Pilot Symbol Assisted Weighted Data Fusion Scheme for Uplink Base-Station Cooperation System

KSII Transactions on Internet and Information Systems (TIIS).
2015.
Feb,
9(2):
528-544

- Received : October 09, 2014
- Accepted : January 21, 2015
- Published : February 28, 2015

Download

PDF

e-PUB

PubReader

PPT

Export by style

Article

Metrics

Cited by

TagCloud

Base Station Cooperation (BSC) has been a promising technique for combating the Inter-Cell Interference (ICI) by exchanging information through a high-speed optical fiber back-haul to increase the diversity gain. In this paper, we propose a novel pilot symbol assisted data fusion scheme for distributed Uplink BSC (UBSC) based on Differential Evolution (DE) algorithm. Furthermore, the proposed scheme exploits the pre-defined pilot symbols as the sample of transmitted symbols to constitute a sub-optimal Weight Calculation (WC) model. To circumvent the non-linear programming problem of the proposed sub-optimal model, DE algorithm is employed for searching the proper fusion weights. Compared with the existing equal weights based soft combining scheme, the proposed scheme can adaptively adjust the fusion weights according to the accuracy of cooperative information, which remains the relatively low computational complexity and back-haul traffic. Performance analysis and simulation results show that, the proposed scheme can significantly improve the system performance with the pilot settings of the existing standards.
A
s the ever increasing demands for high frequency efficiency, multi-cell communication systems have emerged by reusing frequency among different cells. However, Inter-Cell Interference (ICI) has become a dominant factor that restricts the improvement of system performance due to the frequency reuse
[1]
[2]
[3]
. ICI may cause significant detriment to the Quality of Service (QoS) of the mobile terminal especially for those located at the cell edge and the overall system capacity
[4]
. Base Station Cooperation (BSC) has arisen as a promising technique in combating ICI
[3]
[5]
. The basic idea of BSC is that the adjacent Base Stations (BSs) exchange their information through a high-speed optical fiber back-haul, then the cooperative information is exploited by a centralized or distributed Central Processing Units (CPUs) for joint optimization in order to increase the diversity gain.
In the uplink, the received signals at BS can be classified into three groups: local information, adjacent information and additive noise. The local information represents information transmitted by the Mobile Stations (MSs) served by the current BS (denoted as anchor BS), and the information transmitted by the MSs located in the adjacent cells is usually viewed as the inter-cell interference to the anchor BS. However, the anchor BS of the BSC system exploits the dormant information from interference induced by adjacent cells. Two intuitive signal processing methods are widely explored for combating inter-cell interference in Uplink Base Station Cooperation (UBSC) system. With distributed CPUs, the Interference Cancellation (IC) method cancels the adjacent interference by utilizing signals forwarded from adjacent BSs, which are the detected signals of MSs from adjacent cells
[6]
[7]
[8]
. This method is highly dependent on the channel estimation accuracy, which limits the promotion of the attainable performance. The other method is known as data fusion, which aims to enhance the reliability of local information from anchor BS’s serving MSs
[5]
[9]
. Specifically, adjacent BSs recover information from their serving MSs and then transmit them to the anchor BS. The anchor BS combines cooperative information and fuses these data to enhance the reliability of desired MS’s information.
Wu etc. adopted the Soft Combining (SC) approach and proposed a three-stage information exchange technique to perform UBSC in
[5]
. In this scheme, each BS performed local decoding and generated Log-Likelihood Ratios (LLRs) for all the information bits. The LLRs generated in different BSs were then forwarded to a centralized CPU and were combined for enhancing signal estimation. A Distributed Probabilistic Data Association and Soft Combining (DPDA-SC) UBSC scheme was developed
[9]
to combat ICI, where all BSs shared their recovered information with each other and exchanged the recovered information in the term of soft information, then the anchor BS combined the cooperative information as a distributed CPU. Benefited from the information sharing and data fusion, the SC scheme reduced ICI with a mediocre computational complexity. But equal fusing weights were assigned to the cooperative information from different BSs, which can not distinguish the reliability of the cooperative information. However, the channel links suffer different qualities due to their specific scattering environment. Hence, it is necessary to explore weighted data fusion algorithms, which can adaptively update the weights in accordance with channel link’s qualities.
Against this background, a novel DE based pilot aided weighted data fusion is proposed for distributed UBSC system. Using the pilot information as reference, a sub-optimal weighted calculation model is proposed. However, the proposed model is an intractable non-linear programming problem, which is challenge to acquire a closed-form solution. We adopts Differential Evolution (DE) algorithm to approach sub-optimal fusing weights in this paper. Compared with the traditional soft combining scheme with equal weights, the proposed scheme can highlight the information undergone high-quality channel links and weaken the contribution of the information undergone poor-quality channel links. Specifically, the contributions in this work were:
