IDMA: An Overview
Mohanad Abdulhamid
University College of Wisdom
[email protected]
Abstract: This paper studies the system design of interleave division multiple access(IDMA)
with different types of interleavers. The performances of IDMA system are tested using
binary phase shift keying(BPSK) modulation, and additive white gausian noise(AWGN)
channel. Simulation results show that the performances of the IDMA for all interleavers are
approximately the same.
Keywords: IDMA design, Performance analysis, Interleavers.
1- Introduction
As the demand for high data rate services grows in wireless networks, various
challenging problems arise when the existing multiple access technologies are used.
The major problems for orthogonal multiple access (MA) technologies such as
TDMA, FDMA and OFDMA, include their sensitivity to inter-cell interference and
frame synchronization requirement for maintaining orthogonality.
Recently, a new variant of Code Division Multiple Access(CDMA) scheme
known as Interleave Division Multiple Access (IDMA) scheme has evolved on the
horizon of wireless communication [1-9]. The IDMA scheme employs the
interleavers as the only means of user separation in order to ensure privacy related to
data of users. The main idea of IDMA is to separate every layer by interleaving the
spreaded coded information sequence with a unique interleaver. So, it is possible to
transmit the different layers at the same time in the same frequency and separate them
on the receiver side.
IDMA is a new technology that can remove the disadvantages of existing CDMA
technique i.e. multiple access interference (MAI) and intersymbol interference (ISI)
by employing chip-level interleavers for user separation and the receiver employs a
simple chip-level iterative multiuser detector (MUD). In CDMA, interleavers are used
for coding gain. The basic principle of IDMA is that any two users are separated by
an interleaver (and the interleavers should be different for different users).
In IDMA scheme, most of the CDMA problems do not exist due to application of
user-specific interleavers as alternate way of user separation in place of unitary
spreading PN-sequences used in CDMA scheme. With IDMA scheme, user separation
is achieved with the help of user-specific interleavers, having low cross-correlation
amongst them. As the spreaded user data is fed to the user-specific interleavers, it
results in better orthogonality between resultant interleaved data in the channel. The
condition of orthogonality is maintained for removing the risk of collision between
the interleavers in the channel.
Fig.1 shows the block diagram of IDMA system with 𝐾 simultaneous users. It
consists of IDMA transmitter, multiple access multipath channel, and IDMA receiver.
The transmitter and receiver are explained in details in the next sections
Fig.1 IDMA System
2- IDMA Transmitter
2.1- Encoder
This block encodes the input data sequence using forward-error-correcting(FEC)
encoder, which enable a limited number of error detection and correction at the
receiver without retransmitting the data stream. The FEC code can be a block or a
convolutional code. The encoder can be removed from the IDMA transmitter resulting
in uncoded IDMA system. However, if the encoder is there then we have a coded
IDMA system.
2.2- Spreader
The spreader receives a bit and spreads it to 𝑠 − 𝑏𝑖𝑡𝑠, where s is the spreader
length. This spreading process is used for bandwidth expansion and the selection of
spreading sequences does not affect the performance of an IDMA system. A real gain
of spreading concerning the range of data transmission can be achieved in a frequency
selective fading environment. The increased bandwidth of a spread signal provides us
with increased frequency diversity. Such frequency diversity can only be exploited if
the signaling bandwidth significantly exceeds the correlation frequency (i.e. the
coherency bandwidth) of the channel. Therefore the spreader in an IDMA system can
be set the same for all users or simply it can be replaced by a repetition encoder. The
output of the spreader for user 𝑘 is 𝐶𝑘 .
𝐶𝑘 = [𝑐𝑘 (1), 𝑐𝑘 (2), … … … . . , 𝑐𝑘 (𝑗), … … . . , 𝑐𝑘 (𝐽)]𝑇
(1)
where 𝐽 is the frame length. The spreading sequences generated for IDMA should
contain balanced number of { 1 , −1 , 1 , −1 , … }.
2.3- Interleaver
The interleavers {πk}, which are opted for user separation, should be orthogonal
for all users. The generated interleavers disperse the coded sequences so that the
adjacent chips are approximately uncorrelated, facilitating the simple chip-by-chip
detection in the receiver. The coded and spreaded sequence 𝐶𝑘 is permutated by an
interleaver πk producing the following sequence.
