Direct Blind Signal Detection Based on Improved Ant Colony Algorithm

Shujuan Yu College of Electronic Science &Engineering

Nanjing University of Posts & Telecommunications Nanjing, China

yusj@njupt.edu.cn Chuang Yu

School of Information Science and Engineering Shenyang Ligong University

Shenyang , China Yuchuang2002@163.com

Hairong Niu College of Electronic Science &Engineering

Nanjing University of Posts & Telecommunications Nanjing, China

Y071510@njupt.edu.cn

Abstract—Blind signal detection by basic ant colony optimization algorithm which is limited to slow convergence speed and local optimum. An improved ant colony optimization algorithm of the direct blind signal detection is proposed in this paper. The algorithm adjusts the pheromone update methods of ant colony algorithm; adds the corresponding parameter control in the local update rule and the global update rule of pheromone. Simulation results show that the improved algorithm has fast convergence speed and stable performance compared with the literature algorithms.

Keywords- blind detection; blind equalization; ant colony optimization algorithms

I. INTRODUCTION In digital communication systems, inter-symbol

interference (ISI) has always been one of the major factors which affect the communication quality. In order to overcome inter-symbol interference (ISI), equalizer must be added at the receiving end to compensate for channel characteristics and to restore the sending sequence correctly. Blind equalization is a kind of method which only use priori knowledge of the receiving and sending sequence to restore the sending signal rather than use training sequences.

Because of the development of the blind signal processing technology, blind equalization has become one of the most important advances in communications technology. With the deep research in system blind equalization, more and more algorithms continuously enriched in this field [1]~[4]. Ant colony algorithm is a kind of the latest developments in bionic optimization algorithm which simulate foraging behavior of ant group. Because of its high degree of parallel processing ability, strong robustness, it has been successfully used to solve the traveling salesman problem(TSP), assignment problem, system identification, etc[5]~[12]. With the development of blind signal processing technique recently, intelligent optimization algorithm such as ant colony algorithm, etc has been used in signal processing in communications [9].

In this paper, on the base of existing research in traditional and intelligent optimization algorithm of blind detection, an improved ant colony optimization (IACO) blind detection algorithms is proposed: adjust the updated mode of pheromone and adding the parameter control in the

local and the global update regulation. The idea of blind detection algorithm in this paper is as followed: with the role of zeroing of complement projection operator of received data matrix to sending sequence vectors to be measured, the problem of the signal blind detection is transformed into an integer constrained quadratic programming problem. Then, constructing optimal performance function of direct blind detection sending signals, and then the best blind detection signal can be obtained using algorithms proposed in this paper. The simulation results of algorithm performance show that the improved algorithm proposed in this paper in comparison with the literature method has the advantages of low bit error rate, high convergence speed and stable performance to solve blind detection problem very well.

II. PROPOSING OF THE PROBLEM When ignoring the noise, the receiving equation of

single-input and multiple-output discrete-time channel is as follows [3]:

( ) ( )∑=

×× −=M

jqjq jksk

011 )()( hx （1）

( )( ) ( )

( 1) 1

( 1) 1( 1) ( 1)

( )

( ) ( )

L L q

L j L M M LL q M L

k

k+ ×

+ + + ×+ × + +=

x

Γ h s （2）

( 1)[ ( ), ( 1) , ( 1)]N

L L L L q Nk k k N + ×= + + −

=

Xx x x

ΓS

（3）

TTTTNN SΓΓSXX === ~~

（4）

Here, )( jL hΓΓ = is smooth matrix of Toeplitz form

constituted by Mjj ,,1 ,0, =h ;

)1(10 ],,[ +× MqMhhh is impulse response of

communication channel, ( ) qLNN )1( +×X is receiving data

matrix; sending signal matrix is

)1()](,)1(),([ ++×−−−= MLNNNN LMkkk sssS ;

This work was supported in part by the National Natural Science Foundation of China under Grant #60772060

2010 International Conference on Artificial Intelligence and Computational Intelligence

978-0-7695-4225-6/10 $26.00 © 2010 IEEE

DOI 10.1109/AICI.2010.358

573

2010 International Conference on Artificial Intelligence and Computational Intelligence

978-0-7695-4225-6/10 $26.00 © 2010 IEEE

DOI 10.1109/AICI.2010.358

573

S~

NMLMLMLML Nkkk ×+++++ −++= )1()]1(,)1(),([ sss Equation（4）shows，when Γ is full column rank. There must be T

C C=Q U U to meet 0)( =− dkNQs .

