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| ARTICLE |
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| Year : 2009 | Volume
: 55
| Issue : 5 | Page : 205-211 |
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Power Allocation Strategies for Non-regenerative Relay Network in Nakagami-m Fading Channel
Himanshu Katiyar, R Bhattacharjee
Communication and Advance DSP Group, Electronics and Communication Engg. Department, Indian Institute of Technology Guwahati, India
| Date of Web Publication | 5-Nov-2009 |
Correspondence Address:
Himanshu Katiyar
Communication and Advance DSP Group, Electronics and Communication Engg. Department, Indian Institute of Technology Guwahati
India
 DOI: 10.4103/0377-2063.57596
 Abstract | | |
Cooperative relaying is a promising approach to enlarge coverage area and enhance system capacity. Capacity of such a system depends on the SNR of the received signal. Therefore, allocation of available power between source and relay, to achieve maximum SNR, is an important issue. A power allocation scheme depends not only on channel state information (CSI) but also on the degree of knowledge of this CSI. This paper investigates different power allocation strategies in presence of full CSI, without CSI, and statistical CSI through simulation studies. Knowledge of full CSI can be utilized to obtain optimal performance at the cost of system complexity. Use of statistical feedback reduces complexity and its performance is found to be close to optimal one. Its performance is close to optimum one for the placement of relay node near destination or with decrease in fading severity. However, in the absence of CSI, placement of relay at middle is the best solution, for similar channel conditions. Keywords: Channel state information, Ergodic capacity, Non-linear optimization, Non-regenerative relay, Power allocation.
How to cite this article:
Katiyar H, Bhattacharjee R. Power Allocation Strategies for Non-regenerative Relay Network in Nakagami-m Fading Channel. IETE J Res 2009;55:205-11 |
| 1. Introduction | |  |
The next generation wireless systems will require handling high data rates, need to be spectrally efficient, reliable and capable of being deployed in various environments. Such a system suffers from smaller than expected coverage and excessive amount of shadowed areas due to the high operating frequencies. Cooperative relaying is an attractive solution as it enhances coverage as well as signal quality. It also introduces diversity gains which improve robustness against fading for the same transmit power, or substantially reduces transmit power for the same level of performance. It also reduces radio frequency interference to neighboring nodes.
Relays can be broadly categorized as regenerative (digital) or non-regenerative (analog) depending on their functionality. In regenerative case, the relay decodes, encodes, and forwards the received signal; in the latter, a relay simply amplifies and forwards the received signal. Such relays have been reported to outperform regenerative relays despite noise propagation because they do not suffer from error propagation. The non-regenerative mode of operation puts a less processing burden on the relay and causes much smaller delay. Hence, it is often preferred for delay sensitive traffic such as voice and live video. Deployment of nonregenerative relay has little effect on the operations at the source and destination as there is no handshaking requirement for each packet.
For tactical applications, such relays are useful to enhance network reliability, throughput and low probability of detection and/or interception. It contains virtually no information from source and hence no security information even if stolen by enemy. The idea of cooperation among relay was comprehensively studied in [1] ; here capacities of the Gaussian relay channel and certain discrete relay channels are evaluated. In their pioneering work [2],[3] , Laneman has proposed a two-phase cooperation protocol which is able to extract full spacial diversity.
In the first phase (i.e. broadcasting phase), the source transmits to destination and relay terminals. In the second phase (i.e. relaying phase), the relays transmit their received signals to the destination using either orthogonal subchannels (repetition based cooperative diversity) or the same subchannel (space-time coded cooperative diversity). A practical analysis of the uniform power allocation (UPA) scheme, which allocates equal power to source and relay, without taking into account the power efficiency is done in [4] . According to different relaying methods, researches in [5],[6] propose the optimal power allocation (OPA) scheme between the source and relay for the regenerative and the nonregenerative relaying station respectively. In [7] the optimal allocation that minimizes the outage probability is developed for regenerative relay and used as an approximate solution for nonregenerative relay. In [8] , the distributed power allocation scheme for regenerative relay terminals is analyzed.