𝑋𝑘 = [𝑥𝑘 (1), 𝑥𝑘 (2), … … … . . , 𝑥𝑘 (𝑗), … … . . , 𝑥𝑘 (𝐽)]𝑇
(2)
where the element in xk is denoted as “chips”.
The main interleavers which are used in IDMA include Random Interleaver(RI),
Master
Random
Interleaver(MRI)
[or
power
interleaver],
Tree
Based
Interleaver(TBI), and Prime Interleaver(PI). In RI , a lot of memory space is required
at the transmitter and receiver ends. Also, considerable amount of bandwidth is
consumed for transmission of all these interleavers as well as the computational
complexity increases at the receiver end. The MRI alleviates concerns of extra
bandwidth consumption and memory requirement at transmitter and receiver ends.
However, this interleaver raises an additional problem of computational complexity
occurring due to iterative computation of user specific interleavers. The TBI is
basically aimed to minimize the computational complexity and memory requirement
that occur in RI and MRI. The PI is developed to reduce the bandwidth and memory
requirements compared to the pervious interleavers but its complexity is little bit
higher than the complexity of TBI.
Table1 gives comparison among these interleavers considering memory
requirement, bandwidth requirement, and complexity.
Table1 Comparison among interleavers
Parameters
Memory requirement
Bandwidth requirement
RI
MRI(Power)
TBI
PI
High
Low
Low
Lowest
𝟎. 𝟎𝟏 × 𝟏𝟎𝟔
𝟎. 𝟎𝟐 × 𝟏𝟎𝟔
𝟎. 𝟎𝟎𝟎𝟏 × 𝟏𝟎𝟔
Very high
Low
Little high
𝟏. 𝟓 × 𝟏𝟎𝟔
of Interleaver (30 users)
Complexity
High
than TBI
In the following, the interleaving process for each interleaver type are
discussed.
2.3.1- Interleaving Process
This process permutes the input data based on an interleaver pattern which
depends on the interleaver type as discussed below.
2.3.1.1- Random Interleaver
This interleaver permutes the input randomly. All interleaver patterns are stored in
the receiver (base station) to be used in the deinterleaving process later.
2.3.1.2- Master Random Interleaver
According to the user-𝑘, user-specific interleaver 𝜋𝑘 can be generated based on
particular combination of master interleaver such that 𝜋 k ≡ 𝜋 k . Only the master
interleaver will be stored in the receiver (base station), and the number of users is
transmitted to be used for deinterleaving process.
2.3.1.3- Tree based Interleaver
Tree based interleaver needs two master interleavers, master interleaver 𝜋1 and
master interleaver 𝜋2 that are randomly generated. These interleavers are bound to
have orthogonality between each other to ensure the minimal cross correlation
between other generated user specific interleavers that use this interleaving algorithm.
The allocations of the interleaving masks follow the tree format as shown in Fig.2.
User specific interleavers are designed using a combination of randomly selected
master interleavers. The interleaver 𝜋1 is opted for upper branch, while, 𝜋2 is reserved
for initiation for lower branch. Upper branch is selected for the case of odd user count
while lower branch is selected for even user count.
Fig.2 Interleaving strategy for Tree Based Interleaving scheme
2.3.1.4- Prime Interleaver
Prime interleaver determines first a prime number between 1 and 𝐶( where 𝐶 is
interleaver length) , then deletes the prime numbers that are factors of 𝐶. From this
calculation, seed number (number of users) is obtained. The seed must be transmitted
to the receiver to generate the deintereleaver pattern using the same formula in the
interleaving process. Note that all the interleaving mechanisms need memory to store
the interleaver patterns for each user except the prime interleaver.
3- IDMA Receiver
The IDMA receiver adopts an iterative sub-optimal receiver structure. This
receiver consists of an elementary signal estimator (ESE), aposteriori probability
(APP) decoders (DECs), and deinterleaver. The data is iterated for pre-decided
number of iterations before finally taking hard decision on it. Assume single path
propagation, the multiple access and coding constraints are considered separately in
the ESE and DECs. The outputs of the ESE and DECs are extrinsic log-likelihood
ratios (LLRs) about {xk (j)} defined as:
𝑃(𝑦/(𝑥𝑘 (𝑗) )) = +1
𝑒(𝑥𝑘 (𝑗)) = log (
) 𝑗ℎ, ∀𝑘, 𝑗
𝑃(𝑦/(𝑥𝑘 (𝑗) )) = −1
(3)
For the ESE, 𝑦 in Eq.3 denotes the received channel output while for the DECs, 𝑦
in Eq.3 is formed by the deinterleaved version of the outputs of the elementary signal
estimator (ESE) block. A global turbo type iterative process is then applied to process
the LLRs generated by the ESE and DECs blocks.