- A sub-optimal Weight Calculation (WC) model for UBSC system is proposed. As the optimal WC model is difficult to solve, we employ the pilot information establishing a sub-optimal WC model, which reduces the computational complexity of the optimization for the fusing weights compared with the optimal WC model.
- A DE algorithm based data fusion scheme is proposed. Against the non-linear programming problem of the proposed sub-optimal WC model, the DE algorithm is used to optimize the sub-optimal objective function iteratively. Furthermore, we apply the convergence and computational complexity analysis of the proposed DE aided weighted data fusion scheme. The rest of this paper is organized as follows. The UBSC system model is given in Section 2.
A sub-optimal WC model for UBSC system and a DE based weighted data fusion scheme are proposed in Section 3, the convergence and computational complexity of the proposed scheme are also analysed in this section. Section 4 investigates the performance of the proposed scheme, and Section 5 gives the conclusions.
Three-cell base-station cooperation model in a hexangular cellular system
Assume an uplink cooperation area of
N_{r}
BSs, where each BS is equipped with
K_{r}
receive antennas supporting
N_{t}
single antenna co-channel MSs located in these cooperation cells. Here we refer the
n_{r}
-th BS as the anchor BS. The received signal in the frequency domain
at the
k_{r}
-th antenna of the
n_{r}
-th BS can be expressed as:
where
X
_{nt}
∈
C
^{Ncx1}
denotes the transmitted signal by the
n_{t}
-th MS in the frequency domain
1
, diag(ㆍ) represents the diagonal operation, and
N_{c}
is the number of sub-carriers.
denotes the frequency domain channel transfer function(FD-CHTF) of the link between the
n_{t}
-th MS and the
k_{r}
-th antenna of the
n_{r}
-th BS, and
represents the Additive White Gaussian Noise (AWGN) with zero mean and co-variance
. The
N_{t}
indexes of the co-channel MSs can be decomposed into two sub-sets according to whether the
n_{t}
-th MS belongs to the anchor BS(the
n_{r}
-th BS). The indices of the MS belong to the
n_{r}
-th BS cell are classified into the sub-set
A_{nr}
, which contains
C_{A,nr}
= 1 index. By contrast, the rest are classified into the sub-set
B_{nr}
, which contains
C_{B,nr}
=
N_{t}
- 1 indices. The first term
in (2) represents the received signals at the
k_{r}
-th receive antenna of the
n_{r}
-th BS, which are the signals sent by the MS belonging to the
n_{r}
-th BS itself. The second term
represents the received signals sent by the MSs belonging to other cooperating BSs, which is denoted as
.
In the data fusion based distributed UBSC system,
is treated as exploitable cooperating signals instead of interference, as illustrated in
Fig. 2
. After the signal processing of channel estimation and Multi-User Detection (MUD), the anchor BS may recover the initial estimate
concerning the
n_{c}
-th transmitted bit
X_{nt}
(
n_{c}
), which may be an elementary recovered bit information and/or the Log-Likelihood Ratio (LLR)
2
of the bit,
Receiver model of the data fusion based UBSC system
where
where Pr[
Y
_{nr}
,
X
_{nt}
(
n_{c}
) =
u
] is the joint probability of the initial transmitted bit
X_{nt}
(
n_{c}
) =
u
,
u
= 0,1 and
Y
_{nr}
.
The recovered information
are further classified into
and
, which is a subset that consists of
. The
n_{r}
-th BS keeps its desired signal
for data fusion and sends
to their own anchor BSs for their cooperatively processing. The
n_{r}
-th BS gathers
from cooperative BSs by exchanging information with each other, and then fuses the collected cooperative information with
in the data fusion processor.
With the assumption of
n_{t}
∈
A_{nr}
, the fusion result concerning
X_{nt}
in the anchor BS can be written as:
where
Y
_{coop}
represents the assembled result consists of the received signal
Y_{nr}
of the anchor BS and the received signal
Y
_{n'}
,
n'
≠
n_{r}
from the cooperative BSs,
ω_{nt,nr}
denotes the fusing weight of the fused information
. By mapping the initial 1/ 0 bit into the 1/-1, a generalized decision model for (5) can be formulated as:
Compared to the traditional distributed UBSC schemes, the weighted based data fusion scheme could achieve the same performance without imposing additional information exchange, except that the information was exchanged using the backhaul. The proposed scheme of the model of soft cooperative information retains the same information exchange with the soft combining scheme. While the proposed scheme of the model of hard cooperative information remains the same level of information exchanging with the interference cancellation scheme.
1 For simplicity, we do not introduce modulation operations, X _{nt} refers to 1/0 bits vector here. But without loss of generality, the proposed model is also feasible with modulations.
2 The LLR information is an elementary estimated soft information generated from limited receiving signals, so further multi-BS cooperation is needed even the LLR information used here.
. The final object of weighted data fusion is to lead
to approach to the initial transmitted signal
