OFDM FOR COOPERATIVE NETWORKING WITH ... - CiteSeerX

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OFDM FOR COOPERATIVE NETWORKING WITH LIMITED CHANNEL STATE INFORMATION Bo Gui, Leonard J. Cimini, Jr., and Lin Dai Department of Electrical and Computer Engineering University of Delaware Newark, DE 19716 USA Email:{bgui,cimini,dai}@ece.udel.edu

ABSTRACT

In this paper, we investigate the use of OFDM to facilitate cooperation among relays in a wireless network. In particular, we consider different relay and subchannel assignment and combining schemes. Based on the amount of channel state information, resources, such as subchannels, can be allocated to relays to improve the end-to-end performance. Simulation results are provided to compare the performance of these schemes in terms of block error rate. It can be seen that significant performance gains can be obtained even with little channel state information at the relays. I. I NTRODUCTION In cooperative systems, a group of single-antenna nodes transmit together as a ”virtual antenna array,” obtaining diversity gain without requiring multiple antennas at individual nodes. Significant benefits are possible, including a power gain (relay power), a macrodiversity gain (a gain in the median SNR), a microdiversity gain (a gain in the instantaneous SNR), and path diversity (longer times between route failures). Much recent work has addressed aspects of cooperative diversity, and it has been demonstrated that adding this dimension has the potential to enormously expand the capabilities of wireless networks. (for example, see [1]-[5]). The use of multiple antennas is just one of several breakthroughs in wireless communications. Another equally important development is the use of multicarrier transmission, specifically Orthogonal Frequency Division Multiplexing (OFDM), to enable the high bit rates demanded by current and emerging applications [6]-[7]. OFDM is the underlying physical-layer technology for IEEE802.11 (WiFi) [8], as well as for digital audio [9] This material is based on research sponsored by the Air Force Research Laboratory, under agreement number FA9550-06-1-0077. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.

and video broadcasting [10]. In addition, OFDMA, a multiple access technique in which the subchannels of an OFDM symbol are shared by multiple users, has significant advantages that have made it the natural choice for commercial broadband wireless networks, such as IEEE802.16 (WiMAX) [11], as well as for the long-term evolution of third-generation cellular systems (specifically for the downlink). The modularity of OFDM and the fact that it will be used in many current and future systems makes it very appealing for consideration in cooperative wireless networks. More importantly, the use of orthogonal signaling and the inherent frequency diversity in a well-designed OFDM system are especially useful in attempting to obtain the maximum benefits from cooperation - in both single- and multi-source applications. Achieving these gains, however, depends on devising practical relay and subchannel management strategies with different levels of channel state information (CSI). Although there has been a significant effort on the study of cooperative systems, there has been very little work on the use of OFDM in these networks. In most of the work in this area, OFDM is simply the underlying transmission technology. Relatively few works, notably [12] and [13], incorporate the assignment of individual subchannels into the cooperation among relays. In [12], with amplify-and-forward relaying, OFDMA is used to enable a node to transmit both its own information as well as that from another source by partitioning the set of subchannels. The focus of this work is on optimizing the resource assignment problem to determine which nodes help other nodes, how many subchannels are allocated for helping, and how many are allocated for sending their own data. The solutions that are presented come from a complex optimization that requires global knowledge of the channel conditions and the transmit powers. In [13], a subcarrier allocation scheme with two-user cooperation is proposed for cellular systems, and it is assumed that the base station can assign ”good” subchannels to users based on their feedback.

