Design of MIMO Decode-and-Forward Relay Channels Using Optimal Co-operative Spatial Filtering

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1 Design of MIMO Decode-and-Forward Relay Channels Using Optimal Co-operative Spatial Filtering K.SHARMILA(M.E) Electronics and Communication Engg Jaya Engineering College Chennai, India B.K.SANTHOSHM.E Electronics and Communication Engg Jaya Engineering College Chennai, India Abstract-In this project a transmit beamforming design for multiple-input multiple-output (MIMO) decodeand-forward (DF) half-duplex two-hop relay channels with a direct source destination link is considered. For the scenario, where source, relay and destination nodes are equipped with multiple antennas. The optimal beamforming vectors for source, relay and destination nodes are formulated and solved jointly. Especially, several unique properties of the optimal solutions through mathematical derivation are identified, based on that we developed a systematic approach to arrive at the optimal beamforming vectors for the source, relay and destination nodes for different system configurations. The low-complexity expression is derived for the optimal beamforming vectors for some specific scenarios.results show that our proposed beamforming design scheme can achieve the optimal solution with low computational complexity for MIMO DF relay networks. Index Terms-BeamformingDesign, Multiple Input Multiple Output, Decode and Forward Relay channels I. INTRODUCTION Beamforming is a general signal processing technique used to control the directionality of the reception or transmission of a signal on a transducer array. Using beamforming you can direct the majority of signal energy you transmit from a group of transducersin a chosen angular direction. Or you can calibrate your group of transducers when receiving signals such that you pre-dominently receive from a chosen angular direction. The physics and math are essentially the same for both the transmitting and receiving cases, so I will concentrate on the transmission case to explain the concept further. I should mention as well that there are a few general approaches to directing this signal energy, but by far the most common is having a slightly different signal go out of each transducer in your group; this is the approach I discuss here. Another interesting but less common approach is sending the same signal to all transducers but with varying information encoded by frequency in that signal, requiring a broadband signal. However, it is known, the basic point in beamforming is, when you set multiple transducers next to each other sending out signals, you're going to get some kind of interference pattern, just like you see in a pond when you throw several stones in at once and create interfering ripples. If you select the spacing between your transducers and the delay in the transducers' signals just right, you can create an interference pattern that's to your benefit, in particular one in which the majority of the signal energy all goes out in one angular direction. To show this is true and what this looks like, I'm going to show a really simple example, using some sin waves being emitted from several point sources as seen below. In my example, to keep things simple I use a straight line array of transducers within a 2D field, although that introduces some direction ambiguity issues. This 130

2 direction ambiguity is remedied by not putting the transducers all in a line, but first things first. The sin waves below are moving out from all the sources just like ripples do in a pond, and I'm going to assign variables to my arrangement rather than numbers, so that I can change them and see how those changes affect my overall resulting interference pattern. So note I have a constant spacing d between each of my transducers, and an origin of some coordinate system centered on the center transducer. I'm going to use a polar coordinate system because I'm interested in seeing how my interference pattern affects things angularly, so note at each point theta, r in that coordinate system I have a particular wave amplitude. Theta is measured counter-clockwise starting from zero at the axis arrow on the right, matching the usual convention. II. BEAMFORMING TECHNIQUES To change the directionality of the array when transmitting, a beamformer controls the phase and relative amplitude of the signal at each transmitter, in order to create a pattern of constructive and destructive interference in the wave. When receiving, information from different sensors is combined in a way where the expected pattern of radiation is preferentially observed. For example in sonar, to send a sharp pulse of underwater sound towards a ship in the distance, simply transmitting that sharp pulse from every sonar projector in an array simultaneously fails because the ship will first hear the pulse from the speaker that happens to be nearest the ship, then later pulses from speakers that happen to be the further from the ship. The beamforming technique involves sending the pulse from each projector at slightly different times, so that every pulse hits the ship at exactly the same time, producing the effect of a single strong pulse from a single powerful projector. The same thing can be carried out in air using loudspeakers, or in radar/radio using antennas. In passive sonar, and in reception in active sonar, the beamforming technique involves combining delayed signals from each hydrophone at slightly different times, so that every signal reaches the output at exactly the same time, making one loud signal, as if the signal came from a single, very sensitive hydrophone. Receive beamforming can also be used with microphones or radar antennas. With narrow-band systems the time delay is equivalent to a phase shift, so in this case the array of antennas, each one shifted a slightly different amount, is called a phased array. A narrow band system, typical of radars, is one where the bandwidth is only a small fraction of the centre frequency. With wide band systems this approximation no longer holds, which is typical in sonars. In the receive beamformer the signal from each antenna may be amplified by a different weight. Different weighting patterns can be used to achieve the desired sensitivity patterns. A main lobe is produced together with nulls and sidelobes. As well as controlling the main lobe width and the sidelobe levels, the position of a null can be controlled. This is useful to ignore noise or jammers in one particular direction, while listening for events in other directions. A similar result can be obtained on transmission.for the full mathematics on directing beams using amplitude and phase shifts, see the mathematical section in phased array. Conventional beamformers use a fixed set of weightings and time-delays to combine the signals from the sensors in the array, primarily using only information about the location of the sensors in space and the wave directions of interest. In contrast, adaptive beamforming techniques generally combine this information with properties of the signals actually received by the array, typically to improve rejection of unwanted signals from other directions. This process may be carried out in either the time or the frequency domain. As the name indicates, an adaptive beamformer is able to automatically adapt its response to different situations. Some criterion has to be set up to allow the adaption to proceed such as minimising the total noise output. Because of the variation of noise with frequency, in wide band systems it may be desirable to carry out the process in the frequency domain. 131