X
_{nt}
, which means that the optimal objective function of WC can be written as:
where
ω
_{nt}
= [
ω
_{nt,1}
, ⋯,
ω_{nt,nr}
, ⋯ ,
ω_{nt,Nr}
] represents the weight vector. In fact, we don’t know the actual information of
X
_{nt}
, and it is a challenge to acquire the optimal solution of (7).
In typical physical resource blocks, some resource blocks are assigned to pre-defined pilot information to aid channel estimation or some other processing at the receivers
[10]
. Hence, the WC processing at the anchor BS with the proposed pilot-aided distributed UBSC system can be described as:
where F
_{WC}
(·) represents a WC sub-processor within the data fusion processor.
represents the
n_{t}
-th MS’s pre-defined pilot information.
In (7), the receiver doesn’t know the actual
X
_{nt}
. However, the receiver has the information of the pre-defined pilot
, which may be viewed as the sample of
X
_{nt}
. Thus, the optimal objective function (7) can be rewritten as an sub-optimal version, which is a Minimum Mean Square Error (MMSE) problem,
where
represents the fused information at pilot positions. Similarly, a sub-optimal objective function can be written for soft fused information (LLR) as:
where
represents the LLR information at pilot positions after data fusion process,
represents the LLR information at pilot positions with initial pilots. An approximate technique in
[11]
[12]
can be employed for generating the LLR information.
The sub-optimal objective function (9) depends on the pre-defined pilot. Assuming the pilot ratio of initial transmitted symbols is
p_{p}
with 0 <
p_{p}
< 1 . Apparently, if
p_{p}
→ 1, all transmitted symbols will be used as pilot symbols, then we have:
Furthermore, (11) means that the sub-optimal objective function (9) can converge to the optimal objective function (7) with
p_{p}
→ 1, which can be formulated as:
It can be easily seen that (9) and/or (10) is a multi-dimensional global optimization problem with non-linear objective function, it is a challenge to obtain a closed-form solution. In this paper, we propose a DE algorithm based weighted data fusion scheme, which employs DE algorithm to iteratively search the solution space with regard to the Cost Function (CF) of (9) and/or (10).
Flowchart of DE based weight calculation scheme
P_{s}
real-valued weight vectors, where the
p_{s}
-th vector of the population in the first generation of
g
= 1 can be expressed as:
where
N_{ω}
represents the number of weights, which equals to
N_{t}
here. Evaluate the CF value
J
(
ω
_{1,ps}
) of each vector
ω
_{1,ps}
using Equation (9), then sort the CF value according to the descending order.
λ_{ps}
according to a Cauchy distribution
λ_{ps}
= randc
_{ps}
(
μ_{λ}
, 0.1)
[11]
, which controls the rate at which the population evolves. Select the (100
pP_{s}
)% best vector that has the lowest CF value to generate the “best archive”, which includes the vectors owning more meritorious characteristics, and will be further exploited to generate new vectors. Here
p
represents a greedy factor, which determines the greediness of the mutation strategy. For each
p_{s}
,
p_{s}
= 1, ⋯,
P_{s}
, randomly choose a vector index
r
1 from the “best archive” indexes, and select two vector indexes
r
2 and
r
3 from the current population indexes to further generate the difference vector, while
p_{s}
≠
r
1 ≠
r
2 ≠
r
3 . Create a mutant vector
v
_{g,ps}
for the target vector
ω
_{g,ps}
by combining it with the “best” vector
ω
_{g,best,r1}
, the difference vector
ω
_{g,r2}
and
ω
_{g,r3}
, which can be written as:
C_{r}
∈ [0,1] using a uniform random number generator
C_{rps}
= randn
_{ps}
(
μ_{Cr}
, 0.1), which is a problem-specific value that controls the fraction of parameter values that copied from the mutant vectors. For each
n_{ω}
,
n_{ω}
= 1, ⋯ ,
N_{ω}
, build trial vectors out of parameter values that have been copied from the base vectors or the mutant vectors. Specifically, the
n_{ω}
-th parameter value of the
p_{s}
-th vector in the population at the
g
-th generation is given by:
where
n_{ω}
_{,rand}
is a randomly chosen index from
n_{ω}
= 1,⋯,
N_{ω}
, aiming at ensuring the trial parameter with index
n_{ω}
_{,rand}
does not duplicate
ω
_{g,ps}
, which means that at least one element of
t
_{g,ps}
is inherited of
v
_{g,ps}
.
t
_{g,ps}
and valuate the CF value
J
(
t
_{g,ps}
) of each
t
_{g,ps}
according to Equation (9). If the trial vector
t
_{g,ps}
has an equal or lower CF value than that of the target vector
ω
_{g,ps}
, it replaces the target vector in the next generation; otherwise, the target retains its place in the population for at least one more generation. Specifically, the selection procedure can be described as
μ_{λ}
and
μ_{Cr}
is according to:
where
c
∈ (0,1] is the adaptive update factor, which controls the rate of the parameter adaptation.
S_{λ}
and
S_{Cr}
corresponds to the set of successful scaling factors
λ_{ps}
and crossover probabilities
C_{rps}
in the current generation, respectively. The adaptation of
μ_{Cr}
uses the usual arithmetic mean mean
_{A}
, while the Lehmer mean
[11]
[15]
is adopted to augment the weight of larger successful mutation factors, i.e.
.
G
_{max}
has been exhausted.
b. Δ
g
_{max}
generations have passed without a trial vector being accepted.
Obviously, the set of
G
_{max}
and Δ
g
_{max}
is essential. A large enough
G
_{max}
gives an optimizer enough time to find the optimum, while the Δ
g
_{max}
also should not be set too low.