In our system model, relay works in half duplex mode. Full duplex mode is possible, if relay has two sets of antennas, one each for transmission and reception, with full knowledge of what to transmit, so it can cancel out interference from its own transmit antennas at its receive antenna. Such an approach is difficult in the present state of art because of sever attenuation over wireless channel and insufficient electrical isolation created due to power of transmitted signal at the relay typically overshadows the power of desired signal [9] .
We study the dynamic deployment strategies for manned (user cooperative network) or unmanned (infrastructure based fixed relay network) relays and various power al location strategies for improving system performance. The paper uses the versatile Nakagami-m fading channel model between nodes. The Nakagami-m fading, being a parameter-based distribution, makes a justified choice which gives the best fit to land-mobile and indoor-mobile multi-path propagation, as well as scintillating ionospheric radio links.
The paper is arranged as follows: In Section 2, we discuss the channel model for non-regenerative relay node. Section 3 describes various power allocation strategies. Simulation results investigating the ergodic capacity for various power allocation schemes are discussed in Section 4. Finally, conclusions are drawn in Section 5.
| 2. Channel Modeling | | |
We consider a system with a source node s communicating with a destination d with the help of relay node r. Each terminal is equipped with single transmit/receive antenna. The relays operate in the nonregenerative mode. Due to half duplex nature of relay, the source (s) transmits to the relay and destination in first phase and the relay transmits to the destination (d) in second phase. It is assumed that the channel between any node has→ single tap so we are restricting to the case of flat fading.
2.1 General Channel Model
In phase one, when s communicates with r and d, the relationship between x i input at ith node and y j output at jth node can be written as
Here i € {s,r}, j € {r,d}, P i is power transmitted by ith terminal, distribution of n j is complex gaussian with zero mean and σ2/2 variance per dimension, x i is signal vector, drawn from a white complex Gaussian code-book, of independent and identically distributed (i.i.d.) complex gaussian random variable (RV) i.e. N(0, 1). h ij captures the effect of path-loss and multi-path fading, which is modeled as
Here ℓ ij represents distance between node i and j, which is normalized by ℓ sd. ψ is path loss exponent. z ij is Nakagami-m distributed, representing the envelope of fading process. The envelope pdf is given by [ [10] , eq.(2)] i.e.,
where Γ(•) is the Gamma function,
E[•] denotes expectation. We consider here the fading process between nodes to be slow (large coherence time), flat (frequency non-selective) and ergodic over time.
2.2 Relay Channel Model
In nonregenerative mode, signal received at relay is multiplied by the gain of G r and then retransmitted to terminal d. So the received signal through r, at terminal d can be written as
P s is power transmitted by source terminal. SNR at the receiving end through relay path, can then be written as
In case of channel inversion G r is given as [ [11] , eq.(4)]
Here P r is power transmitted by relay. SNR received through relay path is given as
Here
For direct path SNR received at d
We assume that full CSI of both paths is available at d, so coherent combining of γsrd and γsd is possible. In such case, overall SNR at d can then be written as
| 3. Power Allocation | | |
In this section, we formulate the problem which will be investigated through simulation studies. We consider the scenario of a network in which individual node has upper bound of energy (i.e. limited power wireless terminals)
These terminals works in network of cellular type or works in unlicensed (ISM) band (total power radiated by network in this band should not exceed beyond specified level to avoid interfering other networks work in this band.) or total network is battery powered. Such types of network have upper bound on total power transmission. So transmitted power by source is given by
Here P T is total available power in this network. Trans mitted power by supporting relay is given by
Ergodic capacity for cooperative transmission is given as
In above equation (logarithm is of base 2 and for rest of the paper we continue with this representation), we multiply logarithm with 1/2 because, this system model works in two time slots and utilize only half channel degree of freedom. For faithful comparison between noncooperative (NOC) and cooperative transmission, both systems must be evaluated with the same average transmitted power from s. So, in case of NOC transmission, the s should transmit with the following power
Ergodic capacity for non-cooperative transmission is given as
3.1 Uniform Power Allocation
In traditional UPA, power is equally distributed between s and r, without CSI into account
This is one of the simplest schemes and supporting relay placed at middle gives optimum capacity gain [Figure 1].
