Analysis and Design of Tree Based Interleaver

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Analysis and Design of Tree Based Interleaver forMultiuser Receivers in IDMA Scheme

M. Shukla V.K. Srivastava S. TiwariDept. of Electronics Engg. Dept. of Electronics & Comm. Engg. Dept. of Electronics & Comm. Engg.H.B.Technological Institute M.N. National Institute of Technology M.N. National Institute of Technology

Kanpur, India Allahabad, India Allahabad, India

Abstract-Here, we propose a novel Tree Based Interleaver (TBI)for generating user specific chip-level interleaving sequences forvarious users in an IDMA system, which reduces computationalcomplexity drastically. This interleaver also solves the memorycost problem and reduces the amount of information exchangebetween mobile stations and base stations required to specify theinterleaver. Simulation results are presented to show that theproposed TBI perform well as compared to Master Random and

Random Interleavers in an IDMA scheme.

I. I NTRODUCTION

Interleave division multiple access (IDMA) is a technique

where interleaving is the only means for user separation.

IDMA not only inherits many advantages in comparison to

conventional CDMA, such as robustness against fading and

mitigation of cross-cell interference, but also allows very

simple chip-by-chip (CBC), iterative multiuser detection

(MUD) strategy while achieving impressive performance. In

[1], an IDMA system that uses randomly and independently

generated interleavers is presented. The IDMA system with

random interleaver [1] performs better than a comparable

CDMA system with random interleaver.In case, the user specific interleavers are generated

independently and randomly, the base station (BS) has to use a

large amount of memory to store these interleavers as they are

required at transmitter and receiver for interleaving and

deinterleaving purpose. It may cause serious concern, when the

numbers of users is large.

In [4], the method for generation of PEG interleaver is

merely using an algorithm to generate the sequence of random

interleavers, orthogonal in nature, instead of random selection

of respective interleavers [1]. Therefore, the problem of

memory requirement is still present for high number of users.

If the user specific interleavers are generated by master

random interleaver method [2], then problem of high memory

requirement is reduced, but the computational complexity

required to generate the interleaving sequence is increased

extensively, especially when the number of users is large. It is

also an important point to mention that in the turbo processor,

at the receiver section, frequent interleaving and deinterleaving

is required during the process of iterative decoding. Therefore,

large amount of calculations are required in receiver section

and hence, the computational complexity is increased

drastically when number of users is high.

Here, we are examining the proposed Tree Based Interleaver

(TBI) to alleviate this concern. With this method, not only the

interleaver assignment scheme is simplified and memory cost

is greatly reduced, but also the computational complexity

required to generate the interleaving matrix is greatly reduced

without sacrificing the performance.In Section 2, an introduction to IDMA system is presented.

In section 3, we have a brief look over master random

interleaver generation method discussed in [2], and explain the

computational complexity and memory requirement factors of

the interleaver generation methods. Section 4 presents Tree

Based Interleaver (TBI) that reduces both the computational

complexity and memory requirement factors for interleavers in

IDMA scheme. Section 5 presents computer simulations of

IDMA systems with the Tree Based Interleaver (TBI). Section

6 concludes the paper.

II.

IDMA SCHEME A. Scheme Model

Here, we consider an IDMA system [1], shown in Figure 1,

with K simultaneous users using a single path channel. At the

transmitter, a N-length input data sequence d k = [d k (1),

………, d k (i) , … d k (N) ]T of user k is encoded into c k = [c k

(1), ………, c k (j) , … c k (J) ]T based on low rate code C ,

where J is the Chip length.

In encoder-spreader block, the code C is constructed by

serially concatenating a forward error correction (FEC) code

and repletion code of length- sl . The FEC code used here is

Memory-2 Rate-1/2 Convolutional coder. We may call the

elements in c k ‘chips’.

Then c k is interleaved by a chip level interleaver ‘Πk ’,

producing a transmitted chip sequence x k = [x k (1), ……,x k (j)

, … x k (J) ]T . After transmitting through the channel, the bits

are seen at the receiver side as r = [r k (1), ……,r k (j) , … r k (J)

]T . The Channel opted is additive white Gaussian noise

(AWGN) channel, for simulation purpose.