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In this paper, we focus on the use of OFDM as a relay management strategy to facilitate cooperation among nodes in a wireless network. In particular, we study the performance of various schemes for assigning subchannels to nodes in the presence of varying amounts of CSI at the relays. The paper is organized as follows: In Section II, the system model is described. In Section III, we present relay and subchannel assignment strategies that will be evaluated for different CSI conditions in Section IV. Conclusions and a discussion of the next steps in this work are provided in Section V. II. S YSTEM MODEL Consider a network with N + 2 nodes, so that, for a given source-destination pair, there are N potential relays. An OFDM transceiver with K subchannels is available at each node. We assume perfect time and frequency synchronization among nodes and the inclusion of a cyclic prefix that is long enough to accommodate the delay spread of the channel. With these assumptions, the received signal in the k th subchannel of node i from node j is Rij (k) = Xij (k)Hij (k) + Nij (k), where Xij (k) is the transmitted data in the k th subchannel, Nij (k) is additive white Gaussian noise in that subchannel, and Hij (k) is the channel frequency response in the k th subchannel between node i and node j . We assume that the impulse response of the channel is of length L. In general, the channel response includes path loss, shadowing, and Rayleigh fading. As has become customary, a two-stage transmission protocol, as shown in Fig.1, is adopted (for example, see [5]). In the first stage, the source transmits and the other nodes listen - the links in this stage are called source-relay (SR) links. In the second stage, the relays retransmit the message to the destination - the links in this stage are called relay-destination (RD) links. Relaying strategies include amplify-and-forward, where nodes simply amplify the received signals, and decodeand-forward, where the nodes first decode the signal from the source and then re-encode and retransmit it. Here, we focus on the decode-and-forward approach. An illustration of the use of OFDM for cooperative relaying with a single source is shown in Fig. 2. Here, the source transmits the message as an OFDM block of 8 subchannels. Relays R1 and R2 receive the transmission from the source but, because of fading across the frequency band, R1 can only decode subchannels 1, 4, 5, and 8, and R2 can decode subchannels 2, 3, 6, and 7. The relays will then retransmit this information on to the destination using an appropriate protocol for cooperation. In some ways, this is very similar to the uplink of an OFDMA system. There are, however, some significant

Fig. 1. Two-stage transmission protocol: In the first stage, the source transmits; In the second stage, those nodes which can decode the message from the source retransmit it to the destination.

differences, including: (1) the first stage transmission might be received in error which could result in gaps in the transmission and (2) cooperation among the nodes is available to provide an improvement in performance.

Fig. 2. A simple example of using OFDM as a relay strategy in cooperative systems.

Which subchannels to use from each relay to the destination and how to precode them are very important considerations and a main focus of the next section. Under ideal conditions, this approach can provide a significant level of diversity and, consequently, a significant gain in performance. Clearly, the level of CSI at the nodes about the relay-to-destination link is very important, as is the level of communication among the relays. For example, if the relays have complete knowledge of the CSI at the receiver, they can optimally choose a protocol to maximize the throughput and/or minimize the transmitted power. III. RELAY/SUBCHANNEL MANAGEMENT In this section, we discuss the various levels of CSI considered and the implications for relay and subchannel selection and precoding. A. No CSI When there is no information about the RD links available, the relays are limited in what they can do to maximize performance. In this case, the nodes can

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B. Full CSI Here, we assume that the relay nodes have complete knowledge of the channel characteristics for the RD links (measured and fed back by the destination); with this knowledge, significant performance advantages can be obtained. If the channel gain and phase measured at the destination are available, the relay can use the maximal ratio principle to optimally precode the transmitting signals to maximize the SNR at the destination (for example, see [15]). This technique, however, requires a significant amount of feedback. Although it might be possible to implement this in an infrastructure-based network with low mobility, in many applications, it will be unrealistic. C. Partial CSI The most interesting, and realistic, case is one in which some limited amount of information is available at the relays. What information is required and how much is an important issue if these systems are ever to be realized. Here, we will focus on a selection-based approach. We assume that the destination node has some information about the channel from each of the relay nodes to the destination. For a specific subchannel, it is relatively easy for the destination to select the relay with the best signal to retransmit the information in that subchannel. So, the destination can decide which subchannels will be transmitted by which relays; this information can be fed back to the relays in broadcast mode. In this way, each subchannel is transmitted by only one relay. The total feedback information, in this

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transmit in a simple relay scheme or transmit using a space-time (ST) code [4]. With OFDM, however, only those subchannels which were received correctly at a relay can be retransmitted by that relay. For the simple relay approach, all of the relays simultaneously transmit the subchannels they were able to decode. There will be no space diversity advantage in this case because the received signal at the destination is simply the random combination of the retransmitted signals. In the ST-coded approach, each relay transmits one column of a ST block code. To avoid different relays transmitting the same column of the code, the relays could use a pre-assigned column of the ST-code matrix or a central controller could specify which column to use [4]. Alternatively, some random combination of columns could be employed by a given relay [14]. An orthogonal ST block code is favored for its simple decoding method; when there are more than two relays, however, full-rate full-diversity codes only exist for real constellations.