The DE optimization algorithm used in the proposed scheme is capable of converging to the optimal solution, which can be proved in a probability viewpoint. Due to the non-continuous of (9), there may exists more than one optimal solution for the sub-optimal objective function. With a certain accuracy of potential solutions, assume the optimal solutions set as
Ω
_{opt}
, which contains
R
optimal solutions
ω
_{1}
,
ω
_{2}
, ⋯,
ω
_{R}
. For the
g
-th generation, assume the newly generated individual vector
ω
_{g,ps}
stands out the
ε
-neighborhood of its nearest
ω_{r}
,
r
= 1,2,⋯,
R
with a probability of
p_{g}
. As the DE algorithm always choose the best individual vectors to survive into the next generation, as the generation evolving, i.e., the number of generations
g
increases,
p_{g}
decreases monotonically. Thus, when
g
approaches to infinity,
where
ε
is an arbitrary positive but small value, and Pr(·) represents the probability that the given event happens. (19) can be further written as:
Equation (20) shows that, as the number of generations
g
increasing to infinity, the DE optimization algorithm can converge to one of the optimal solution’s
ε
-neighborhoods. Considering both (12) and (20), it is obvious that the proposed scheme has the ability to converge to the optimal fusing weights.
N_{r}
BSs uplink cooperation, where the block-fading channel is time-invariant over
N_{s}
consecutive OFDM symbols. Assume
K
sub-carriers are used and an
M
-QAM modulation is employed. For a given population size
P_{s}
terminated after
G
generations, the proposed DE based weighted data fusion scheme needs
times additions and
times multiplications.
Due to the additional procedure, the computational complexity of the proposed DE based weighted data fusion scheme was analyzed and compared with other receiving procedures in non-cooperative systems. Compared with the DE algorithm based Multi-User Detection (DE-MUD) technique
[11]
, using the default parameters in
Table 1
, the proposed DE based weighted data fusion scheme needs 0.0059% times additions and 0.0119% times multiplications of DE-MUD technique, respectively. Thus, the proposed DE based weighted data fusion scheme holds an affordable computational complexity.
Default parameters settings in DE algorithm
P_{s}
and the terminating criterion Δ
g
_{max}
.
Fig. 4
shows the average required number of CF-Evaluations(CF-Evals.) under different combination of (
P_{s}
, Δ
g
_{max}
) when
E_{b}
/
N
_{0}
= 6dB and
G
_{max}
= 40. Observed in
Fig. 4
that the average required number of CF-Evals. increases with the population size
P_{s}
increases. Actually, the number of CF-Evals. equals to (
G
+ 1)
P_{s}
, where
G
is the number of generations. But increasing the terminating criterion Δ
g
_{max}
, the average required number of CF-Evals. shows an uneven increase. This can be explained by the relationship between
G
and Δ
g
_{max}
. Apparently,
G
≥ Δ
g
_{max}
and is highly dependent on Δ
g
_{max}
. The larger Δ
g
_{max}
is, the more difficulty it takes the iterations to be terminated, thus, the faster the average required number of CF-Evals. increases. The BER performance under different combination of (
P_{s}
, Δ
g
_{max}
) is carried out in
Fig. 5
, where
E_{b}
/
N
_{0}
is also set as 6 dB . It can be seen that the increase of either
P_{s}
or Δ
g
_{max}
leads to the decrease of BER. This is because small settings of
P_{s}
and Δ
g
_{max}
can make the termination appear earlier than when the convergence is achieved. Especially for
P_{s}
≤ 5 or Δ
g
_{max}
≤ 4, the BER performs very badly.
Fig. 5
shows a convergence of BER is achieved when
P_{s}
≥ 12 and Δ
g
_{max}
≥ 8 , which means the suitable (
P_{s}
, Δ
g
_{max}
) should be set under these regions. Considering the computational complexity of CF-Evals. shown in
Fig. 4
, we set
P_{s}
= 15 and Δ
g
_{max}
= 10 in this paper.
Average required number of CF-Evals. under different combination of (P_{s} , Δg _{max})
BER performance under different combination of (P_{s} , Δg _{max})
Fig. 6
illustrates the impact of pilot ratio
p_{p}
as the second experiment. As pilot ratio
p_{p}
increases, the BER performance shows a steady trend when
E_{b}
/
N
_{0}
equals 6 dB , 10dB and 14dB , respectively. When
p_{p}
= 0.02%, the pre-defined pilot information is enough to generate accurate fusing weights. As the pilot ratio increases, more pilot information can be adopted, but little improvement can be performed. This means that even with a low
p_{p}
of 0.02%, the proposed pilot aided sub-optimal data fusion scheme performs well. However, in existing standards such as IEEE 802.11 a/p std.
[17]
[18]
, 1-2 OFDM symbols in each frame are usually set as pilots to aid channel estimation or other receiver processing, i.e., the pilot ratio is set as 0.02 - 0.04%. Therefore, the proposed scheme in this paper can effectively perform the WC based on the pilot settings according to the existing standards, without increasing extra pilot cost.
BER performance with different pilot ratio P_{p}
In
Fig. 7
, we investigate the performance of the proposed DE based weighted data fusion scheme in UBSC systems. The equal-weighted based soft combining scheme is included as a reference for comparison. Assume the 2-nd BS as the desired MS’s serving BS, as the channel link qualities between the MS and three BSs are different, the accuracy of cooperative information from three BSs is different. The traditional soft combining scheme assigns equal weights to cooperative information from three BSs, which neglects the difference among cooperative information’s accuracies, and can not extract useful information effectively. Observed in