3 Beamforming can be computationally intensive. Sonar phased array has a data rate low enough that it can be processed in real-time in software, which is flexible enough to transmit and/or receive in several directions at once. In contrast, radar phased array has a data rate so high that it usually requires dedicated hardware processing, which is hard-wired to transmit and/or receive in only one direction at a time. However, newer field programmable gate arrays are fast enough to handle radar data in real-time, and can be quickly reprogrammed like software, blurring the hardware/software distinction. III. COOPERATIVE COMMUNICATION SYSTEMS Ad-hoc wireless networks are based on multi-hop communications, where the information from the source to the destination is relayed via other mobiles. An ad-hoc network does not have a fixed infrastructure, so this relaying operation is essential in order to overcome the path loss incurred over large distances. Multi-hop ideas are also utilized in cellular and wireless LAN systems to provide higher quality of service, power savings and extended coverage. Information theory of multi-hop communication dates back to the relay channel model, which contains a source, a destination and a relay whose goal is to facilitate information transfer from the source to the destination. The relay channel wasintroduced by Van der Meulen and investigated extensively by Cover and El Gamal. Cover and El Gamal provided a number of relaying strategies, found achievable regions and provided upper bounds to the capacity of a general relay channel. They also provided an expression for the capacity of the degraded relay channel, in which the communication channel between the source and the relay is physically better than the source-destination link. The capacity of the general relay channel is still unknown. Motivated by the recent interest in multi-hop, a number of recent papers investigate the use of multiple relays. Some relevant references include. Even though the information theoretic model allows for the destination to listen to both the source and the relay, in most multi-hop systems the destination only processes the signal coming from the relay. This is justified in a wireless channelwhere path loss has the dominant effect. Since the source is generally further away from the destination than the relay, the received signal at the destination due to the source would be much weaker than the relay signal. However, when fading is also taken into account, this scheme would incur considerable loss, especially in diversity, compared to one in which the destination processes both signals. Hence one can use multi-hop not just to overcome path loss, but also to provide diversity. Motivated by the above observation, cooperative communication involves two main ideas: (i) Use relays to provide spatial diversity in a fading environment, (ii) Envision a collaborative scheme where the relay also has its own information to send so both terminals help one another to communicate by acting as relays for each other. One can think of a cooperative system as a virtual antenna array, where each antenna in the array corresponds to one of the partners. The partners can overhear each other s transmissions though the wireless medium, process this information and re-transmit to collaborate. This provides extra observations of the source signals at the destinations, the observations which are dispersed in space and usually discarded by current implementations of cellular, wireless LAN or ad-hoc systems. However, since the elements of this array are not co-located and are connected via noisy, fading links, it is not clear a priori how much the benefits of this cooperation would be. Our goal in this paper is to argue that the benefits, in terms of achievable data rates, diversity and error performance, are significant. In our discussion, we briefly describe some of our prior and ongoing work along with relevant literature, and provide directions for future research. We first provide an information theoretic model to describe the cooperative system, a set of achievable rates and an outage probability analysis. Then we talk about how one can design and analyze channel codes that can exploit the predicted benefits of a cooperative system. IV. MULTIPLE INPUT MULTIPLE OUTPUT In radio, multiple-input and multiple-output, or MIMO is the use of multiple antennas at both the transmitter and receiver to improve communication 132

