PCA Relay Strategies for Sensor Networks and Co

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PCA Relay Strategies for Sensor Networks and Co- operative Communications Systems

Sara Sahebdel, Hamidreza Bakhshi, Mona Nasseri, Mohammad Naser-Moghaddasi

Department of Electrical Engineering, Science and Research Branch, Islamic Azad University Tehran Iran Department of Electrical Engineering, Shahed University Tehran Iran

Young Researchers club, Science and research Branch, Islamic Azad University Tehran Iran Department of Electrical Engineering, Science and Research Branch, Islamic Azad University Tehran Iran [email protected], [email protected], [email protected], [email protected]

Abstract--- Sensor networks are a way to combat the fading in cooperative communications systems due to spatial diversity cha- racteristic and they are so popular in the new generation of wire- less networks. In this research the PCA relay strategies on a two- hop protocol sensor network is proposed and the better BER performance than the conventional relay matrix is achieved. It is considered one antenna for all nodes of the network including relays in the same distance from source and destination. The PCA method is applied for relay strategies, based on the eigen- vectors corresponding to the largest eigenvalues of channels at both sides of relays, constraining total power usage. The BER and MSE criterion of the proposed scheme are derived.

Index Terms---Amplify-forward scheme, Relay network, Relay matrix.

I. INTRODUCTION

Wireless communications is influenced by attenuation in the amplitude of signal resulted by fading when it is traveling from the transmitter to the receiver. Fading decreases the performance of the wireless network when signal components add destructively which degrades the system reliability [1], [2].

Cooperation diversity as a most effective way to decrease the fading effect of wireless channels has been the issue of many researches [3], [4], [5]. Cooperative diversity causes the improvement in the capacity and reliability of a wireless network by providing copies of transmitted signal at receiver [6], [7]. Actually the idea behind diversity is to send the same data over independent fading paths. In multi-user wireless network; different users are assumed as a relay node and can relay messages from a distinct user toward the terminal node.

So they can provide cooperative diversity to moderate fading effect.

Relays are small, and low cost so they are attractive to be used in wireless communications which make it cheaper and more reliable. As they have limited power, in this study constraining the relay network total power usage is considered to make them more practical.

The use of multiple antennas can progress the capacity and reliability but it is not practical to implement multiple antennas for some users due to limited size and power. Multiple antenna technique is discussed in some papers and introduced Space-

time coding as the most successful method to develop multiple-antenna systems. Specially mentioned method can achieve full diversity when there is no channel information at the transmitter [8].

Different topologies and strategies for relay networks are defined in some literatures [3] – [8]. For example one transmitter and multiple receivers are considered involving relays in different or the same distance from source and destination.

In this paper the relay network with one transmitter and one receiver node is assumed whereby each node applies one antenna [9].

Relay schemes can be categorized into three general groups:

amplify-forward (AF), compress-forward (CF) and decode- forward (DF) scheme. In the AF scheme, the relay nodes amplify the received signal and resend it toward the target node.

In conventional AF method the relays compensate the phase of the received signal to achieve coherent signal combination at destination [10] - [14]. In the DF method, each relay decodes the whole received message and re-encoded it, then sends the resulting signal to the destination node [15], [16]. In the CF scheme, the relay node sends a compressed form of received signal [17].

The Principal Component Analysis (PCA) relaying strategies is proposed in this paper and compared with the conventional relay strategies with total power usage constrained. The network is assumed with a dual-hop protocol, including two phases. First the relays listen to the source to attain the signal and in the second phase, they resend the amplified signal to the target node.

The PCA relay strategy is based on the eigenvectors related to the largest eigenvalues of channels at both sides of relays considering a phase to compensate the incoming signals phase to obtain coherent combination of signal. In conventional amplify-forward relay schemes, each node utilizes its maximum permissible power. The proposed schemes will use very low power whereby with the same total power usage, the PCA relay strategies achieved better BER performance than the conventional rely strategies.

This paper is organized as follows. In the section II, the relay network model is described in details. Then in section III, the idea of PCA relay strategies is examined. Section IV contains the simulation results, finally the paper is concluded in section V.

2011 International Conference on Business, Engineering and Industrial Applications (ICBEIA)

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II. RELAY NETWORK MODEL

Fig. 1, shows a sensor network with n relay nodes in the same distance between a source node and a destination node, in which no direct link between the source and the destination nodes is considered. A simple two-phase protocol is used to transmit data from the source. In the first phase the relay nodes listen until the source node transmits a signal towards the relay sensors. In the second phase the relay sensors send their signals to the destination sensor. Each node in the sensor network, source, relays and destination uses one antenna. Each channel is assumed to have quasi-static fading condition, so that for the duration of a single frame of data the channel stay fixed. In equations the n×1 channel vector between the source and the relay nodes is shown by F, and 𝐺 denotes 1× n channel vector between the relay sensors and the destination sensor.

Synchronous transmission and reception at relays nodes is assumed. The relay matrix is calculated with PCA method. K, an n×n diagonal linear matrix is determined in order to enforce better BER performance, as explained later. The received scalar signal at the destination sensor is given by:

d = GKFs + GKv + v (1)

Fig. 1. scheme of a n-relay network with one source and one destination

It is assumed that each node only can access to local channel information so the relay matrix will be diagonal. vs is the n×1 zero-mean complex noise with covariance matrix 𝜎 𝐼. As- suming the relay nodes far enough from each other, their nois- es are considered uncorrelated. vt is a zero-mean scalar noise with variance 𝜎 . The conventional relay matrix can be written as:

k =

‖ ‖

∗ ∗

| || | (2)

Where 𝜎 denotes the desired transmit power for each relay node.