Fig. 7
we can see the soft combining scheme even performs worse than the one of 2-nd BS without cooperation. However, the proposed DE based weighted data fusion scheme, which adopts pilot information as reference, designs fusing weights with consideration of different channel links’ qualities to improve system performance.
Fig. 7
shows that, compared with soft combining scheme, the proposed DE based weighted data fusion scheme can achieve about 2 dB improvement at the level of BER = 10
^{-3}
.
BER performance of the proposed DE based weighted data fusion scheme
Fig. 8
shows the BER plots of the proposed DE based weighted data fusion scheme and the soft combining scheme under different channel qualities. We use the channel gain ratio to represent the cooperative link’s channel quality, which is specified as the ratio of cooperative link’s channel gain over local link’s channel gain. Assume the
n_{r}
-th BS as the anchor BS, the
n'
-th cooperative link’s channel gain ratio can be written as
ρ_{n'}
= ║
H_{n',nr}
║
_{F}
/ ║
H_{nr,nr}
║
_{F}
,
n'
= 1,⋯,
n_{r}
-1,
n_{r}
+1, ⋯,
N_{r}
, where ║·║
_{F}
represents the Frobenius norm. Generally, we have that 0 ≤
ρ_{n'}
≤ 1 . It can be seen from
Fig. 8
that under higher
ρ
_{1}
and
ρ
_{2}
values, the system could achieve lower BER values both with the soft combining scheme or the proposed DE based weighted data fusion scheme. This is because the higher
ρ_{n'}
(
n'
= 1,2) refers to the higher channel quality of the
n'
-th cooperative link, which means more accurate cooperative information can be applied to the data fusion process on the
n'
-th cooperative link. Further, as shown in
Fig. 8
, the proposed DE based weighted data fusion scheme always performs better than the soft combining scheme. Especially for the lower
ρ_{n'}
case, the gain is higher. This is benefited from the fusion weights designing process in the proposed DE based weighted data fusion scheme, which fully considered the impact of different channel link’s quality to design the fusion weights and thus improve the system performance. When
ρ_{n'}
is lower, the channel links’ qualities radically exhibit different. Then the fusion weights should be deliberately designed in order to fully achieve the cooperative gains.
BER performance under different channel qualities
The efficiency of the proposed scheme under imperfect channel estimation is investigated in
Fig. 9
, where the cooperative information is in term of hard information. The traditional Maximum Ratio Combining (MRC) scheme and the Interference Cancellation (IC) scheme
[6]
[7]
[8]
are included as the benchmarks. The Least Square (LS) estimation is referred as the imperfect Channel State Information (CSI) in this experiment. Apparently, the proposed scheme outperforms both the MRC scheme and the IC scheme, and it shows stronger robustness to channel estimation errors. Due to the reuse of CSI in the cooperation procedure, the MRC and IC scheme suffers from the channel estimation errors again. Besides, the IC scheme cooperates with the BSs of the interfering MSs instead of all BSs in the cooperation area, which may further limit the achievable cooperative diversity. However, the proposed scheme exploits the pilot information as the reference for designing the fusing weights without CSI, which shuns from the propagation of channel estimation errors.
BER performance using hard cooperative information under imperfect channel estimation
^{-3}
.
Zhe Zhang received her B.E. Degree in Electrical Information Engineering from The First Aviation Academy of Chinese Air Force, China in 2009. She is currently working toward the Ph.D. Degree with the School of Information Engineering, Zhengzhou University, China. Her research interests are cooperative communications, signal processing and optimization algorithms.
Jing Yang received her Ph.D. Degree from Beijing Institute of Technology, Beijing, China in 2011. Since then, she joined the College of Information Science and Engineering, Henan University of Technology. Now, she is a lecturer. Her research interests include cooperative communication systems and rateless codes.
Jiankang Zhang received the B.Sc. Degree in Mathematics and Applied Mathematics from Beijing University of Posts and Telecommunications in 2006, and the Ph.D. Degree in Communication and Information Systems from Zhengzhou University in 2012. Since then, he has been a lecturer in School of Information Engineering, Zhengzhou University. From September 2009 to December 2011 and from January 2013 to May 2013, Dr. Zhang was a visiting researcher in Electronics and Computer Science, the University of Southampton, UK. His research interests are in the areas of wireless communications and signal processing, including channel estimation, multi-user detection, beamforming/precoding and optimization algorithms.
Xiaomin Mu received her B.E. Degree form the Beijing Institute of Technology, Beijing, China in 1982. She is currently a full professor with the School of Information Engineering, Zhengzhou University. She has published many papers in the field of signal processing and co-authored two books. Her research interests include signal processing in communication systems, wireless communications and cognitive radio.

