10-04-2012, 04:48 PM
A Fast Converging Multi-user Detection for IDMA Based on Time Reversal
A Fast Converging Multi-user Detection for IDMA Based on Time-Reversal.pdf (Size: 238.02 KB / Downloads: 28)
Abstract
In this paper, we propose a fast converging multiuser
detection for interleave-division multiple access (IDMA)
system based on time-reversal (TR) technique. The proposed
algorithm uses the time-reversed version of the channel impulse
responses (TR-CIR) obtained from the uplink to process the
received signal before the elementary signal estimator (ESE).
With the help of the weak correlation of fading channel for
difference user end (UE), the signal to interference and noise
ratio (SINR) at the beginning of turbo-like detection of the
proposed algorithm is much higher than that of the traditional
methods. Thus the SINR evaluation speed is much faster, and less
iteration number can be achieved in the proposed algorithm.
Keywords— IDMA, TDR-IDMA, CDMA, TR, convergence
I. INTRODUCTION
Efficiency and adaptability are the major features for the
future mobile communication systems. Such systems should be
high spectral efficiency, high data rate, low power consumption
and low complexity. IDMA [1][2] system is proposed to meet
such requirements. As a special case of code division multipleaccess
(CDMA) system, IDMA employs chip-level interleavers
for user separation. IDMA inherits many advantages from
CDMA, e.g., diversity against fading and mitigation of the
worst-case other-cell user interference. Furthermore, it allows a
very simple chip-by-chip (CBC) iterative multi-user detection
(MUD) strategy. Thus the complexity of MUD in IDMA
system is a linear function of the user number. It is much
simpler than the MUD algorithms used in CDMA systems.
However, the signal convergence speed is the bottleneck for the
iterative MUD in IDMA system, since the convergence speed
is mainly depended on the SINR evaluation [1]. The SINR is
low and grows slowly at the beginning of the iterative detection
in traditional IDMA. So the iteration number for chip by chip
detection is large, especially for the heavy loaded IDMA
system [1].
The convergence of iterative MUD has been widely studied
for CDMA systems and many results has been made in the
recent ten years [6]-[14]. The main difference between IDMA
and CDMA is the chip-level interleaving used for the former,
while the bit-level interleaving is adopted for the latter. In
IDMA, the chips of different users are weakly correlated after
random chip-level interleaving. But the chip level is heavily
correlated for CDMA systems, since the bit information is
spectrum spreaded with the same pseudonoise sequence.
Therefore, we cannot directly apply the MUD algorithms of
CDMA to IDMA. It is necessary to develop a new and fast
MUD algorithm for IDMA.
In this paper, we propose a fast converging multi-user
detection algorithm for IDMA system based on TR technique
[3][15][16][17]. This technique is applied in the uplink and
downlink of IDMA system to alleviate the multi-user
interference (MUI), intersymbol interference (ISI) and simplify
UE design. Time-division duplexing (TDD) mode is adopted
to share the common channel information and simplify UE
design. We refer to this scheme as TDR-IDMA. In this paper,
we focus on the signal processing of base station (BS). The
TDR-IDMA system uses the TR-CIR obtained from the uplink
to process the received signal before the ESE. With the help of
the weak correlation of fading channel for difference UE [4],
the SINR at the beginning of turbo-like detection of TDRIDMA
is much higher than that of the traditional methods. The
SINR evaluation speed is accelerated, and less iterative
processing can be achieved in the TDR-IDMA system.
The paper is organized as follows. Section II introduces the
system model used. Section III investigates TDD mode, TR
technique and MUD algorithms for IDMA system based on TR
technique. Section IV shows performance analysis and
simulation result. Section V concludes this work.