4 performance. Multiple antennas may be used to perform smart antenna functions such as spreading the total transmit power over the antennas to achieve an array gain that incrementally improves the spectral efficiency (more bits per second per hertz of bandwidth,) or achieving a diversity gain that improves the link reliability (reduces fading,) or both. However, today the term MIMO usually refers to a method for multiplying the capacity of a radio link by exploiting multipath propagation. [1] This modern MIMO is an essential element of wireless communication standards such as IEEE n (Wi- Fi), IEEE ac (Wi-Fi), 4G, 3GPP Long Term Evolution, WiMAX and HSPA+. More recently, MIMO has been applied to power line communications for 3-wire installations as part of standard ITU G.hn and specification HomePlug AV2. V. OPTIMAL BEAMFORMING ALGORITHM In this project we consider the joint sourcerelay beamforming design for the three-node MIMO DF relay network with source-destination direct link. We assume that both the source and relay nodes are equipped with multiple antennas while the destination node is only deployed with single antenna. Such a transmission scenario is readily applicable to the downlink transmission of a relayenhanced cellular system where the base-station and the relay can accommodate multiple antennas but the mobile user equipment can only afford a single antenna due to size or other constraints. Note that downlink transmission to resource-limited mobile terminals limits the overall performance of cellular systems. As such, our design aims to fully explore the spacial diversity advantage of MIMO-DF relay channel to enhance system throughput to the destination node. Unlike existing work with MIMO DF relay channels, which relies on complex numerical solutions, we strive to derive the explicit expressions for the optimal beamforming design for our concerned model. Specifically, we identify several unique properties of the optimal solutions through mathematical derivation, based on which we develop a systematic approach to arrive at the optimal beamforming vectors for the source and relay nodes for different system configurations.we would like to stress that deriving the explicit expressions of the optimal beamforming design for our concerned model with single-antenna destination node is by no means trivial. This is because the MIMO channel between the source and the relay nodes and the multiple-input multiple-output (MISO) channel between the source and the destination nodes have to be jointly considered and balanced. In addition, our explicit solutions, which cannot be otherwise obtained as the special cases of previous work, offer interesting new insight to the design of MIMO DF beamforming. First, we formulate an optimization problem on the joint source and relay beamforming design for themimo DF relay channel, which actually is a max-min fairness optimization problem. For a better understanding of the optimal beamforming design, we do not follow some commonly used approaches, such as the semi-definite relaxation (SDR) method Instead, we first examine the properties of the optimal solutions. We effectively separate the phase angle design and real norm design problems for the optimal vectors. We also prove that the signal to noise ratio (SNR) of the MISO relay to destination channel can be regarded as a concave function of the SNR of the MIMO source to relay channel. Based these properties, we solve the optimal beamforming design problem in three cases. For the first and the second cases, we derive the explicit expressions for the optimal solutions. For the third case, as it is hard to drive the unified explicit result, we further divided it into three different subcases in terms of the number of antennas deployed at the source and relay nodes. For the scenario that two antennas are deployed at both the source and the relay nodes and single antenna is deployed at the destination node, i.e 2:2:1 scenario we derived the explicit expression of the optimal solution. For the scenario where Ns>1, antennas are deployed at the source and only one antenna is equipped on the relay and the destination nodes, i.e., Ns:1:1 scenario we present a non-iterative numerical method to calculate the optimal solution. For the general Ns:Nr:1 we present a non-iterative numerical method to calculate the optimal solution. scenarios, we first fix the SNR of the source-relay link and design the optimal beamforming vector to maximize the SNR of source-destination link. Then, we design 133

5 a Bisection based algorithm to find the optimal solution. Finally, we arrive at an optimal beamforming design solution. Extensive simulation results show that our proposed solution can achieve the optimal beamforming design for themimo DF relay channel with low complexity. Figure2:Achievable information rate vs the number of antennas N where NS=Nr=N VI. SIMULATION RESULTS In this section, we show the effectiveness of our proposed optimal beamforming design for MIMO DF relay channels through numerical examples. Without loss of generality, we assume Ps = Pr = Pin all simulations. Figure3: Beamforming Design for 4:4:4 Scenario using the optimal beamforming design for 4:4:4 attained are upto 7(bits/sec) Figure1:Average computing time of our proposed scheme vs the number of antennas,ns=nr=n Figure4: Beamforming Design for 4:1:4 Scenario using the optimal beamforming design for 4:1:4 attained are upto 4.6(bits/sec) 134