Which, { }LMddkN +=− ,,1,0|)(s ,( )( 1)N N L M

C R × − + +∈U is the singular value decomposition

of NX , [ ]0

TN C

⎡ ⎤= ⋅ ⋅⎢ ⎥

⎣ ⎦

DX U, U V . According to this, we

construct performance function and optimization problem.

0 ˆ ˆ( ) ( )T TN NJ k d k d= − − =s Qs Qs s （5）

{ }0minargˆ JNAs∈

=s , { }1±=Α （6）

The goal in this paper is to use ant colony optimization algorithm for solving optimization problem of equation (6), namely to solve the blind detection problem of BPSK signals.

III. BASIC ANT COLONY OPTIMIZATION BLIND DETECTION MODEL

In this paper, ant-cycle model of ant colony algorithm proposed by M Dorigo is used [6] , the cost function of ant k is set as follows:

ss ˆˆ0 QTk JF ==

(7) The update rule of pheromone is as follows:

( ) (1 ) ( )j j jt n tτ ρ τ τ+ = − ⋅ + Δ (8)

1

mk

j jk

τ τ=

Δ = Δ∑ (9)

, 00,

k kkj

F if Felse

τ⎧Δ Δ >

Δ = ⎨⎩

(10)

Where, (0 1)ρ ρ< < represents the evaporation coefficient of pheromone；

{ }, 1, ,10kk k

last

L LF kF F

Δ = − ∈ ，L is the largest cost

function of ant colony in initial tour. It is a fixed value. kF

is the cost function of ant k finishing this tour, klastF is the

cost function of ant k finishing the last tour. Equation (8) is the update formula of pheromone for each node on the traveling path, equation (9) represents the total pheromone added in node j of ant colony.

The update rule of inspired information for each node is as follows:

max 1, 1

1,

k kj

F if note isF

elseη

⎧ >⎪= ⎨⎪⎩

or

min

max

min

1, 1

1,

kj k

F if note isF

F elseF

η

⎧ <⎪⎪= ⎨⎪ ≥⎪⎩

(11)

In equation (11)，if the node j is for 1, thinking that ant k pass through the node, and if the worst (most excellent) ants also pass through the node, heuristic

information min

max

kj

FF

η =（

maxkj k

FF

η =）

，where, minF

is the minimum cost function of ant colony this tour, maxF is the largest cost function of ant colony this tour; if the node j is for -1，thinking that ant k don’t pass through the

node.

IV. THE BLIND DETECTION ALGORITHM BASED ON IMPROVED ANT COLONY OPTIMIZATION

Because different pheromone update methods have great influence on the performance of ant colony optimization algorithm, if all the pheromone on the path to be updated, then the algorithm is not easy to converge. If only updating the pheromones having searched on the optimal path, the role of positive feedback is strengthened, and it is easy to lead to fall into local optimal solution. Therefore, according to the idea of improved algorithm in the reference literature [9]~ [12], the updating method of pheromone of ant colony algorithm is adjusted in this paper and a new blind detection algorithm based on improved ant colony optimization is proposed. It can be proved to be feasible by simulation results. The improved algorithm alter the pheromone update rule of the basic ant colony optimization algorithm ,adding the parameter control of 1, 2, 3λ λ λ ， for the global update rule and the local update rule of pheromone. A. Local Pheromone Updating

The role of local pheromone updating is to make the selected edges has less attractiveness for the ants on the subsequent, thereby enhancing the search capabilities of ants. In this paper, controlling parameter 1λ is added on the base of equation (8). After ant k pass from node i to node j by the transition probability, the pheromone of node was revised to equation (12).

( 1) (1 ) ( ) ( , 1)j j jt t t tτ ξ τ ξ τ+ = − + ⋅ Δ + (12)

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Where ， ( , 1) 1j k

Lt tF

τ λΔ + = ⋅ ，kF is the cost

function of ant k finishing this tour, ξ indicate volatile, (0,1)ξ ∈ ， parameters 1λ and parameter

2λ mentioned in the global pheromone updating later both are random numbers within rage[0,2], respectively control the role of the local and global optimum to pheromones. They make the pheromone of all path distributed more evenly, so the pheromone of optimal path can't much more greater than others'. This can effectively avoid falling into local optimum, reducing the probability of path that has been chosen being chosen again, and the global search capability of algorithm is improved.