Uplink base station cooperation
;
inter-cell interference
;
weighted data fusion
;
pilot symbols
;
differential evolution algorithms

1. Introduction

2. Weighted Data Fusion Model for Uplink Base-Station Cooperation System

A distributed base-station cooperation scheme for the scenario of three cells in term of hexangular cellular is illustrated in
Fig. 1
. Three adjacent cells surrounded by the thick solid line form a cooperative transmission area indicated by the shaded hexagon, where the three cooperative cells exchange their information through the optical fiber back-haul between BSs.
PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

3. Differential Evolution Algorithm Based Weighted Data Fusion Scheme

- 3.1 Optimization Criterion of Weights Calculating

Without loss of generality, we use the elementary recovered bit information as the fused information, i.e.
PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

- 3.2 Differential Evolution Algorithm based Weights Optimization

As a relatively new member in the family of Evolutionary Algorithms (EAs), the DE
[13]
algorithm constitutes a random guided population-based optimizer, which employs difference vectors to explore the objective function landscape. Compared to most other EAs, DE holds easier operation steps and lower space complexity while exhibits remarkable performance on a wide variety of problems including the multi-dimensional global optimization
[14]
. Hence, it is suitable to circumvent the optimization problem in Equation (9).
Fig. 3
shows a flow chart of DE, which mainly includes the initialization, mutation, crossover, selection, adaptation steps to constitute an iterative progression. Specifically, the algorithmic steps in DE are formulated in more details as follows:
PPT Slide

Lager Image

- 1) Initialization.