II. SYSTEM MODEL
c1 1 π
k c k π
Multiple
Access
Channel
(MAC)
DEC
1 π
))
{ ( ( } 1 e c j ESE
))
{eDEC (c1 ( j }
MESE
{e ES (x1 ( j))}
E
))
{e DE (x1( j }
C
DEC
−1
π k
k π
{e (c ( j))} ESE k
))
{e (c ( j } DEC k
))
{e (x ( j } ES k
E
{e (x ( j))} DEC k
*
h1
*
k h
1
1
π −
1 C
k C
1 X
k X
1 d
k d
1
dˆ
k dˆ
r
1 r
rk
Figure 1.Uplink structures of a TDR-IDMA scheme
User End 1
User End k
Base Station
Conjugate
of TR-CIR
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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ESE-1
{ ( ( ))} 1 e x j ESE
{ ( ( ))} 1 e x j DEC
ESE-K
{e (x ( j))} ESE k
{e (x ( j))} DEC k
( ) 1 r j
rk ( j)
MESE
Figure 2.Structrue of the Modified ESE
•
•
•
•
•
•
•
•
•
As shown in Fig. 1, we consider the uplink structure of the
TDR-IDMA scheme with K simultaneous users in a quasistatic
fading channel environment. The single path channel
environment is used in the discussion for simplification. The
same conclusion can also be achieved for the multi-path
channel environments. The input data sequence dk of user k is
encoded based on a low-rate code C, generating a coded
sequence ck= [ck(1), . . . , ck(j), . . . , ck(J)]T, where J is the frame
length. Then ck is permutated by an interleaver k π , producing
xk = [xk(1), . . . , xk(j), . . . , xk(J)]T. We call the elements in xk as
“chips”.
The key element of the TDR-IDMA system is the signal
processing before the ESE,which is the conjugate of TR-CIR
at the receiver of the BS. hk
* is the conjugate of TR-CIR
coefficient of the user k. The CIR is obtained by channel
estimator at the BS. TR-CIR processing performs match
filtering for the air signal transmitted through the fading
channel. The basic principle of TR-CIR technique will be
demonstrated in section Ⅲ. The ESE is also modified, we call
it as modified elementary signal estimator (MESE). The
estimation of the mean and variance of received signal,
{E( r ( j) k )}and {Var( r ( j) k )}, are used only by user k, as
shown in Fig. 2. It also is the main different for the ESE
between TDR-IDMA and traditional IDMA. With the help of
the channel state information, TDR-IDMA can enhance the
desired signal component and weaken the MUI component at
the receiver of the BS. Thus the SINR evaluation is
significantly accelerated in TDR-IDMA. One of the main
contributions of the TDR-IDMA scheme is to reduce the
iteration number greatly for BS receiver.
III. DATA DETECTION
A. Time-Division Duplexing and Time-Reversal
The TDD mode and the TR technique are applied in TDRIDMA
system at the same time. TDD has many prominent
advantages. First, the uplink and downlink shares the same
frequency, which is convenient to estimate the CIR and use
smart antenna. Second, TDD has high spectral efficiency.
Finally, TDD is convenience for the asymmetric service, so it
has high data rate in uplink or downlink.
TR was originally employed in wideband transmission in
underwater acoustics and ultrasound [15][16], was introduced
to the field of UWB communications [17][18] to alleviate the
problem arising from the large number of multipath
components in UWB channels. In this paper, TR-CIR is also
used to alleviate multipath components. We use TR-CIR to preprocess
the received signal to accelerate convergence. The TRCIR
processing is very simple. We get the CIR from channel
estimator at the base station first. Then we use the CIR to
obtain the conjugate of TR-CIR. Finally, the conjugate of TRCIR
is used to enhance the desired signal component and
weaken the MUI component at the receiver of BS, since the
CIR for deferent channel is weakly correlated. Thus the SINR
at the beginning of turbo-like detection of TDR-IDMA is much
higher than that of the traditional IDMA. It significantly
contributes to the acceleration of convergence speed of signal
detection at the receiver of the BS. hk * (−t ) is the conjugate of
the TR-CIR with CIR hk (t ) , let
y(t ) = hk * (−t) ⊗ hk ′ (t) (1)
⊗ denotes the convolution operation. When k = k′
, y(t) is the autocorrelation of h (t) k . When k ≠ k′ , y (t ) is
the crosscorrelation of h (t) k and h (t) k′ for the mutlipaths of
different users.