III. PCA RELY STRATEGIES

Relay matrix is determind to maximize the power of the received signal at the receiver node:

K = argMax J(K) (3) Where

J(K) = E|Gx| = E|FKGs + GFv | (4) For dual-hop protocols, the relay nodes amplify their received signal and send it to the destination node simultaneously which provide F and G channel vectors, from source node to the relay nodes and from relay nodes to the destination node sequentially. In this paper the PCA method is used to calculate the relay matrix applying eigenvectors corresponding to the largest eigenvalues of the channels at both sides of relays.

Main diagonal components of relay matrix K is considered as bellow, which it needs to determine parameter 𝛼:

k = α V V _{| |}^∗ _{| |}^∗ (5) Each relay amplify coefficient is indicated by the elements of the main diagonal of the relay matrix. In equation (5), Vf is the eigenvector corresponding to the largest eigenvalue of the backward channel F and Vg is the eigenvector corresponding to the largest eigenvalue of the forward channel G and also there are two phases to remove effects of channels. Total power usage by the network is calculated as following:

P_T= ∑ |k | σ |f | + σ (6)

So it can be written as

P_T= ∑ α V V σ |f | + σ (7) The parameter 𝛼 is calculated to maximize the power of the received signal at the destination node

α = argMax J(α) (8)

So (4) can be written as J(α) =

σ ∑ g α V V _{| |}^∗_{| |}^∗f ∑ g^∗α^∗ V V _{| | | |}f^∗ + σ ∑ g^∗α^∗ V V _{| | | |}α V V _{| |}^∗_{| |}^∗g (9)

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To maximize the J(𝛼) :

J =

σ g f ∑ g^∗α^∗ V V _{| | | |}f^∗ +

σ α^∗V V _{| | | |}|g | = 0 (10)

In different way, 𝛼 is determined as below by restricting total power usage. It means that equation (6) must be equaled to constant P.

α =

| | (11)

So total power usage by the network can be calculated to limit the total power usage to constant P with substituting (11) into the (7), gives:

α = ^P

∑ V V

/

(12)

Substituting (12) into the (11) gives

α = ^P

( | | ) ∑ V V

/

(13)

The elements of the main diagonal of PCA relay matrix can be determined as bellow:

k = ^P

( | | ) ∑ V V

/

Vf_i Vg_i f_i^∗

|fi| g_i^∗ g_i (14)

IV. SIMULATION RESULTS

In this section the performance of the proposed scheme are simulated for a relay network with one source node and one destination node. It is assumed that all relay nodes are at the same distance from the receiver and transmitter and there is no direct link between them. Using this assumption, both mentioned channels have the same second moment statistics. F and G is assumed to have Zero-mean unit variance complex Gaussian channel models, also QPSK modulation with unit power is chosen for transmitted signal. The BER and MSE criterion are applied to evaluate the performance of the proposed scheme. In Fig. 2, the BER performance of one-relay network and 3-relay network of the proposed schemes (14) is shown and then is compared with the conventional relay strategies (2). Investigating Fig.2 shows, the PCA relay strategies achieved better BER performance comparing with conventional amplify-forward relay schemes. In Fig. 3, the BER performance of a network with one, 5 and 8 relays with PCA strategies is demonstrated, as the number of relay increases the

proposed PCA scheme achieves better BER result. Fig. 4, shows the MSE performance of the suggested relay matrix for 1, 5, 15 and 45-realy networks and it is shown, by increasing the number of relays, the PCA scheme reaches better result.

Power performance of PCA schemes for a one-relay network and 8- relay network is examined in Fig. 5. It shows the low power consumption of relay network. As a result it can be concluded, the PCA relay strategy has better performance in limited power than the conventional strategy. The results indi- cate, as the number of relay nodes increases, the performances get better. Although PCA matrix operations reach higher order if the number of relays increases, there are some ways to deal with this calculation problem such as applying Expectation Maximization (EM) algorithm.

Fig. 2. Comparing BER performance of two strategies

Fig. 3. BER performance of the proposed PCA relay matrix

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BER

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1 relay 3 relay 1 relay PCA 3 relay PCA

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1 relay PCA 5 relay PCA 8 relay PCA

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Fig. 4. MSE performance of the proposed PCA relay matrix

Fig. 5. Power performance of the proposed PCA relay matrix

V. CONCLUSION

In this paper, a dual-hop protocol is assumed for the wireless sensor network with one transmitter and one receiver including relays in the same distance of them. The diagonal relay matrix is considered due to providing uncorrelated relay network. The PCA relay strategies that improve the BER performance are proposed and analyzed. The PCA relay matrix is based on the eigenvectors corresponding to the largest eigenvalue of channels at both sides with a parameter αi. Then it is calculated by limiting the total power usage of the relay network. In simulation results The PCA relay strategy is compared with the conventional relay strategy, which shows the better BER performance achievement. The BER and MSE performances improve as the number of relay sensors increases.

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MSE performance

1 relay PCA 5 relay PCA 15 relay PCA 45 relay PCA

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8 relay PCA 1 relay PCA

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