The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’07)
RELAY-ASSISTED RE-TRANSMISSION SCHEME BASED ON MUTUAL INFORMATION FOR WIRELESS MESH NETWORKS Hironobu HATAMOTO, Shinsuke IBI, Seiichi SAMPEI Graduate School of Engineering, Osaka University, JAPAN
[email protected], {ibi, sampei}@comm.eng.osaka-u.ac.jp A BSTRACT This paper proposes a relay-assisted re-transmission scheme based on mutual information for wireless mesh networks. In the proposed scheme, re-transmission is done not from the source node but from the relay node, and minimal amount of spectrum corresponding to the remaining uncertainty for the data sequence is re-transmitted, where the number of spectrum components to be fed back is determined based on expected mutual information after re-transmission. Moreover, to directly convert reduction of feedback spectrum to spectrum efficiency improvement in carrier sense multiple access with collision avoidance (CSMA/CA) introduced systems, the re-transmitted spectrum is mapped on whole the bandwidth with equal spacing, thereby the time duration for the retransmission is reduced. Computer simulation confirms that the proposed scheme can achieve much higher system throughput efficiency especially than the conventional two-hop transmission schemes. I
I NTRODUCTION
Realization of broadband networking society having throughput of 100 Mbit/s to 1 Gbit/s is the most important challenge for broadband wireless communication technologies [1]. However, such high throughput cannot be achieved without increase of transmit power or reduction of cell size, because currently achievable receiver sensitivity is already very close to Shannon limit [1]. Heterogeneous networking by integration of hot spot wireless local area network (LAN) and cellular system is a current technology to partially solve this problem. However, wireless LAN is not sufficient to cover a large area because huge number of access points are necessary. Therefore, it is necessary, we believe, to deploy a high coverage broadband infrastructure that covers a dead spot of broadband cellular systems not by hot spots but by hot areas using more organised wireless mesh networks [2]. In the mesh networks, throughput from source to destination nodes is determined by the tradeoff between the link throughput enhancement due to reduction of inter-node distance and the number of hops; although throughput is increased by the reduction of distance, it is decreased by the number of hops. Therefore, this paper will discuss how to increase inter-node distance by the assist of a relay node to enhance throughput in mesh networks. Automatic repeat request (ARQ) is a very popular technique to enhance reliability of radio links. Among many ARQ protocols, Chase combining [3] and incremental redundancy [4] are very popular in the 3G networks. In the Chase combining, c 1-4244-1144-0/07/$25.002007 IEEE
when the received frame is not correctly detected, the same frame signal is re-transmitted and they are coherently combined in the destination node [3], whereas, parity bits not yet transmitted are transmitted in the re-transmission process in the incremental redundancy protocol [4]. However, from the viewpoint of information theory, it is sufficient to re-transmit the amount of information that corresponds to conditional entropy given by the difference between entropy of the source signal and obtained mutual information between the original information and the received signal. In the case of both Chase combining and incremental redundancy protocols, the amount of re-transmitted information is not determined by the information theory basis. Therefore, this paper will consider a network information theory-based re-transmission protocol [5] suitable for wireless mesh networks. A strategy to increase inter-node throughput is how to reduce re-transmission frequency as well as to reduce the amount of information in the ARQ process [6]. To clarify problems and strategies for ARQ protocols in the mesh networks, we will assume a three node scheme that consists of source, destination and relay nodes, where the distance between source and destination nodes is longer than the distance between source and relay nodes as well as that between destination and relay nodes. In such a case, when the source node transmits a data stream to the destination node, although the destination node cannot correctly detect the signal, the relay node can detect the signal with higher probability. Thus, it is more reasonable to conduct retransmission, not from the source node but from the relay node. However, it is not economical to prepare a dedicated relay node for all the possible combination of nodes; How to reduce relay node assisted time duration would be a key to enhance overall throughput. Thus, this paper will propose a re-transmission scheme in which the re-transmission is done not from the source node but from the relay node, and minimal amount of information corresponding to the remaining uncertainty for the data sequence is re-transmitted. In this case, how to identify the remaining uncertainty after the first transmission is a key. In the case of broadband transmission, serious distortion in the received signal is mainly caused by deeply faded spectra, which suggests that deeply faded spectra could be the main cause of uncertainty in the received signal. Therefore, the relay node will re-transmit a certain amount of deeply faded spectra, and they are combined with previously received signal in the frequency domain to increase mutual information in the destination node. In the proposed scheme, we will also assume carrier sense multiple access with collision avoidance (CSMA/CA) as a media access control (MAC) protocol. In the case of CSMA/CA applied systems, reduc-
The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’07)
Source node
Destination node 1st Transmission
NACK 1st Transmission Re- transmission
Relay node