3.1- Basic Elementary Signal Estimator (ESE)
Assuming memoryless channel. After chip matched filtering, the received signal
from 𝐾 users for single path propagation can be written as:
𝐾
𝑟(𝑗) = ∑ ℎ𝑘 𝑥𝑘 (𝑗) + 𝑛(𝑗) ,
(4)
𝑗 = 1,2, … 𝐽
𝑘=1
where 𝑥k (j) ∈ {+1, -1} is the jth chip transmitted by user-k, the coefficient ℎ𝑘 for
user-k represents the combined effect of power control and channel loss, and {𝑛(𝑗)}
are samples of an AWGN process with zero-mean and variance σ2 = N0/2. Assuming
that the channel coefficients {ℎ𝑘 } are known apriori at the receiver. Due to the use of
random interleaver { πk }, the ESE operation can be carried out in a chip-by-chip
manner, with only one sample 𝑟(𝑗) used at a time.
(5)
𝑟(𝑗) = ℎ𝑘 𝑥𝑘 (𝑗) + 𝜉𝑘 (𝑗)
𝜉𝑘 (𝑗) = 𝑟(𝑗) − ℎ𝑘 𝑥𝑘 (𝑗) = ∑ ℎ𝑘′ 𝑥𝑘′ (𝑗) + 𝑛(𝑗)
(6)
𝑘′≠𝑘
where, 𝜉𝑘 (𝑗) is the distortion (including interference-plus-noise) in 𝑟(𝑗) with respect
to user-k. From the central limit theorem, 𝜉𝑘 (𝑗) can be approximated as a Gaussian
variable, and 𝑟(𝑗) can be characterized by a conditional Gaussian probability density
function:
𝑃(𝑟(𝑗)/(𝑥𝑘 (𝑗) = ±1) =
1
√2𝜋𝑉𝑎𝑟(𝜉𝑘 (𝑗))
exp (−
(𝑟(𝑗) − (±ℎ𝑘 + 𝐸(𝜉𝑘 (𝑗))))2
2𝑉𝑎𝑟(𝜉𝑘 (𝑗))
)
(7)
where 𝐸 (. ) and 𝑉𝑎𝑟 (. ) are the mean and variance functions, respectively. The
following is the ESE detection algorithm based on Eqs.5&7, assuming that the apriori
statistics { 𝐸(𝜉𝑘 (𝑗))} and {𝑉𝑎𝑟 (𝑥𝑘 (𝑗)) } are available.
Algorithm 1: Chip by chip (CBC) detection
Step (i): Estimation of Interference Mean and Variance
𝐸(𝑟(𝑗)) = ∑ ℎ𝑘 𝐸(𝑥𝑘 (𝑗))
(8)
𝑘
𝑉𝑎𝑟(𝑟(𝑗)) = ∑|ℎ𝑘 |2 𝑉𝑎𝑟(𝑥𝑘 (𝑗)) + σ2
(9)
𝑘
𝐸(𝜉𝑘 (𝑗)) = 𝐸(𝑟(𝑗)) − ℎ𝑘 𝐸(𝑥𝑘 (𝑗))
𝑉𝑎𝑟(𝜉𝑘 (𝑗)) = 𝑉𝑎𝑟 (𝑟(𝑗) − |ℎ𝑘 |2 𝑉𝑎𝑟(𝑥𝑘 (𝑗)))
(10)
(11)
Step (ii): LLR Generation
𝑒𝐸𝑆𝐸 (𝑥𝑘 (𝑗)) = 2ℎ𝑘
𝑟(𝑗) − 𝐸(𝜉𝑘 (𝑗))
𝑉𝑎𝑟(𝜉𝑘 (𝑗))
(12)
3.2- Iterative Interleaving / Deinterleaving Operation
This operation is used within the process of iterative decoding leading to increase
the computational complexity of the receiver end. The computational complexity is
increased drastically in case of large user count. The ESE generates metrics that are
deinterleaved before input to the soft-in / soft-out (SISO) decoder. The decoder soft
output is interleaved and then used by the ESE on the next iteration as apriori
information, this improves the output metrics and the process continues. At final, hard
output decision is made by the decoder on the last iteration. The interleaving /
deinterleaving is used between the ESE and the decoder to remove correlations
between the receiver / decode operations.
