The Throughput for Multi hop Relay Wireless Sensor Network Based on Cooperative Diversity

2016 International Conference on Electronic Information Technology and Intellectualization (ICEITI 2016) ISBN: 978-1-60595-364-9

The Throughput for Multi-hop Relay

Wireless Sensor Network Based

on Cooperative Diversity

Genjian Yu and Jinglan Wu

ABSTRACT

This paper studied the problem of the throughput of multi-hop multi-relay wireless sensor network based on the cooperative diversity technology. At first, the paper established the cooperative diversity model for multi-source, multi-sink and multi-relay wireless sensor network, on which the specific expression of throughput of wireless sensor network was deduced, it not only prove that the throughput performance of multi-hop multi-relay wireless sensor network would be increased by the cooperative diversity technology, but also gave the criterion for discussing further the application effect of the technical scheme such as the cooperative selection strategy and so on in actual multi-hop multi-relay wireless sensor network.

INTRODUCTION

Wireless communication went through the development from analog to digital, fixed to mobile and centralization to distribute. With multiple antenna elements equipped both in transmitter and receiver, the structure of MIMO channel could be formed by the existing Multiple Input Multiple Output (MIMO) technology, and then the capacity of channel greatly improved with the full use of airspace resources1, but the existing antenna technology was mainly applied in base station, and it was difficult to install multiple antennas in mobile terminal, because for realizing the transmit diversity, the space between neighboring antenna was greater

________________________

than the wavelength and the transmission channel between several transceiver antennas was independent or irrelevant at least, and the requirement of mobile terminal for volume, quality and power were extremely exacting, so it was difficult to realize the uplink transmit diversity in mobile terminal [1].

As it was made of multi-user in existing communication system of wireless sensor network, so cooperative diversity, which the transmit diversity in mobile terminal, was caused with it [2]. The basic idea is to share their antenna between mobile terminals, transmit information by virtual multi-antenna array composed of themselves and other mobile nodes terminal, so as to achieve diversity way of launch diversity gain. As to reduce the effect of fading and instability of wireless channel, cooperative diversity may evidently reduce the bit error ratio, piece error ratio and interrupt possibility, and It could also improve the reliability, data transfer rate and throughput of network[3]. Many techniques of cooperative diversity have obtained in recent year [4].

This article focuses on the study of throughput in the model of cooperative diversity wireless sensor network that is source, destination and multi-relay.

This paper is organized as follows. Firstly, cooperative diversity technology of wireless sensor network is given. Secondly, the cooperative diversity model of multi-hop multi-relay wireless sensor network is presented. The code technology and decode relay in this paper are also presented in thirdly. Finally, our work of this paper is summarized in the last section.

COOPERATIVE DIVERSITY TECHNOLOGY

The principle of cooperative diversity is shown in Figure 1. A simple diversity cooperation system is formed by source node, relay node and destination node. The specific process is divided into two steps: firstly, source node send the information to relay nodes and destination node in the form of broadcast, and relay node process the received information; secondly, source node and relay node send the information to destination node, then destination node combined the received information by some method of combining.

source relay sink

S 1 S 2 S 3

S m

R 1 R 2 R 3

R n

... ..

.

Figure 1. diversity of wireless sensor network. Figure 2. cooperative diversity model.

information. Each signal cycle includes three bits space. X t1( ) and X t2( ) are expressed as the signal of user 1 and user 2, respectively, so the signal is

(1) (2) (2) (2)

1( ) 11 1 1( ), 12 1 1( ), 13 1 1( ) 14 2ˆ 2( )

X t =é_êa b C t a b C t a b C t +a b C t ù_ú

ë û (1)

(1) (2) (2) (2)

2( ) 21 2 2( ), 22 2 2( ), 23 1ˆ 1( ) 24 2 2( )

X t =é_êëa b C t a b C t a b C t +a b C t ù_úû (2)

Each user sent itself bit information and detected the second bit of other users in the first and second interval. Two users sent the linear combination involving the second bit of itself and its partners in the third interval. To the first, second and third interval, the power is variable, According to the condition between uplink and user channel, the related transmission power is optimized, and the method has self-adaptability for the state of channel.

The power is allocated by ai j, , which the average transmit power is invariant. In short, when the channel status was good, more power will be allocated for collaboration, otherwise the power will be decreased.