B. Global pheromone updating In this paper, on the base of equation (8), control

parameters are 2λ and 3λ . Volatile coefficient ρ is added. For the global optimal solution, pheromone updating is processed by equation (13).Using a modified strategy of global pheromone updating to enhance the pheromone on the path of global optimal solution , and the role of positive feedback of algorithm is strengthen, thereby the convergence speed of the algorithm is accelerated.

( ) 3 ( ) ( , 1)j j jt n t t tτ λ τ ρ τ+ = ⋅ + ⋅ Δ + (13)

Where, 1

( , 1) 2 ( , 1)m

kj j

kt t t tτ λ τ

=

Δ + = ⋅ Δ +∑ ,

( , 1)kj k k

last

L Lt tF F

τΔ + = − ， max3 ( ) /A t B NCλ = − × ，

maxNC is the total number of iteration, A and B are parameters set by experience.

V. SIMULATION In order to prove the effectiveness of the algorithm in

this paper, performance simulation is carried out for classical literature channel and random channel. The literature channel is by reference literature [1], setting delay=[0,1/3], weight coefficient w=[1,-0.7] to generate. Head and tail of the channel fill q of zero; time delay and weight of random channel will be randomly generated. Taking noise into account, the received signal equation is:

( ) ( ) ( ) 10

11 (k) )()(~×

=×× +−=∑ q

M

jqjq jkk nsHx

(k))( nx += k . Therein, supposing input signal is the

BPSK signal， ( ) { }1,1k ∈ −s ， )(kn is a normal white

noise, being independent from )(ks . Yet the SNR is defined

as ( )( )⎟⎟

⎟

⎠

⎞

⎜⎜⎜

⎝

⎛= 2

2

10)(

)( log10

knE

kxESNR

j

j， qj ,,1=∀ ，

over-sampling factors are set to 3q = . All simulation results are obtained by 100 times of Monte Carlo experiments. In order to draw a chart conveniently, the test figure shows the bit error rate (BER) 0 is treated as 10-5.

A. Experiment 1 In the situation of random channel, blind detective

performance can be compared among Improved Ant Colony Algorithm (IACO), Ant Colony Algorithm (ACO) and Genetic Algorithm (GA).

The construction of blind detective algorithm based on IACO and ACO is as follows: 10 ants are used to construct 10 group of BPSK blind detective sequence, the length of blind detective sequence is N＝80. The parameter choice of blind detective algorithm based on IACO is as follows: after 100 times of Monte Carlo simulation experiments, the best parameter determination is as follows:

2 1.5λ = , max 150NC = , 0.95A = , 0.75B = . The construction of blind detective algorithm based on

GA is as follows: the number of population is 30， the length of blind detective sequence is N＝80.

TABLE I. SNR=3DB，THE OPERATION EXPERIMENTAL RESULT OF 100 TIMES OF MONTE CARLO EXPERIMENT

algorithm Ant Colony Algorithm（ACO）

Improved Ant Colony

Algorithm（IACO）

Genetic Algorithm（

GA）

Operation time(s)

260.57

252.69

4981．65

The simulation result of bit error performance is shown

in Figure 1, The analysis and comparison result of operation time is shown on Table 1. Under the situation of using random synthetic channel of the weight and delay change:(1)Figure 1 can be seen under the condition of random channel: three kinds of blind detection algorithms ,including IACO, ACO and GA, are able to successfully achieve blind detection ,and the performance of this improved algorithm (IACO) is the best, with the increase of signal-to-noise ratio ,bit error rate drops most quickly for IACO .(2) Table 2 can be seen that the operation time based on GA is much more than the operation time based on ACO, and yet the operation time based on IACO proposed in this paper is less than the operation time based on ACO.

B. Experiment 2 In the case of classical literature channel, the

performance compare among Improved Ant Colony Algorithm (IACO), classical blind equalization based on second-order statistics - subspace algorithm (SSA) and TXK[1] algorithm.