Generate the population of
PPT Slide

Lager Image

- 2) Mutation.

Randomly generate the scaling factor
PPT Slide

Lager Image

- 3) Crossover.

Randomly generate the crossover probability
PPT Slide

Lager Image

- 4) Selection.

Normalize the trial vector
PPT Slide

Lager Image

- 5) Adaptation.

The update of
PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

- 6) Termination.

When any of the following stopping criteria are met, the optimization procedure should be halted:
a. The pre-defined maximum affordable number of generations
PPT Slide

Lager Image

PPT Slide

Lager Image

- 3.3 Computational Complexity

Generally, the computational complexity of population-based stochastic search techniques like DE usually depends on the stopping criterion
[16]
. Neglecting the very simple operations like copy/assignment, etc., we only consider the multiplication and addition operations in our analysis. Observing the algorithmic steps, we can see that the computational complexity is introduced by the initialization, mutation, selection and adaption operations.
Assume an
PPT Slide

Lager Image

PPT Slide

Lager Image

Default parameters settings in DE algorithm

PPT Slide

Lager Image

4. Simulation Results and Discussions

In this section, Monte Carlo simulations have been carried out in order to investigate the attainable performance of the proposed DE assisted weighted data fusion scheme in UBSC systems. Assuming that two MSs equipped with single transmit antenna located in two adjacent cells and they cause ICI to each other. Each BS has eight receive antennas, and three adjacent BSs (including the anchor BSs and two interfering MSs) constitute a cooperating area. A (2,1,3) convolution code and 16 -QAM is employed. The number of sub-carriers in one OFDM symbol is 64 , and each frame includes 50 OFDM symbols. A 5 -paths Rayleigh fading channel is considered for each channel link. Unless specified, the first two OFDM symbols of each block are used as pilots, i.e., the default pilot ratio is set as 0.04%
[17]
[18]
. At the receiver, the cooperative information defaults to using the LLR information, and an approximate technique in
[11]
[12]
is adopted to generate the cooperative soft LLR information. Unless otherwise specified, the default parameter values in DE algorithm are listed in
Table 1
.
The first experiment investigates the effect of settings about population size
PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

PPT Slide

Lager Image

5. Conclusion

In this paper, a DE based pilot aided weighted data fusion scheme is proposed for UBSC system in order to combat ICI. A sub-optimal WC model is proposed for pilot aided data fusion in UBSC system, which employs pilot information as the sample of transmitted data. In order to solve the non-linear programming problem brought by sub-optimal model, the DE based weighted data fusion scheme is proposed by iteratively optimizing fusing weights. Convergence, computational complexity analysis and simulation results show that the proposed scheme can perform weights optimization effectively based on pilot settings in existing standards and remain back-haul traffic and a low computational complexity. Compared with the traditional equal-weighted soft combining scheme, the proposed scheme is capable of achieving about 2 dB improvement at the level of BER = 10
BIO

Marsch P.
,
Fettweis G.
2011
“Uplink CoMP under a constrained backhaul and imperfect channel knowledge,”
IEEE Transactions on Wireless Communications
10
(6)
1730 -
1742
** DOI : 10.1109/TWC.2011.041311.100259**

Blum R. S.
2003
“MIMO capacity with interference,”
IEEE Journal on Selected Areas in Communications
21
(5)
793 -
801
** DOI : 10.1109/JSAC.2003.810345**

Gesbert D.
,
Hanly S.
,
Huang H.
,
Shamai Shitz S.
,
Simeone O.
,
Yu W.
2010
“Multi-cell MIMO cooperative networks: A new look at interference,”
IEEE Journal on Selected Areas in Communications
28
(9)
1380 -
1408
** DOI : 10.1109/JSAC.2010.101202**

Ge X.
,
Huang K.
,
Wang C. -X.
,
Hong X.
,
Yang X.
2011
“Capacity analysis of a multi-cell multi-antenna cooperative cellular network with co-channel interference,”
IEEE Transactions on Wireless Communications
10
(10)
3298 -
3309
** DOI : 10.1109/TWC.2011.11.101551**