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Fig. 3. CBR adaptive loading. The number of bits per symbol in each subchannel (solid line) is matched to the frequency response of the multipath channel (dashed line).

case, will be N K bits. The destination could make these decisions based on the instantaneous channel gains or based on some statistic, such as the mean channel gain. D. Adaptive Loading The knowledge of the channel characteristics can also be used to optimally assign subchannels to each relay and to control both the power and modulation on each subchannel (for example, see [16]). Here, we focus on adjusting the modulation to match the multipath channel - often called adaptive loading [17]-[18]. This approach can best exploit the frequency diversity inherent in a frequency-selective channel. The basic idea is simple put more bits in the good subchannels and less in the bad subchannels. It has been shown that dramatic gains can be achieved with adaptive loading. There are two types of adaptive loading algorithms: constant-bit-rate (CBR) and variable-bit-rate (VBR). For CBR, the number of information bits in each block is the same (that is, the loading only happens in frequency domain), while the VBR algorithm changes the number of bits in each block (that is, the loading is done in both the time and frequency domains). Here, to maintain the same information rate, we adopt the CBR approach and use the classic algorithm in [18]. In Fig. 3, an example is given using adaptive loading with sixteen subchannels. The number of bits per symbol in each subchannel (solid line) is matched to the frequency response of the multipath channel (dashed line). Here, the modulation type of each subchannel is either QPSK, 8PSK or 16QAM. Because the destination has information about all of the RD links, the parameters for the adaptive loading

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In this section, we compare the performance of the different relay schemes in terms of the end-to-end block (OFDM symbol) error rate. In the simulated system, there are N = 2 relay nodes, which are located in the middle of the source-to-destination path. Each relay has the same distance to the source and the destination. This effectively ignores the effects of path loss. Shadowing is not considered in the simulation. We also assume that the channels between the source and each relay and the channels between each relay and the destination are independent. The power delay profile is assumed to be exponential with a root-mean-square delay spread τrms = 0.1T , where T is the time duration of one OFDM symbol (block) and T = KTs . In the simulation, we use a discrete-time model with an impulse response limited to 16 samples spaced by Ts . This is sufficient to encompass all of the paths with significant energy. We assume the total transmit power of the relay nodes is the same as the transmit power of the source node. The average SN R of the SR link and the average SN R of the RD link is represented by γsr and γrd , respectively. QPSK is assumed on each subchannel, except for the adaptive loading case, where QPSK, 8PSK and 16-QAM are employed. For the ST-Coded case, the Alamouti scheme is employed [19]. Performance is given in terms of the Block Error Rate, which is the probability that an OFDM symbol was received in error. We consider two scenarios. In the first scenario, we assume γsr = ∞ so that the SR link is error-free. In the second scenario, the SR link is not perfect. The first scenario is similar to the conventional OFDMA uplink; however, in the cooperative system, all the relays have the same data to transmit. The performance of this scenario serves as a bound for the more realistic second scenario, in which errors occur in the first stage of transmission. We first consider the perfect SR link case, i.e., γsr = ∞. The Block Error Rate as a function of the average SN R of the RD link γrd is shown in Fig. 4 for spacetime coding (STC), selection, maximal ratio transmission (MRT), and adaptive loading, illustrating the benefits of increasing levels of CSI. We can see that the STC scheme has the worst performance, which is reasonable, because it does not require any CSI. The selection scheme is

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IV. S IMULATION RESULTS

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(that is, the number of bits/symbol for each subchannel) can be computed at the destination and fed back to the relays. Assuming there are 2M possible modulation types, the total number of feedback bits is N KM (N relays, K subchannels, M bits).

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Fig. 5. Imperfect SR link scenario ( γsr = γrd ). As expected, the performance deteriorates for all the strategies.

only a little bit worse than MRT, which requires full CSI at the relays. Under these conditions (small number of relays), the significant overhead required for MRT results in only a minimal performance advantage. As expected, with adaptive loading, a significant gain is possible at the expense of increased complexity. Next, consider the practical scenario, where the SN R in the RD link is finite. Specifically we will assume that γsr = γrd . When there are errors in the SR link, the performance, as expected, is worse for all of the techniques because some subchannels are now not available at the relays for transmission. Simulation results are shown in Fig. 5. The adaptive loading approach is most sensitive to the errors in the SR link. The STC, selection and MRT schemes, however, are now very similar in performance. For any approach, the end-to-end performance is limited by the worst link in the transmission. In Figs. 6 and 7, we illustrate the more general