COOPERATIVE DIVERSITY MODEL

Consider a source sink relay wireless sensor network W( )N , the number of node was N_{. As shown in Figure 2, the source (or relay) node sent the sign} zi to the

destination (or relay) node Rj(j=1,2,...,n) at the rate of _i, respectively ,expressed

as Si ¾¾¾zi R_j，

in which z Îi i.

To be more specific, the node Si ,Rj (i=1,2,...,m , j=1,2,...,n ) could be configured for sending out complex value base-band signal flow aik 和

jk

b

(k=1,2,...N ), respectively, which satisfied the conditions of node power in the

average significance, 2

1

1 N _{| | ( )} ik i k

P S N

å

 ， 2

1

1 N _{| | ( )}

jk j k

P R N

å

 (3)

When the source (or relay) node Si send the signal to the destination (or relay)

node Rj at the ratepSi, and the other destination (or relay) node R ww( ¹j) can listen and assist the distribution process by relay cooperation. Noted that the signal received by the destination (or relay) node Rj(j=1,2,...,n ) as ¡( )Rj , and the

circle symmetrical IDD complex random variable. The channel gain between Si and

j R

was gij , and the cooperative diversity gain between Rj and R_w is (cosq_jw +isinq_jw)

G

, in which, i _{is the unit of imaginary number, the range} G _is

constant, the phase qjw is the random variable distributed in [-p p, ], thus, based on

i

S ¾¾¾zi R_j

, the model of receiving signal of source (or relay) node is

1,2, ,

( ) (cos sin ) w

j ij jw jw j j

w m w j

R _i i

¡ z q q z

¹

= +

å

= ...

g G C ，j=1, 2,...n (4)

In which, zwj is sent by R_w in S_i ¾¾¾zi  R_j

, Cj is Additive Gaussian White Noise. The formula (4) can be noted as

1,2, , ,

( , )_{j ij ik} (cos _jw sin _jw) _{wk jk} w n w j

R k i

¡ a q q b

¹

= +

å

= ...

g G C ，j=1, 2,...n，k =1,2,...N (5)

CODING TECHNOLOGY AND DECODE RELAY

According to the information of receiving node, Code Word transferred many kind of information, supposed the sender node sent the information

1

1 {1, 2,...,2 }

k

z Î  _, 2

2 {1,2,...,2 }

k

z Î  _{, …, {1, 2,..., 2}k m_} m

z Î  ₍₆₎

So the sender node will form a generalized information matrix, that is 1 2

2k ´2k ´ ´ 2km , matrix elements is random Gaussian code, noted as 

1 2, m

X( ,z z  )

. If channel capacity is  1+2++m, then z1，z2，…，zm

are decoded by the receiver node. If zi1,...,zij ，1i1,...,ij m，and 1 2, ,...,j k k i i i

z

¹

å

 

,

then the receiver node decoded zk (k¹i1,..., ,1ij  k m) _{by the generalized} information matrix.

If the wireless channel, which the information is choose according to a uniform probability by the information set in (6) and sent from the source (or relay) node to the destination (or relay) node, was point-to-point. For the wireless relay channel, Block Markov Coding was first developed by Madsen in [5]. Each block of signal was encoded alone, supposed the signal zi is divided into M blocks

(1), (2),..., ( )M

i i i

z z z

, the encoding function of the source (or relay) node is XSi( (1))i

，XSi( (2))i ，…，XSi( ( ))i M , the relay node R ww ( j)

¹

decoded the Code Book



( ( )) i S i

X l

of l _block. i <log(1 |+ gij |2⋅P S( ))i . When

2

log(1 | | ( ))

i < + ij ⋅P Si

 g

signal of Decode Block, the relay node send the signal series

0,XRw( (1))i ,XRw( (2))i ,…,XRw( ( ))i M decoded in the next Block Slot, the transport method of block code signal is called Decode Relay.

