Performance Analysis for Cooperative Relay with Power Control Scheme over Fading Channel

Anis Izzati Ahmad Zamani, Rozeha A. Rashid, Mohd Adib Sarijari, Sharifah Kamilah Syed Yusof, Norsheila Fisal

anis_izzati86@yahoo.com, {rozeha | adib_sairi | kamilah | sheila |}@fke.utm.my

Abstract – Performance of a system is determined by the probability of error of the channel. In this paper, the error probability of cooperative relay channel is analyzed for Quadrature Phase Shift Keying (QPSK) using simple linear block coding. Focusing on a network with single source to destination with one relay station, the upper bound of symbol error rate (SER) is derived. A power control scheme is also proposed to improve the performance of the system. Computer simulations confirm the presented mathematical analysis. Keywords - Cooperative Relay, Symbol Error Rate,

Cooperative Transmission, Decode-and-Forward Strategy

I. INTRODUCTION

The demand for high data rate services in wireless communication has grown rapidly over the years. This scenario motivates the idea of cooperative relay to increase data rates by relay station(s) cooperatively forward data from source to destination. Cooperative transmission in its basic form consists of three terminals [1]: a source (S), a relay (R), and a destination (D). The relay node forwards the transmission of the source towards the intended destination. Performance advantages achievable from collaboration include power gains and diversity gains [2].Based on previous research on capacity [3], [4], the performance is improved for wireless network using cooperative diversity. The IEEE 802.16 Work Group has developed a standard that supports cooperative relay system which is IEEE 802.16j [5], Wimax Mobile Multihop Relay. 802.16j uses tree topology which allows a relay station (RS) to have only one superordinate RS. The system model for this work should satisfy this requirement.

One of the limiting factors in wireless communication is multipath fading. Exploiting cooperative diversity can mitigate fading effectively. Liu et. al [6] derive necessary conditions for optimal relay signaling that minimizes error probability at the destination node which shows performance improvement over the cooperative relay strategies. The strategies include amplify-and-forward (AF); relay acts as a repeater by simply amplify the received signal and forward the signal to the destination, and decode-and-forward (DF); relay decodes the received signal and regenerate the received signal before forward it to the destination.

There is several works done in discussing the performance of cooperative relay networks. The authors in [3] discussed the performance of relaying configurations

and signaling algorithms for either limited feedback or non-feedback channels. Out of three relaying types; analogue relaying, digital relaying and hybrid relaying, the digital selective relaying outperforms other configurations with highest signaling overhead. In this configuration, the source is required to know the SINR value at each relay and destination for each relay route. Zhao et. al [4] analyzed outage probability for decode-and-forward cooperative relay system. A closed-form solution is attained for independent and identically distributed (i.i.d.) channels, and two tight lower bounds are presented for correlated channels.

In this paper, the symbol error rate of a cooperative relay channel is derived assuming all channels are orthogonal. The relay employs DF relaying strategy. The rest of the paper is organized as follow. Section II presents the system model to be analyzed. The analysis on symbol error rate is given in Section III. In Section IV, the simulation results are presented and finally, conclusions are given in Section V.

II. SYSTEM MODEL

Consider a wireless communication system with one source node, one receive node and a relay station as depicted in Fig. 1. The binary data stream is first encoded using linear block code. Then, the encoded symbols is fed into QPSK modulator and then transmitted over two fading channels. For a RS in half-duplex mode, in the first time slot, the source uses the broadcast nature of wireless channel to sent message to the relay node and destination node. The relay only listens in the first time slot and transmits during the next. The received signal at the relay is given by

𝑦𝑦𝑠𝑠,𝑟𝑟 = ℎ𝑠𝑠,𝑟𝑟𝑥𝑥𝑠𝑠 + 𝑛𝑛𝑠𝑠,𝑟𝑟 As the receive signal at the destination can be written as

𝑦𝑦𝑠𝑠,𝑑𝑑 = ℎ𝑠𝑠,𝑑𝑑𝑥𝑥𝑠𝑠 + 𝑛𝑛𝑠𝑠,𝑑𝑑 For half-duplex mode, during the second time slot, the relay forwards the message received to the destination.