In receiver section, after chip matched filtering, the received

signal form the K users can be written as

1k =

( ) ( ) ( ), 1, 2, ....... . K

k k r j h x j n j j J = + =∑ (1)

978-1-4244-3805-1/08/$25.00 ©2008 IEEE ICON 2008



where h k is the channel coefficient for user and

{ } are the samples of an additive white Gaussian noise

(AWGN) process with mean as zero and variance σ 2 = N 0 / 2.

An assumption is made that {h k } are known priori at the

receiver.

thk ( )n j

Figure 1. Transmitter and Receiver structures of IDMA scheme with K

simultaneous users.

The receiver consists of a signal estimator block (SEB) and a

bank of K single user a posteriori probability (APP) decoders

(DECs), operating in an iterative manner. The modulation

technique used for simulation is binary phase shift keying

(BPSK) signaling. The outputs of the SEB and DECs are

extrinsic log-likelihood ratios (LLRs) about {x k } defined as

( / ( ) 1)( ( )) log , , .

( / ( ) 1)k

k

k

p y x je x j k j

p y x j

⎛ ⎞= += ∀⎜

= −⎝ ⎠⎟ (2)

These LLRs are further distinguished by the

subscripts i.e., and , dependingupon whether they are generated by SEB or DECs.

( ( ))SEB k e x j ( ( )) DEC k e x j

Due to the use random interleavers {Π k }, the SEB operation

can be carried out in a chip-by-chip manner, with only one

sample r(j) used at a time. So, rewriting (2) as

( ) ( ) ( )k k k r j h x j jζ = + (3)

where

' '

'

( ) ( ) ( ) ( ) ( )k k k k k k k

j r j h x j h x j n jζ ≠

= − = +∑ (4)

is the distortion in r( j) with respect to user-k.

B. Algorithm for Chip-by-Chip Detection

A brief description of CBC algorithm [1] has been presentedhere. The operations of SEB and APP decoding are carried out

user-by-user.

Algorithm for Chip-by Chip Detection in a single path

Channel:

Step (i):

Set

Then( ( )) ( ( ))k k

k

E r j h E x j⇐ ∑

2 2( ( )) ( ( ))k k

k

Var r j h Var x j σ = +∑

,

2

( ( )) ( ( )) ( ( ))

( ( )) ( ( )) ( ( ))

k l k k

k k

E j E r j h E x j

Var j Var r j h Var x j

ξ

ξ

= −

= −k

( )k jξ is the distortion (including interference-plus-noise)

in received signal with respect to user-k.

Step (ii): Process for LLR Generation:

Step (iii): Process for updating of data:

Now, these steps are repeated depending on no. of iterationsand users.

III. MASTER R ANDOM I NTERLEAVER GENERATION METHOD

In an IDMA scheme, each user has a user specific

interleaver {Π k } having length equal to chiplength ‘J’.

Therefore, a considerable amount of memory will be required

to store the indexes for these interleavers.

To minimize this memory cost problem, a master random

er method is proposed in [2]. In this paper, a master

interleaver Φ is taken, and the subsequent k-interleavers are

generated using Π k = Φk .

interleav

where Φk

(c) is defined as Φ1(c)= Φ(c).

Φ2(c) = Φ ( Φ(c)).

where Φ is an ideal random permutation.

This method not only reduces the amount of information

exchange between Base Station (BS) and Mobile Stations

(MSs), but also greatly reduces the memory cost in comparison

to random interleaver.

In generation of interleaver, if the intermediate variables like

Φ2 , (Φ2 ) 2, are not stored, then for generating the interleaving

sequence for the k th user , (k-1) cycles are needed. Even if the

intermediate values are stored as stated in the paper [2], it is

mentioned that a maximum of 2(n-1) cycles are needed for

generating the required interleaver, if 2 n-1 <k<2 n , where n>1is an integer .

In this paper, we examine a Tree Based Interleaver (TBI) to

alleviate this concern.

IV. TREE BASED I NTERLEAVER

The Tree Based Interleaver is basically aimed to minimize

the computational complexity and memory requirement that( ( ) )e x j = 0

D E C k

2

( ) ( ( )) ( ( ))( ( )) 2 .

( ) ( ( ))

k k SEB k k

j k k

r j E r j h E x je x j h

Var r h Var x j

− +=

−

1

( ( ( ))) ( ( ( )))S

DEC k SEB k

j

e x j e x jπ π =

= ∑1,..., j S =



occurs in power interleaver and random interleavers

respectively.