Supposed the destination (or relay) node had received the signal zi( )k of k

block, and Meanwhile, the Code Book XSi( (i k 2))

is decoded by the small misunderstanding code probability, then the form of parallel decoding signal based on the model of received signals in the target (or relay) nodes is

   _

i S

1 2

( ( )) (cos sin ) ( ( 1)) , ( ( 1))

w i

i jw jw R i j S i j

w w j

X k q i q X k X k

¹

é ù

ê _{+ + - + - +} ú

ê ú

ê ú

ë = , ...m,

å

G C C (7)

If the source (or relay) node S ii( =1,2,..., )m _{sent a code word that described the}

information received by the destination (or relay) node, the relay node R ww ( ¹j) will decode the information before Rj , when the information is decoded successfully, every receiver node begin to use another scheduled code word and send the same information in the average power conditions. Supposed the decoding time of the node Rj in a code block cycle is represented in time slot tj, then tj means a period of a fading code block cycle when Rj decoded the information to the

node R ww ( ¹j) _{. According to the condition of right decoding, we have} 2

log(1 | | ( )) 1 i + ij ⋅P Si <

 g

.

Based on the actual physical channel and decoding conditions, we suppose that

j R

will neither decode nor send information when tj ³1. Let pj to represent the probability when Rj is decoded successfully. In addition, the mutual information related to Si, Rj is

2 2

1 1

( )log(1 | | ( ) ( 1))

j

j l l ij i

l

I t t_- P S l

=

=

å

By solving equation Ij =i，j=1,2,...,n, we have

1 2

1

log(1 | | ( ))

i i i t P S = + ⋅  g ， 2 2 2 1 2 2

2 2 2

2

1 | | ( ) log

1 | | ( ) log(1 | | ( ) )

i i i i i i i P S t P S t P S + ⋅ + + + ⋅ = + ⋅ +

 g G

g

g G ，…, tn =

2 2 2 2 2 2

2 3

1 2 2 2 2 1 2 2

2 3

2 2

1 | | ( ) 1 | | ( ) 2 1 | | ( ) ( 1)

log log ... log

1 | | ( ) 1 | | ( ) 1 | | ( ) ( 2)

log(1 | | ( ) ( 1) )

i i i i in i

i n

i i i i in i

in i

P S P S P S n

t t t

P S P S P S n

P S n

-+ ⋅ + + ⋅ + + ⋅ +

-+ + + +

+ ⋅ + ⋅ + + ⋅ +

-+ ⋅ +

- g G g G g G

g g G g G

(i=1,2,..., )m （9）

When tj <1 and tj+1 ³1, then pj >0_，pj+1 =0_，(j=1,2,..., )m , pj =Pr{tj <1}, in the sense of probability expectations, the throughput of multi-hop relay sensor network based on cooperative diversity is expressed as

1 1 i m n

i throughput S j

i j

C p p

n = =

=

åå

CONCLUSIONS

In this paper we mainly studied the throughput of multi-hop relay wireless sensor network based on cooperative diversity, a cooperative diversity model of wireless sensor network, which is multi-source relay, is set up. Based on the model, the formulae of throughput is derived, and so the quantitative calculation for the throughput performance of multi-source relay wireless sensor network under cooperative diversity will provide us theoretical judging rule for discussing farther the application of technical proposal such as cooperative selection scheme in the actual network environment of multi-hop relay wireless sensor network. On the other hand, it is proved theoretically that throughput performance of multi-source relay wireless sensor network will be improved by cooperative diversity.

According to the conclusions of throughput based on cooperative diversity, a valuable judgment scale is given in the application environment of multi-hop relay wireless sensor network for balancing the relationship between the throughput and network cost.

ACKNOWLEDGMENTS

This work is supported by the funds of Department of Education of Fujian Province under Grant. No. JA14249 and founds of Minjiang university under Grant. YKY13005.

REFERENCES

1. Nahas, M.; Saadani, A.; Hachem, W.; Performance of asynchronous two-relay two-hop wireless cooperative networks. IEEE Transactions on Wireless Communications, Vol. 9 , Issue: 3, 2010, Page(s): 1086-1096.

2. Host-Madsen A., “Capacity bounds for Cooperative diversity”, IEEE Trans. on Inform. Theory, Vol.52, Issue 4, 2006:1522-1544.

4. Asaduzzaman; Hyung Kong; Coded diversity for cooperative MISO based wireless sensor networks. IEEE Communications Letters, Vol. 13, Issue: 7, 2009, Page(s): 516 - 518.