Let ( * / * )
k k k k ρ = E h h ′ h h ′ , where { k h ′ } are the
channel coefficients of user k′ , and { *
k h } are the conjugate of
the TR-CIR coefficients for user k. ρ →0, when the distance
between the two UEs is sufficiently far [4]. ρ = 1, when
k = k′ .
B. Data detection
We assume that the channel is memoryless and single path
to simplify the analysis. The same conclusion can be obtained
in the multipath environments. The received signal can be
expressed as
r j h x j h xk j n j j J
k k
( ) = k k ( ) + k ′ ( ) + ( ), =1,2,...,
′≠
Σ ′ (2)
Where { n( j) } are samples of an AWGN process with
variance /2 0
2 N N σ = . After TR-CIR processing, r ( j) k for user
k can be expressed as
( ) ( ) ( ) ( ) k
r j h *h x j h *h x j n j k
k k
k k k k k k = + ′ +
≠ ′
Σ ′ (3)
Where ( ) k n j are samples of an AWGN process with variance
2 * 2 2
Nk k N σ =h δ . Generally, r j r j r j j J K ( ) ( ) ... ( ), 1,2,..., 1 2 ≠ ≠ ≠ = .
Without losing generality, Σ≠
′
′
k k
hk hk xk ' ( j)
* in (3) can be
approximated by Σ≠
′
′
k k
hk hk xk ' ( j)
ρ * when k is big enough
[4].
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For r ( j) k we denote the total interference and noise as
j h h x j n j j J k
k k
k k k ( ) ( ) ( ), 1,2,..., k
= * + = ′
≠ ′
ξ Σρ ′ (4)
We can rewrite (3) as
( ) ( ) ( ) 2 r j h x j j k k k k = +ξ (5)
Assume that { x j k k ( ),∀ } are independent and identically
distributed (i.i.d.) random variables. Based on the central limit
theorem, ( j) k
ξ in (5) can be approximated by a white
Gaussian random variable. The mean and variance of ( j) k
ξ
are
( ( )) ( ( )) ( ( )) 2 E j E r j h E x j k k k k ξ = − (6)
( ( )) ( ( )) ( ( )) 4 Var j Var r j h Var x j k k k k ξ = − (7)
For BPSK modulation, the following are the modifications
for ESE detection algorithm based on (2)-(7). Assuming that
the priori statistics {E(x ( j)) k }and {Var(x ( j)) k } are available
[1] , where
E(x ( j)) tanh(e (x ( j))/ 2) k DEC k = (8)
Var(x ( j)) 1 (E(x ( j)))2 k = − k (9)
Algorithm Chip-by-Chip Detection in a Single-Path
Channel
Step (i): Estimate the Mean and Variance of r ( j) k
( ( )) 2 ( ( )) * ( ( )) Σ≠
′
= + ′ ′
k k
k k k k k k E r j h E x j ρ h h E x j (10)
4 2 * 2 2 2 ( ( )) ( ( )) ( ( )) Nk
k k
k k k k k k j x Var h h j x Var h j r Var σ ρ + + = Σ≠
′
′ ′ (11)
Step (ii): ESEK {k=1,2,…K}Generates LLR
k K
Var j
e x j h r j E j
k
k k
ESE k k , 1,2,...,
( ( ))
( ( )) 2 ( ) ( ( )) 2 = − =
ξ
ξ (12)
The detection algorithm of the TDR-IDMA is similar to
that of traditional IDMA [1]. The detection procedure at BS
receiver is realized with parallel mode. The main difference of
the two schemes is the SINR at the beginning of iterative
detection and the update of { e (x ( j)) ESE k }.