3.2.1-Deinterleaving Process
After demodulation process, the deinterleaver sequences are generated. The way
of generating the deinterleaver sequences depends on the type of interleaver as
discussed below.
(3.3)
3.2.1.1-Random Interleaver
The random interleaver generates the deinterleaver patterns using the already
stored interleaver patterns. It compares the value of vector 𝒆 with the location of their
appearance in the interleaver patterns. The vector 𝒆 is a row vector defined as
[1,2,3, … , C], where 𝐶 is interleaver length. The deinterleaver sequence permutes the
received sequences to obtain the spreaded sequences which equals to the chip
sequences at the transmitter.
3.2.1.2-Random Master Interleaver
Depending on the number of users we generate the deinterleaver pattern from the
already stored mester interleaver patterns by comparing the value of 𝒆 vector with
master interleaver locations of their appearance in itself. The deinterleaver pattern
permutes the received sequences to obtain the spreaded sequences which equals to the
chip sequences at the transmitter.
3.2.1.3-Tree Based Interleaver
Depending on the two master interleaver patterns that are already stored at
receiver, we generate the corresponding deinterleaver patterns depending on the
number of users. The received signal is permuted by the deinterleaved patterns
3.2.1.4-Prime Interleaver
Depending on the seed number (the number of user), the deinterleaver patterns are
generated by using the same formula for the interleaving process. After deinterleaving
process the spreaded sequences are apply to the decoding process, resulting the
original data.
3.3- Signal Decoder (SDEC)
The SDEC in Fig.1 carries out a posteriori probability(APP) decoding using the
output of the ESE as the input. With binary phase shift keying (BPSK) signaling, its
output is the extrinsic log-likelihood ratios (LLRs) {𝑒𝐷𝐸𝐶 (𝑥𝑘 (𝑗))} of 𝑥𝑘 (𝑗) defined in
Eq.3, which is used to generate the following statistics. In the iterative process, ESE
and SDEC exchange the extrinsic information about 𝑥𝑘 (𝑗).
𝑆
𝑒𝐷𝐸𝐶 (𝑥𝑘 (𝜋(𝑗))) = ∑ 𝑒𝐸𝑆𝐸 (𝑥𝑘 (𝜋(𝑗)))
(13)
𝑗=2
𝐸(𝑥𝑘 (𝑗)) = tanh(𝑒𝐷𝐸𝐶 ((𝑥_𝑘 (𝑗))/2))
(14)
𝑉𝑎𝑟(𝑥𝑘 (𝑗)) = 1 − (𝐸(𝑥𝑘 (𝑗)))2
(15)
The chip by chip (CBC) detection for IDMA scheme can be concluded as follows:
1.
Elementary signal estimator generates 𝑒𝐸𝑆𝐸 (𝑥𝑘 (𝑗)) by Eq.12 for decoder
DEC-k.
2.
DEC-k generates 𝑒𝐷𝐸𝐶 (𝑥𝑘 (𝜋(𝑗))), which are used to update mean and
variance of 𝑥𝑘 (𝑗).
Under the assumption that {𝑥𝑘 (𝑗)} are independent, Eqs.8&11 are a
straightforward consequence of Eq.5&6. The Step (ii), shown in algorithm 1, is
obtained by evaluating Eq.3 based on Eq.7. The operations in Eqs.8 &9, i.e.,
generating 𝐸(𝑟(𝑗)) and 𝑉𝑎𝑟(𝑟(𝑗)), are shared by all users, costing only three
multiplications and two additions per coded bit per user. Overall, the ESE operations
shown in step (i) and step (ii), cost only seven multiplications and five additions per
coded bit per user, which is very modest. Interestingly, the cost per information bit
per user is independent of the number of users K. This is considerably lower than that
of other alternatives.
4- Simulation Results
Computer simulation tests have been carried out on the system shown in Fig.1 with
K=30 and data length of 512bits, using BPSK modulation, and AWGN channel with
single path. The four interleavers are involved in the simulations.
Fig.3 shows the performances [bit error rate(BER) versus signal-to-noiseratio(Eb/No)] of the IDMA system. It seems that the performances of the four
interleavers are approximately the same(even though TBI and PI perform little bit
better) which is true since all interleavers were designed to maintain approximately
the same bit error rate. The only differences among the interleavers are related to
memory requirement, bandwidth requirement, and computational complexity as
shown previously in Table1.
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