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case where the SN R in the two links are different. Specifically, we assume that the SN R in the SR link γsr is higher than the SN R in the RD link γrd by some amount ∆γ , i.e., γsr = γrd + ∆γ . For example, the SR link might be heavily coded to guarantee improved reception at the relays. The end-to-end performance of the adaptive loading scheme with different values of ∆γ is presented in Fig. 6. The performance of the selection scheme with different values of ∆γ is presented in Fig. 7. Compared to the improvement of adaptive loading scheme, the end-to-end performance improvement of selection is much smaller. The diversity benefit for this approach is limited by the fact that only two relays are employed. this is also true for MRT. We can also interpret these results in terms of different network configurations. For example, the case where γsr = ∞ could correspond to the situation where all of the relays are very close to the source - similar to conventional MIMO transmission. On the other hand, when γsr is small, but γrd is large, the relays are close to the destination and behave essentially as a receive antenna array. In addition to coding in the SR link, the performance can also be improved by utilizing more relays. Here, we consider the case where N = 4. Again, all of the relays are assumed to be located in the middle of the sourceto-destination path. We also assume that γsr = γrd . The end-to-end block error rate performance of the different relaying schemes is presented in Fig. 8. Because there are no full-rate and full-diversity orthogonal ST block codes for four antennas, we consider the following three cases. The first one (STC1)still uses the Alamouti code (i.e, a 2X2 matrix) and assigns the the first column of the code to the first two relays and the second column to the other two relays. The diversity order is only two in this case.

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To get better performance, in the second case (STC2), we select the best two of the four relays and again use the Alamouti scheme for retransmission. In the third case (STC3), we employ a 3/4-rate 4×4 orthogonal ST block code over the 4 relays. Obviously, the STC schemes perform the worst because they require no CSI at the relays. STC3 provides the greatest diversity benefit, but at a lower rate. STC2 performs fairly well with no sacrifice in rate but requires some communication among the relays. The techniques that require some level of CSI (selection, MRT, and adaptive loading) can provide significant gains in performance with varying levels of complexity. In all cases, however, the addition of more relays provides increased diversity and power gain. V. C ONCLUSIONS AND F UTURE W ORK In this paper, we consider the use of OFDM as a relay management strategy to facilitate cooperation in wireless networks. In particular, we take preliminary steps in

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evaluating different relay and subchannel assignment and combining strategies with different levels of CSI at the potential relay nodes. Simulation results are presented for an idealized network configuration, with no path loss and shadow fading, to illustrate the potential space and frequency diversity benefits, as well as the limitations when subchannels may not be available for retransmission. As expected, when complete information about the relay-destination link is available at the relay nodes, dramatic gains are possible. Nevertheless, significant gains are still possible with more limited CSI, even with little or no node communication. Much remains to be investigated in this area. First, a more complete study of the diversity benefits of subchannel assignment must be performed. This would include path loss and shadow fading (and a random distribution of nodes in space). Second, an investigation of some of the practical issues related to OFDM and OFDMA systems is warranted. This would include synchronization (such as timing and frequency offset estimation) and channel estimation. Finally, the extension of these approaches to both multihop networks and multi-source transmission will be pursued. R EFERENCES [1] A. Sendonaris, E. Erkip, and B. Aazhang, ”User cooperation diversity-Part I: system description,” IEEE Trans. on Commun., vol. 51, pp. 1927-1938, Nov. 2003. [2] A. Sendonaris, E. Erkip, and B. Aazhang, ”User cooperation diversity-Part II: implementation aspects and performance analysis,” IEEE Trans. on Commun., vol. 51, pp. 1939-1948, Nov. 2003. [3] A. Nosratinia, T. E. Hunter, and A. Hedayat, ”Cooperative communication in wireless networks,” IEEE Commun. Mag., vol. 42, pp. 74-80, Oct. 2004. [4] J. N. Laneman and G. W. Wornell, ”Distributed space-time coded protocols for exploiting cooperative diversity in wireless networks,” IEEE Trans. on Inform. Th., vol. 49, pp. 2415-2425, Oct. 2003. [5] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, ”Cooperative diversity in wireless networks: efficient protocols and outage behavior,” IEEE Trans. on Inform. Th., vol. 50, pp. 3062-3080, Dec. 2004. [6] R. V. Nee and R. Prasad, OFDM for Wireless Multimedia Communications, Artech House, 2000. [7] L. Hanzo, M. Munster, B. J. Choi, and T. Keller, OFDM and MC-CDMA for Broadband Multi-user Communications, WLANS, and Broadcasting, Wiley, 2003. [8] IEEE802.11, Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, IEEE August 1999. [9] ETSI, Digital Audio Broadcasting (DAB), 2nd ed., May 1997, ETS 300 401. [10] ETSI, Digital Video Broadcasting (DVB); Framing structure, channel coding and modulation for digital terrestrial television, Aug. 1997, EN 300 744 V1.1.2. [11] IEEE802.16-2004, IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface, IEEE, 2004.

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