IV. PERFORMANCE ANALYSIS AND SIMULATION RESULTS
A. Performance Analysis
As shown in Fig. 2, with the parallel mode, every ESE
operations are conducted simultaneously. ESEk for user k only
uses r ( j) k and{ e (x ( j)) DEC k ,k=1,2,…K} to generate
{ e (x ( j)) ESE k }. DECk for user k generates extrinsic loglikelihood
ratios (LLRs), e (x ( j)) DEC k , are shared by all
ESEs. In the next iteration, the ESEk will use the extrinsic
information { e (x ( j)) DEC k ,k=1,2,…K} to update the values
of {E( ( j) k
ξ )} and {Var( ( j) k
ξ }. The disadvantage of this
detection procedure is that TR-CIR needs more hardware
consumption. But the additional hardware is modest.
In the r ( j) k , the desired signal x ( j) k is enhanced by TRCIR
processing. While the MUI is alleviated due to ρ →0 .
Thus the SINR at the beginning of turbo-like detection of TDRIDMA
is much higher than that of the traditional IDMA. The
SINR evaluation speed is much faster, and less iteration
number can be achieved in the TDR-IDMA system as
compared with traditional IDMA [1]. To get further insight into
the convergence we use the mean of absolute value of extrinsic
information (MAV-EXI) [5] of ESE to analyze the
convergence behaviors of TDR-IDMA and traditional IDMA.
0 2 4 6 8 10 12 14 16 18 20
0
0.5
1
1.5
2
2.5
3
3.5
4
Iterations
MAV-EXI
TR, 0dB
without TR,0dB
TR, 3dB
without TR,3dB
TR, 6dB
without TR,6dB
TR, 9dB
without TR,9dB
Figure 3. The MAV-EXI comparison of TDR-IDMA and
traditional IDMA, Ninfo=1024,K=24,ρ =0.1
0 1 2 3 4 5 6 7 8 9
10
-
5
10
-
4
10
-
3
10
-
2
10
-
1
100
Eb/B0
BER
Single-user
K=24, =0.1,TR,IT=5
K=24, =0.5,TR,IT=5
K=24,without TR,IT=5
K=24,without TR,IT=15
ρ
ρ
Figure 4. Performance comparison of TDR-IDMA and traditional
IDMA in AWGN channel.Ninfo=1024.
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B. Simulation result
Let Ninfo be the number of information bits in a frame, K be
the number of simultaneous users in the system, and IT be the
number of iterations, ρ be the correlation of fading channel for
difference user. We consider a simple system model similar
with [1]. Each user’s information data are encoded by a rate-
1/16 repeat code. The resulting signal are interleaved by
randomly generated interleavers, and transmitted over an
AWGN single path channel with BPSK modulation.
We use MAV-EXI to evaluate the convergence speed of
IDMA systems. For each channel environment, there is an
optimal MAV-EXI. The better channel situation can get higher
MAV-EXI. When the MAV-EXI attains to the optimum
values, the IDMA system cannot get the further processing
benefit with additional iteration. From Fig. 3, we learn that
TDR-IDMA can achieve the optimal MAV-EXI faster than
traditional IDMA.
The bit error rate (BER) performance of TDR-IDMA
system is shown in Fig. 4. The BER performance of traditional
IDMA system is also studied for comparison. TDR-IDMA can
achieve the better BER performance than traditional IDMA.
The BER performance of the TDR-IDMA for 24 weakly
correlated users, ρ =0.1, is close to the single-user system with
5 iterations. According to Fig. 4, we also learn that the
correlation of different fading channel does not affect the
performance of TDR-IDMA significantly when ρ less than
0.5. Certainly, IDMA is the degradation of TDR-IDMA when
ρ =1.
The observation of Fig. 4 agrees with Fig. 3. As we can see,
the performance of TDR-IDMA is better than that of traditional
IDMA when the number of users is equal.