The parameter choice of improved ant colony algorithm is the same as experiment 1；According to the literature ，subspace algorithm (SSA) and TXK algorithm both use the fifth-order equalizer, the length of valid data 400N = .

The simulation results show in the case of classical literature channel, when the SNR is less than 15dB, the bit

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error rate of IACO is significantly lower than that of classical SSA and TXK algorithm which are based on second-order statistics. That indicates that the improved algorithm in the low noise's situation has certain superiority of application.

VI. CONCLUSION In this paper, the blind detection algorithm based on

IACO is proposed in view of the defect of ACO, namely the updating method of pheromone is adjusted in ACO, the control of parameter is added in the local pheromone update rule and the global update rule. In this paper ,the restraint of "limited character set "is used in restoring the sending signal, therefore, the receiving amount of data for restoring the signal is very few. In general, so long as Ns is sufficient

stimulus, that is （ N Mq> ）. But for the algorithm of the classical literature[1] ， To ensure the second-order statistics close to expectations, the required receiving amount of data N is usually 20 times or more of Mq ; The simulation results show: in the case of classical literature channel, in the low-noise case, the bit error rate of improved algorithm is significantly superior to the classical literature algorithm; In the case of random time-varying channel, the bit error rate of improved algorithm is significantly lower than that of blind detection algorithm based on ACO or GA and its computational speed is also improved, so the improved algorithm has a certain value. Like all intelligent algorithm, the disadvantage of improved algorithm has long operational time. In order to be more suitable for engineering, it needs to be further studied and improved.

REFERENCES

[1] Z.Ding, Blind equalization and identification. Marcel

Dekker,Inc,2000. [2] Q Y Li, E W Bai, and Z Ding, Blind Source Separation of Signals

With Known Alphabets Using ε -Approximation Algorithms, IEEE Trans Signal Processing, 2003,51(1), pp. 1-10.

[3] Z. Y. Zhang ,E. Bai, Zhang, Direct Blind Sequence Detection of SIMO Channels with Common Zeros, Acta Electronic sinica ，vol.33(4), 2005, pp. 671-675.

[4] Z. Y. Zhang，G. X. Yue , The fading channel Blind Multi-User Detection by the algorithm of discrete particle swarm optimization . Proceedings of the 6th World Congress on Intelligent Control and Automation, June, pp. 21 - 23,2006,Dalian, China.

[5] Dorigio M, Birattari M, Stuttzle T., Ant colony optimization. IEEE Computational Intelligence Magazine, November, 2006, 1(4), pp. 28-39.

[6] Dorigio M, Maniezzo V, Colorni A, Ant system: optimization by a colony of cooperating agents. IEEE Transactions on System, Man and Cybernetics, part B, February, 1996, 26 (1), pp. 29-41.

[7] Dorigio M, Maniezzo V, Colorni A, Ant system: optimization by a colony of cooperating agents, IEEE Transactions on System, Man and Cybernetics, part B, February, 1996, 26 (1), pp. 29-41.

[8] Dorigio M, Birattari M, Stuttzle T, Ant colony optimization , IEEE Computational Intelligence Magazine, November, 2006, 1(4), pp. 28-39.

[9] YIN Zhi-feng,,CAI Zi-liang, TIAN Ya-fei,.Ant colony optimization and its improvement for multiuser detection, Computer Engineering and Design,2007,28(7), pp. 1511-1513.

[10] LI Jin-han DU De-sheng., Simulation Study of an Improved Ant Colony Algorithm, Techniques of Automation And Applications,2008,27(2), pp. 58-60.

[11] Li Shi-Yong,.Ant Colong Algorithms with Applications, Harbin:Harbin Institute of Technology Press,2004.

[12] Dorigo M, Gambardella L M, Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation, April, 1997, 1 (1), pp. 53-66.

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3 4 5 6 7 8 9 10 11 1210

-5

10-4

10-3

10-2

10-1

100

SNR(dB)

BE

R

GA

ACO

IACO

Figure 1. The performance compare among IACO, ACO and GA

0 5 10 15 20 25 3010

-5

10-4

10-3

10-2

10-1

100

SNR(dB)

BE

R

IACO

SSA

TXK

Figure 2. the performance compare between Improved Ant Colony Algorithm（IACO）and classical blind equalization algorithm based on second-order

statistics

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