3.2 Optimum Power Allocation
This is a centralized power allocation technique in which source should have full CSI between all nodes prior to transmission. In practice, it is feasible that the channels are estimated by sending training sequence before the actual message transmission, when each node operates in TDMA mode. When the source transmits the train ing bits, all relay nodes can simultaneously estimate their source-to-relay CSI due to the broadcast nature of the wireless medium. Similarly, when relay (r) transmits the training bits, the CSI of source-to-relay and relay-to-destination can be estimated at the source and destination respectively (We assume that forward and backward channels between the relay and destination are the same due to reciprocity. These transmissions occur on the same frequency band and same coherence interval). However, CSI of relay-to-destination can be available at the source only through channel feedback.
In a slow fading environment, frequent training is not necessary. Hence, in this case, we can neglect training period as compared to actual data transmission period. On the basis of CSI (i.e. γsd, γsr, γrd ), s distributes the avail able power (P T ) between s and r. So our primary objective is effectively utilizing the available power to boost γT at destination i.e.
It should be noted here that this problem is a convex problem, which means that it has a single global solution. Clearly, the objective function is γT of the channel. Using Lagrange multiplier maximization method, the modified objective function can be written as [7]
Here η1 , η2 , η3 , η4 and η5 are constants. Taking partial derivative of (19) with respect to P s, P r, η1 , η2 , η3 , η4 , η5 and equated to zero, gives optimal solution for P s and P r. Closed form expression for P s and P r from the prob lem formulated in (18) is difficult; so numerically we find the value of P s, P r and its average value is plotted in [Figure 2]. However, If we relax our problem such that
Then, optimal solution for P s and P r can be given as [ [6] , eq.(9)]
Here
and
On putting values of P s and P r in (14), we can calculate ergodic capacity.
3.3 Sub-optimum Power Allocation
In optimum power allocation, all instantaneous SNR (i.e. δsr , δrd and δsd ) should available at the source. Channel realization of δsr and δsd may be available to source through channel estimation but δrd will be available through channel feedback from r. Such feedback for each realization consumes a lot of bandwidth and power, so it may be impractical in real scenario.
Thus, we investigate suboptimum power allocation schemes when the source has full CSI of δsr and δsd and statistical CSI between r to d (i.e.  Statistical realization of channel  may remain constant for a long time and not require frequent update. Thus our modified objective function is to find the power allocation parameter P s and P r that maximize γT of the channel i.e.
Since finding an analytical solution to this problem is difficult, we numerically find the value of P s, P r for the problem formulated in (22) and its average value is plotted in [Figure 3].
| 4. Simulation Results | | |
This section presents the simulation model. In our scenario, source and destination are located at (0, 0) and (0, 100) respectively. Relay terminals are located at distance, which ranges from 2 to 98 and angular displacement from s-d reference plane ranges from -45° to +45°, shown in [Figure 4]. Path loss exponent (ψ) between s to r, s to d and r to d is 3. Noise variance at r and d is unity. The total network power (i.e. PT) and individual maximum transmitted for nodes (i.e. Psmax and Prmax ) is kept at 30 dbm and 29 dbm respectively.
Independent and uncorrelated RVs have been generated from (3), using rejection method [12].