Wu K.
,
Guo X.
“Uplink multi-BS MIMO with limited backhaul bandwidth,”
in Proc. of 2011 IEEE Wireless Communications and Networking conference (WCNC)
March 28-31, 2011
1443 -
1448

Li Y.
,
Wang X.
,
Zhou S.
,
Alshomrani S.
2014
“Uplink coordinated multipoint reception with limited backhaul via cooperative group decoding,”
IEEE Transactions on Wireless Communications
13
(6)
3017 -
3030
** DOI : 10.1109/TWC.2014.042914.131505**

Balachandran K.
,
Kang J. H.
,
Karakayali K.
,
Rege K. M.
2011
“NICE: A network interference cancellation engine for opportunistic uplink cooperation in wireless networks,”
IEEE Transactions on Wireless Communications
10
(2)
540 -
549
** DOI : 10.1109/TWC.2010.120610.100169**

Li P.
,
Lamare R. C.
2014
“Distributed iterative detection with reduced message passing for network MIMO cellular systems,”
IEEE Transactions on Vehicular Technology
63
(6)
2947 -
2954
** DOI : 10.1109/TVT.2013.2295532**

Yang S.
,
Lv T.
,
Maunder R. G.
,
Hanzo L.
2011
“Distributed probabilistic-data-association-based soft reception employing base station cooperation in MIMO-aided multiuser multicell systems,”
IEEE Transactions on Vehicular Technology
60
(7)
3532 -
3538
** DOI : 10.1109/TVT.2011.2159822**

Tomasoni A.
,
Bellini S.
,
Ferrari M.
,
Gatti D.
,
Siti M.
“Efficient OFDM channel estimation via an information criterion,”
in Proc. of 2012 IEEE International Conference on Communications (ICC)
June 10-15, 2012
3936 -
3941

Zhang J.
,
Chen S.
,
Mu X.
,
Hanzo L.
2012
“Turbo multi-user detection for OFDM/SDMA systems relying on differential evolution aided iterative channel estimation,”
IEEE Transactions on Communications
60
(6)
1621 -
1633
** DOI : 10.1109/TCOMM.2012.032312.110400**

Zhang J.
,
Chen S.
,
Mu X.
,
Hanzo L.
2011
“Joint channel estimation and multiuser detection for SDMA/OFDM based on dual repeated weighted boosting search,”
IEEE Transactions on Vehicular Technology
60
(7)
3265 -
3275
** DOI : 10.1109/TVT.2011.2161356**

Price K. V.
,
Storn R. M.
,
Lampinen J. A.
2005
Differential evolution: A practical approach to global optimization
Springer

Das S.
,
Suganthan P. N.
2011
“Differential evolution: a survey of the state-of-the-art,”
IEEE Transactions on Evolutionary Computation
15
(1)
4 -
31
** DOI : 10.1109/TEVC.2010.2059031**

Qin A. K.
,
Huang V. L.
,
Suganthan P. N.
2009
“Differential evolution algorithm with strategy adaptation for global numerical optimization,”
IEEE Transactions on Evolutionary Computation
13
(2)
398 -
417
** DOI : 10.1109/TEVC.2008.927706**

Das S.
,
Abraham A.
,
Chakraborty U. K.
,
Konar A.
2009
“Differential evolution using a neighborhood-based mutation operator,”
IEEE Transactions on Evolutionary Computation
13
(3)
526 -
553
** DOI : 10.1109/TEVC.2008.2009457**

1999
Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications: High-speed physical layer in the 5 GHz band, IEEE Std. 802.11a-1999

2009
Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications. Amendment 7: Wireless access in vehicular environments, IEEE Std. P802.11p/D9.0
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=5325058

Citing 'Pilot Symbol Assisted Weighted Data Fusion Scheme for Uplink Base-Station Cooperation System
'

@article{ E1KOBZ_2015_v9n2_528}
,title={Pilot Symbol Assisted Weighted Data Fusion Scheme for Uplink Base-Station Cooperation System}
,volume={2}
, url={http://dx.doi.org/10.3837/tiis.2015.02.003}, DOI={10.3837/tiis.2015.02.003}
, number= {2}
, journal={KSII Transactions on Internet and Information Systems (TIIS)}
, publisher={Korean Society for Internet Information}
, author={Zhang, Zhe
and
Yang, Jing
and
Zhang, Jiankang
and
Mu, Xiaomin}
, year={2015}
, month={Feb}