𝑦𝑦𝑟𝑟 ,𝑑𝑑 = ℎ𝑟𝑟 ,𝑑𝑑𝑥𝑥𝑟𝑟 + 𝑛𝑛𝑟𝑟 ,𝑑𝑑 where the ℎ𝑠𝑠,𝑟𝑟 represent the channel gain between the source node and relay node, ℎ𝑠𝑠,𝑑𝑑 is the channel gain between source node and destination node and ℎ𝑟𝑟 ,𝑑𝑑 is the channel gain between relay node and destination node. The

(1)

(2)

(3)

additive expressions, 𝑛𝑛𝑠𝑠,𝑟𝑟 , 𝑛𝑛𝑠𝑠,𝑑𝑑 , 𝑛𝑛𝑟𝑟 ,𝑑𝑑 are the Gaussion noise (AWGN) with zero mean and No

/2 variance at relay node and destination node from source and relay nodes respectively.

Fig. 1: Cooperative relay system model

III. PROBABILITY OF ERROR ANALYSIS

FOR COOPERATIVE RELAY

A. Probability of Error over One Channel

The system developed is using hamming encoder which is a linear block coding characterized by (n,k) notation. The encoder will transform k data bit from the source into n data bit. Say, the data from the source is as follow

𝑊𝑊𝐾𝐾 = [𝑊𝑊0,𝑊𝑊1, … ,𝑊𝑊𝑘𝑘] Then, the codeword generated by the encoder is

𝑿𝑿 = 𝑮𝑮𝑮𝑮 where 𝑮𝑮 is a generator matrix with the size 𝑘𝑘 × 𝑛𝑛. In [7], it defines a term Hamming weight, wH

(𝑿𝑿) as the number of nonzero elements in 𝑿𝑿. While Hamming distance is the number of differences between two codewords.

Hamming distance �𝑥𝑥𝑚𝑚 , 𝑥𝑥𝑚𝑚′� = 𝑑𝑑𝐻𝐻𝑚𝑚′ Both terms relate as the Hamming distance between two codewords is equal to the Hamming weight of their sum.

𝑑𝑑(𝑥𝑥𝑚𝑚−1, 𝑥𝑥𝑚𝑚) = 𝑤𝑤𝐻𝐻(𝑥𝑥𝑚𝑚−1 + 𝑥𝑥𝑚𝑚)

The probability of error would depends on the value of 𝑑𝑑𝐻𝐻𝑚𝑚′ between codewords as for 𝑑𝑑𝐻𝐻 is even, the probability of error that the receiver decode 𝑥𝑥𝑚𝑚′ instead of 𝑥𝑥𝑚𝑚 is

𝑃𝑃(𝑥𝑥𝑚𝑚′ ) = � �𝑛𝑛𝑘𝑘�𝑑𝑑𝐻𝐻

𝑘𝑘=𝑑𝑑𝐻𝐻 2� +1

𝑝𝑝𝑘𝑘(1 − 𝑝𝑝)𝑛𝑛−𝑘𝑘

+12𝑝𝑝𝑑𝑑𝐻𝐻

2� (1 − 𝑝𝑝)𝑛𝑛−𝑑𝑑𝐻𝐻

2� And for 𝑑𝑑𝐻𝐻 is odd,

𝑃𝑃(𝑥𝑥𝑚𝑚′ ) = � �𝑛𝑛𝑘𝑘�𝑑𝑑𝐻𝐻

𝑘𝑘=𝑑𝑑𝐻𝐻+12

𝑝𝑝𝑘𝑘(1 − 𝑝𝑝)𝑛𝑛−𝑘𝑘

where 𝑝𝑝 is the bit error probability. Since this paper is considering QPSK, the symbol error probability is [7]

𝑝𝑝𝐸𝐸 ≈ 2𝑄𝑄 ��2𝐸𝐸𝑠𝑠𝑁𝑁𝑜𝑜𝑠𝑠𝑠𝑠𝑛𝑛 𝜋𝜋

𝑀𝑀�

in which 𝐸𝐸𝑠𝑠 is the received symbol energy with 𝐸𝐸𝑠𝑠 =𝐸𝐸𝑏𝑏(𝑙𝑙𝑜𝑜𝑙𝑙2𝑀𝑀) and 𝑁𝑁𝑜𝑜 is the noise for the symbol. 𝐸𝐸𝑏𝑏 represents received bit energy. From 𝑝𝑝𝐸𝐸, 𝑝𝑝 can be obtained by [7]

