i,:) = xor(hopped_sig(i),spread_seq); end

spread_sig = reshape(spread_sig',1,m*s); end

4. walsh.m

function [w] = walsh(n)

if mod(n,2)~= 0 disp('Incorrect matrix parameters. Enter an even number.'); return else

w=0;

for k = 1:log2(n); i = xor(w,1); w = [w w; w i]; end end