In a Tree Based Interleaver generation, two randomly

generated interleavers are chosen, let Π 1 and Π 2 is the two

randomly selected interleavers. These interleavers are tested to

have zero cross correlation between each other. The

combinations of these two interleavers in a particular manner

as shown in the figure 2 are used as interleaving masks for the

users.The allocations of the interleaving masks follow the tree

format. The interleaving masking diagram is shown upon

fourteen users only for the shake of simplicity. It is shown

through the figure that, for obtaining the interleaving sequence

of the 14th user, it needs only 2 cycles of clock, as compared to

many more cycles needed in case of master random interleaver

method.

Π 14 = Π 2 ( Π 2 ( Π 2 )).

The memory required by the Tree Based Interleaver

generation method is only slightly more than that required for

master random interleaver generation method [2] due to

requirement of two orthogonal interleavers in place of oneinterleaver [2].

The Tree Based Interleaving scheme reduces the

computational complexity that occurs in the power interleaving

scheme. It is shown by the help of a table below. The results in

the figure 3 are shown if the intermediate variables are not

stored.

The mechanism involved in generation of tree based user

specific interleavers is shown in figure 2. The two randomly

selected interleavers are solely responsible for generation of

other interleavers related to other users.

Figure 2. Interleaving Figure mask allocation for the proposed Tree BasedInterleaving scheme.

The Tree Based Interleaving scheme is extremely

efficient for reduction of computational complexity as

compared to that in Master Random Interleaving scheme [2] as

shown in figure 1.

The algorithm for tree based interleaver is based on selection

of combination of two master interleavers which are having

zero cross correlation between them. The odd number of users

is taken upside while even number of users is taken downside

as shown in figure 2. In this manner, large number of users

may be allocated with user specific interleavers with extremely

less complexity.

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

User Number

C o m

p l e x i t y

o f i n t e r l e a v e r ( N o .

o f I n t e r l e a v i n g s / u s e r )

Comparison Graph shoeing Complexity of 3 Interleavers

With Random Interelaver

With Mast er Random Interleaver

With Tree Based Interleaver

Figure 3: Graph Showing Computational Complexity b/n Random Interleaver,Power Interleaver, and Tree Based Interleaver.

The Memory requirement of Tree Based Interleaver is

extremely low as compared to that of the Random Interleaver,

while is slightly high if compared with master random

interleaver [2], as shown in figure 4.

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

6

User Number

M

e m

o r y

R e q u i r e m

e n t o f I n t e r l e a v e r ( N o . o

f b i t s

r e q u i

r e d / u s e r )

Comparison Graph shoeing Memory Requirement of 3 Interleavers with m=256 sl=16

With Random Interleaver

With Master Random Interleaver

With Tree Based Interleaver

Figure 4: Graph Showing Memory Requirement b/n Random Interleaver,Power Interleaver, and Tree Based Interleaver

V. NUMERICAL RESULTS

For simplicity, assuming IDMA system with BPSK

signaling in single path AWGN channels and hk =1, ∀ k.

Without loss of generality, a uniform CREP {+1, -1, +1, -1, ------

---} is used with spread length sl =16, for all users and 20



iterations. In figure 5, uncoded IDMA cases are considered,

where no forward error correction (CFEC) coding is introduced.

The data length is 256 bits is used, for an uncoded system.

From figure 5, the performances of IDMA scheme is found

to be similar for random and tree based interleavers, while on

the front of computational complexity, the tree based

interleaver is outperforming the master random interleaver

while having very small hike when compared with random

interleaver.

Figure 5. Comparison of Random Interleaver and TBI with 64 users in single path AWGN channel, with uncoded IDMA systems.

Considering the memory requirement, the proposed Tree

Based Interleaver is far better than random interleaver while

having slight increment in memory requirement when

compared with master random interleaver. So, we may

conclude that Tree Bases Interleaver may replace the random

interleaver and master random interleaver efficiently without

compromise in system performance.

VI. CONCLUSION

The proposed ‘Tree Based Interleaver’ is very easy to

generate and is better than the random interleavers in terms of

memory requirement problems. The ‘Tree Based Interleaver’ is

better than master random interleaver in terms of

computational complexity. The proposed interleavers can take

the place of the random and master random interleaver

techniques without performance loss.

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Analysis and Design of Tree Based Interleaver

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