𝑝𝑝 =𝑝𝑝𝐸𝐸

𝑙𝑙𝑜𝑜𝑙𝑙2𝑀𝑀

where 𝑀𝑀=4 for QPSK, that results in

𝑝𝑝 = 𝑄𝑄��4𝐸𝐸𝑏𝑏𝑁𝑁𝑜𝑜

𝑠𝑠𝑠𝑠𝑛𝑛𝜋𝜋4�

As a system usually have a number of codewords, the

expression for probability of error must consider the summation of all probability that destination node decode incorrectly. Equations (8) and (9) can be used to create an upper bound for computing probability of error. Say, a source node transmits 𝑥𝑥𝑚𝑚 , the probability that the destination node decode incorrectly is given by 𝑃𝑃𝑒𝑒(𝑥𝑥𝑚𝑚 𝑠𝑠𝑠𝑠 𝑠𝑠𝑒𝑒𝑛𝑛𝑠𝑠) = 𝑃𝑃(𝑑𝑑𝑒𝑒𝑑𝑑𝑜𝑜𝑑𝑑𝑒𝑒 𝑥𝑥𝑚𝑚′ 𝑠𝑠𝑛𝑛𝑠𝑠𝑠𝑠𝑒𝑒𝑖𝑖𝑑𝑑 𝑜𝑜𝑜𝑜 𝑥𝑥𝑚𝑚 ∀ 𝑚𝑚′

≠ 𝑚𝑚) = 𝑃𝑃 � � 𝑑𝑑𝑒𝑒𝑑𝑑𝑜𝑜𝑑𝑑𝑒𝑒 𝑥𝑥𝑚𝑚′

𝑚𝑚′ ≠𝑚𝑚

�

≤ � 𝑃𝑃(𝑥𝑥𝑚𝑚′ )𝑚𝑚′≠𝑚𝑚

From the relation obtained in equation (), the above equation can be written as

� 𝑃𝑃(𝑥𝑥𝑚𝑚′ )𝑚𝑚′≠𝑚𝑚

= � 𝑛𝑛𝑤𝑤(𝑥𝑥)=𝑑𝑑𝐻𝐻

𝑛𝑛

𝑤𝑤𝐻𝐻=𝑑𝑑𝐻𝐻𝑚𝑚𝑠𝑠𝑛𝑛× 𝑃𝑃(𝑥𝑥𝑚𝑚′ 𝑤𝑤𝑠𝑠𝑠𝑠ℎ 𝐻𝐻𝑖𝑖𝑚𝑚𝑚𝑚𝑠𝑠𝑛𝑛𝑙𝑙 𝑑𝑑𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖𝑛𝑛𝑑𝑑𝑒𝑒,𝑑𝑑𝐻𝐻)

The first right-hand expression is the summation of all weight of the number of codeword with Hamming distance, 𝑑𝑑𝐻𝐻. B. SER Analysis for Cooperative Relay Channel From the derivation in part A, the SER at the destination of a cooperative relay channel is given by

𝑆𝑆𝐸𝐸𝑆𝑆= 𝑃𝑃(𝑆𝑆𝑒𝑒𝑙𝑙𝑖𝑖𝑦𝑦 𝑑𝑑𝑒𝑒𝑑𝑑𝑜𝑜𝑑𝑑𝑒𝑒 𝑠𝑠𝑛𝑛𝑑𝑑𝑜𝑜𝑟𝑟𝑟𝑟𝑒𝑒𝑑𝑑𝑠𝑠𝑙𝑙𝑦𝑦)× 𝑃𝑃�(𝑥𝑥�𝑚𝑚′ ≠ 𝑥𝑥𝑚𝑚)�𝑆𝑆𝑒𝑒𝑙𝑙𝑖𝑖𝑦𝑦 𝑑𝑑𝑒𝑒𝑑𝑑𝑜𝑜𝑑𝑑𝑒𝑒 𝑠𝑠𝑛𝑛𝑑𝑑𝑜𝑜𝑟𝑟𝑟𝑟𝑒𝑒𝑑𝑑𝑠𝑠𝑙𝑙𝑦𝑦�+ 𝑃𝑃(𝑆𝑆𝑒𝑒𝑙𝑙𝑖𝑖𝑦𝑦 𝑑𝑑𝑒𝑒𝑑𝑑𝑜𝑜𝑑𝑑𝑒𝑒 𝑑𝑑𝑜𝑜𝑟𝑟𝑟𝑟𝑒𝑒𝑑𝑑𝑠𝑠𝑙𝑙𝑦𝑦)× 𝑃𝑃�(𝑥𝑥�𝑚𝑚′ ≠ 𝑥𝑥𝑚𝑚)�𝑆𝑆𝑒𝑒𝑙𝑙𝑖𝑖𝑦𝑦 𝑑𝑑𝑒𝑒𝑑𝑑𝑜𝑜𝑑𝑑𝑒𝑒 𝑑𝑑𝑜𝑜𝑟𝑟𝑟𝑟𝑒𝑒𝑑𝑑𝑠𝑠𝑙𝑙𝑦𝑦�

which also can be written as

S

R

D

hs,r hr,d

hs,d (for 𝑝𝑝𝐸𝐸 ≪ 1)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

𝑆𝑆𝐸𝐸𝑆𝑆 = 𝑃𝑃(𝑥𝑥�𝑚𝑚′ ≠ 𝑥𝑥𝑚𝑚) = 𝑃𝑃(𝑥𝑥�𝑚𝑚′ ≠ 𝑥𝑥𝑚𝑚 , 𝑥𝑥�𝑚𝑚′ ≠ 𝑥𝑥𝑚𝑚)

+𝑃𝑃(𝑥𝑥�𝑚𝑚′ ≠ 𝑥𝑥𝑚𝑚 , 𝑥𝑥�𝑚𝑚′ = 𝑥𝑥𝑚𝑚)

IV. PROPOSED POWER CONTROL SCHEME

Since the relay is also operating in half-duplex mode, the transmission through a RS should consider two time slots; the first is for the RS to listen and the second one is for data transmission. Thus, if a source node sent a set of codewords with the size of 2n for each codeword, the first n will be received with diversity (from both source node and RS) at destination node and the second one will only be received via direct transmission.

Power control is only been done at the source node. As mentioned, the first half of a codeword is received with diversity, hence the source node only transmit at average power with certain limitations. During the second half of the codeword, the source node transmits with full power as the receiver will only received this part of data via direct transmission only. This can be understood easier using the illustration in Fig. 2. The shaded part of the box noted that source node transmit with full power and non-shaded part of the box says that the source transmit at average power.

Fig. 2: A set of codewords

V. SIMULATION RESULTS

This section presents numerical results to illustrate and verify two scenarios: (1) The benefit of cooperative relay with DF strategy in terms of error probability analysis and (2) Power control scheme of cooperative relay channel.

Fig. 3 shows the first scenario where a comparison in SER for a system operates without RS and a cooperative relay system with DF strategy over fading channels at full-duplex mode RS. Channel gain denoted by [1,1,0.5] in the figure represents the channel condition from source node to relay node and from relay node to destination node is good, while the channel condition between source node and destination node is average. This shows an increasing SER performance when a system employs cooperative relay for data transmission.

The second scenario is illustrated in Fig. 4 that shows the difference in SER performance for cooperative system with and without using power control scheme proposed in previous section. The scheme proposes the source to vary transmission power according to portions of codewords that would be received at the destination. RS is operating in

half-duplex mode. Note that the performance between a system without relay and cooperative relay with no power control is almost similar. This happens because the probability of symbol error for data transmission through relay is low. At the destination, the signal received from relay and source nodes are combined. Since the probability of symbol error from source to destination is high making the symbol error probability for the signal through relay negligible. Hence, the performance of cooperative relay system with no power control is almost similar to a system with no RS. With the proposed power control scheme, the cooperative relay performance increases.

Fig. 3: SER of system without relay and cooperative relay

with DF strategy

Fig. 4: SER of system without relay and cooperative relay

with different power control

VI. CONCLUSION

The error probability of cooperative relay channel has been studied in fading channel using QPSK modulation and Hamming encoder. An upper bound for symbol error rate for the system model was derived with combinations of full-duplex and half-duplex modes for RS. As for half-duplex mode RS, a power control scheme at the source node has been proposed. The performance improved for cooperative relay compared to direct transmission for full-

n 2n = a codeword

Tx at average power Tx at full power

rx

rx relay

relay (16)

duplex mode. The power control scheme also shows improved in performance for cooperative relay with half-duplex mode RS.

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