6 Figure5: Beamforming Design for 4:2:4 Scenario using the optimal beamforming design for 4:2:4 attained are upto 5.8(bits/sec) Figure7: Beamforming Design for 2:2:4 Scenario using the optimal beamforming design for 2:2:4 attained are upto5.2(bits/sec) CONCLUSION In this work, the beamforming design for MIMO DF relay channels is considered, where the source node, relay node, and the destination node are equipped with multiple antennas. We developed an efficient scheme to solve the optimization problem and determine the optimal beamforming vector for MIMO DF relay networks. Simulation results show that our beamforming design can achieve high accuracy and the optimal solution with lowcomputational complexity for MIMO DF relay channels. REFERENCES Figure6: Beamforming Design for 2:4:4 Scenario using the optimal beamforming design for 2:4:4scenariothe maximum achievable information rates attained are upto6.5(bits/sec) [1] Y. Yang, H. L. Hu, J. Xu, and G. Q. Mao, Relay technologies for WiMAX and LTE-advanced mobile systems, IEEE Commun. Mag., vol. 47, no. 10, pp , Oct [2] R. U. Nabar, H. Boölcskei, and F.W. Kneubühler, Fading relay channels: Performance limits and space-time signal design, IEEE J. Sel.Areas Commun., vol. 22, no. 6, pp , Aug [3] Q. H. Li et al., MIMO techniques in WiMAX and LTE: A feature overview, IEEE Commun. Mag., vol. 48, no. 5, pp , May [4] B.Wang, J. Zhang, and A. H.Madsen, On the capacity ofmimo relay channel, IEEE Trans. Inf. Theory, vol. 51, no. 1, pp , Jan [5] M. Gastpar and M. Vetterli, On the capacity of large Gaussian relay networks, IEEE Trans. Inf. Theory, vol. 51, no. 3, pp , Mar [6] S. Jin, M. R. McKay, C. Zhong, and K.-K. Wong, Ergodic capacity analysis of amplify-and-forward MIMO dual-hop 135

7 systems, IEEETrans. Inf. Theory, vol. 56, no. 5, pp , May [7] X. Tang and Y. Hua, Optimal design of non-regenerative MIMO wireless relays, IEEE Trans. Wireless Commun., vol. 6, pp ,Apr [8] O. M. Medina, J. Vidal, and A. Agustin, Linear transceiver design in nonregenerative relays with channel state information, IEEE Trans.Signal Process., vol. 55, pp , Jun [9] W. Guan and H. Luo, JointMMSE transceiver design in nonregenerativemimo relay systems, IEEE Commun.Lett., vol. 12, pp ,Jul [10] A. S. Behbahani, R. Merched, and A. M. Eltawil, Optimizations of a MIMO relay network, IEEE Trans. Signal Process., vol. 56, pp , Oct [11] Y. Rong and F. Gao, Optimal beamforming for nonregenerative MIMO relays with direct link, IEEE Commun. Lett., vol. 13, no. 12, pp , Dec [12] H. B. Wang, W. Chen, and J. B. Ji, Efficient linear transmission strategy for MIMO relaying broadcast channels with direct links, IEEE Wireless Commun. Lett., vol. 1, no. 1, pp , Feb [13] D. H. N. Nguyen, H. H. Nguyen, and D. H. Tuan, Distributed beamforming in relay-assisted multiuser communications, in Proc. IEEEICC, Dresden, Germany, Jun. 2009, pp [14] S. Vishwakarma and A. Chockalingam, Decode-and-forward relay beamforming for secrecy with imperfect CSI and multiple eavesdroppers, in Proc. IEEE SPAWC, Cesme, Turkey, Jul. 2012, pp [15] Y. Lu, N. Yang, H. Y. Dai, and X. X. Wang, Opportunistic decode- and-forward relaying with beamforming in two-wave with diffuse power fading, IEEE Trans. Veh. Technol., vol. 61, no. 7, pp , Jul [16] Z. F. Xu, P. Y. Fan, H. C. Yang, K. Xiong, M. Lei, and S. Yi, Optimal beamforming for MIMO decode-and-forward relay channels. GLOBECOM 2012: , in Proc. IEEE Globecom, Dec. 2012, pp [17] H.Bölcskei, R.U. Nabar, O. Oyman, and A. Paulraj, Capacity scaling laws in MIMO relay networks, IEEE Trans. Wireless Commun., vol. 5, no. 6, pp , Jun Second Author: B.K.Santhosh, he served as an Assistant Professor in reputed Engg colleges for more than 6 years. He received his Bachelor s degree from the Department of Electronics and Communication Engineering and Master Degree in the field of Applied Electronics. He has presented his paper in many National level Conferences and published his paper in many famous Journals. He served many roles in the Department such as Project co-ordinator, placement co-ordinator, and symposium co-ordinator and discipline committee member. His research interest include signals and systems, VLSI and wireless communication. First Author: K.Sharmila, She is been a creative professional with passionate towards teaching and convey educational concepts through innovative approaches. She received the Bachelor s degree from the Department of Electronics and Communication Engineering in 2008 and currently studying M.E, in the field of Applied Electronics in Jaya Engg College(affiliated by Anna University). Her B.E project is based on wireless identification system, titled Optically Interrogated Smart Tagging and Identification System. In 2015, her research work is based on Design of MIMO D-F Relay channels using Spatial Filtering.She has won many awards for her academic performances and Prizes in many competitions including Oratorical,Debate. Her research interested fields also include wireless communication, system performance and energy efficient communication. 136