Problems formulated in (18) and (22), are solved with the help of the optimization toolbox given in MATLAB. Closed form empirical expression for ergodic capacity is difficult to calculate, so we are calculating it with the help of the Monte Carlo method. Ergodic capacity for UPA and NOC scheme is calculated at various locations of the relay placement (for Nakagami parameter m =1) and plotted in [Figure 1]. In [Figure 2] and [Figure 3], power allocation between source and relay is plotted for the case of OPA and SPA, respectively. Ergodic capacity achieved by the system with the help of OPA and SPA schemes is plotted in [Figure 5] and [Figure 6] respectively, here each case is also compared with NOP scheme. In [Figure 7] and [Figure 8], we compare all four schemes when relay is placed at various locations of a line which forms angle of 0° at s from s-d reference plane, for the case of m is equal to 0.5 and m is equal to 4, respectively. We observe that, when m is equal to 0.5, ergodic capacity of SPA is below compared to OPA by 0.030 bits/sec/hertz and 0.012 bits/sec/hertz at 10 m and 90 m from source respectively. For case of m is equal to 4, performance of SPA is below than OPA is only 0.015 bits/sec/hertz and 0.002 bits/sec/hertz at 10 m and 90 m from source respectively.
| 5. Conclusion | | |
Efficient power utilization is an important issue in limited powered wireless relay network. In this paper we study the power allocation problem in a two-hop relay for different conditions. Ergodic channel capacity, for case of UPA, suffers when relay located near either of the source or the destination. As position of relay node moves to middle of s and d, it gives maximum performance. We observe that the SPA gives performance close to that of OPA without requiring full CSI. The difference of system performance for SPA compared to OPA decreases as relay moves towards d. Performance of SPA with respect to OPA improves (i.e. percentage of line of sight increases). However, OPA outperforms all the schemes in cost of system complexity. SPA is a suboptimum technique which greatly simplifies the implementation issue as it requires only statistical CSI between r and d along with instantaneous CSI between s-d and s-r. Performance of SPA outperforms UPA with a large margin. The schemes described in this paper are expected to be useful in designing cooperative relay network in real scenario.
| Authors | | |
 Himanshu Katiyar received his B.Tech. degree in Electronics and Communication from M.J.P. Rohilkhand University, Bareilly, Uttar Pradesh, India in 2001 and M.Tech. from Madan Mohan Malviya Engineering College, Gorakhpur, Uttar Pradesh, India in 2004. From 2004-2005 he was lecturer of Electronics and Communication Engineering Dept. at SRMSCET, Bareilly, Uttar Pradesh, India and from 2005-2006 he was lecturer of Electronics and Communication Engineering Dept. at NIEC, Lucknow, Uttar Pradesh, India. He is currently pursuing his Ph.D. in area of wireless communication at Indian Institute of Technology (IIT), Guwahati, Assam India. His research interests include almost all aspects of wireless communications with a special emphasis on MIMO systems, channel modeling, infrastructure-based two-hop/multi-hop and relay networks, cooperative diversity schemes. He has been selected for IETE Research Fellowship.
 Ratnajit Bhattacharjee received his B.E. in Electronics and Telecommunication Engineering (First Class Honors) from Gauhati University (REC (at present NIT) Silchar), M.Tech. (E and ECE Department, Microwave Engineering specialization) from IIT Kharagpur and Ph.D. (Engineering) from Jadavpur University Kolkata. Presently he is an Associate Professor in the Department of Electronics and Communication Engineering, IIT Guwahati. Prior to joining IIT Guwahati, he was a faculty member in REC (NIT) Silchar. His research interest includes Wireless communication, Wireless networks, Microstrip antennas, Microwave Engineering and Electromagnetics. He has published over sixty research papers in journals, international and national conferences. He has developed the web course on Electromagnetic Theory under the NPTEL project of MHRD. He has also been involved in several research projects. He has been a Co-investigator for the contracted research from NICT Japan in the area of Next Generation Wireless Networks and currently a member of the research team of the Tiny6 STIC project (funded by French ministry of Foreign Affairs), which deals with IPv6 and Sensor Networks. In NIT Silchar, he was a coordinator for the setting up of Campus Wide Optical Fiber based network under the Centre for Excellence scheme. He was also associated in a number of sponsored projects in the field of development of antenna system. He is a member of IEEE and life member of Indian Society of Technical Education.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8]
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