Figure 1: Mesh network model tion of the transmission time duration is the most direct way to save radio resource. Therefore, reduction of the amount of retransmitted spectrum is converted to reduction of transmission time duration using a dynamic spectrum control technique [7] in the proposed scheme. The reminder of this paper is organised as follows. Section II describes the considered system model in this paper. A mutual information based re-transmission control is proposed in Section III. Simulation results are presented and discussed in Section IV. Section V concludes this paper. II
S YSTEM MODEL
Wireless mesh networks are intended to build more robust, more reliable and higher throughput than what is called ad hoc and multi-hop configurations. When a mesh network is constructed, we usually expect capacity enhancement due to shorter link distance in each hop and route diversity effects. However, larger number of hops could cause overall throughput reduction. Therefore, enhancement of link throughput while minimising the number of hops would be the most important issue for system level throughput enhancement in wireless mesh networks. Figure 1 shows a primitive unit that consists of a mesh network. This unit consists of source, destination and relay nodes. Key points for link throughput enhancement are 1. to increase distance between source and destination nodes to minimize the number of hops. 2. to reduce time period for re-transmission to minimize radio resource usage for re-transmission in the CSMA/CA applied systems. In single carrier broadband transmission schemes, when distortion due to channel is equalized, the quality of each symbol in a frame is just the same, and whether each symbol is errored or not is determined by the probability. This means that it is very hard to detect which part of the received signal in the time domain should be re-transmitted. Therefore,
whole the frame or parity bits that are not transmitted yet are retransmitted in the conventional ARQ process. However, when the received signal is observed in the frequency domain, we can easily find the main cause for performance degradation; deeply faded frequency components due to frequency selective fading. In other words, we can expect an efficient re-transmission if deeply faded spectrum components are transmitted again in the re-transmission process. For such a purpose, the transmitted signal should be decomposed in a discrete spectrum form. Fortunately it can be done by framing the transmitted symbol sequence every Nd symbols, and conversion of the signal to frequency domain signal using a discrete Fourier transform (DFT), because DFT process is equivalent to carrying out the Fourier transform assuming that the Nd symbol block continues periodically. Of course, cyclic prefix (CP) that appends the last part of each frame at the head of the frame is necessary to guarantee periodicity of the received frame even under frequency selective fading conditions. Moreover, once the spectrum can be decomposed in a discrete spectrum form, we can flexibly change locations of the components provided that such a spectrum location exchange rule is agreed between source and destination nodes. Let us assume that only a part of the spectrum is retransmitted, and the spectrum ratio for the re-transmission is β (= 1, 1/2, 1/4, . . .). In this case, when the re-transmitted spectrum components are distributed in whole the bandwidth with an equal frequency separation, we can reduce the time period of transmission by 1/β, which means that we can reduce a necessary time period for re-transmission if the number of feedback spectrum components are getting smaller. Moreover, to further improve reliability of the re-transmitted signal, re-transmission is done not by the source node but by the relay node because the relay node received the first transmission with higher quality than the destination node, and it can also re-transmit necessary spectrum components to the destination node with higher quality than the source node. As a result, a remaining problem is how to determine the re-transmitted spectrum ratio β. In the proposed scheme, β is determined by the estimation of mutual information at the output of the adaptive equalizer, which will be detailed in the next section. III
P ROPOSED RE - TRANSMISSION
A Calculation of mutual information In order to perform an efficient re-transmission, we consider mutual information I (0 ≤ I ≤ 1) by the detection of the received signal. Mutual information is a percentage of the acquired knowledge on the transmitted information by the detection of the received signal. A key point is that it does not matter whether the detected frame is error or not. When a frame error is occurred, it means that the obtained mutual information at the equalizer output is insufficient for the following channel decoder to correct every errors. Even though the frame is errored in the detection process, the destination node acquired a certain amount of mutual information. Therefore, in the retransmission process, the relay node re-transmits deeply faded
The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’07)
spectrum components in the first transmission in a shorter time period, and the received signal is coherently combined with the received signal for the first transmission based on maximum radio combining (MRC). As a measure for mutual information, we use a J-function that converts SNR of the equalizer output to mutual information [8], [9]. However, mutual information calculation with J function is premised on the Gaussian process of the received symbols. To satisfy this condition, it is assumed that the frame size that corresponds to the DFT size K, is sufficiently long. As for the equalizer, a frequency domain equalizer (FDE) based on minimum mean square error (MMSE) is employed. B
When a destination node fails in demodulation of the received symbol vector rSD with its size of K × 1, it transmits a negative acknowledgement (NACK) signal to the relay node. When the relay node receives the NACK signal, it performs the re-transmission in the following procedures. Just after the reception of the first transmission from source to destination nodes, the relay node demodulates the signal and stores the detected data. Once the NACK signal is received at the relay node, the stored data are coded, and the transmitted signal vector in the frequency domain with its size of K × 1 s˜f is regenerated. According to the spectrum index for re-transmission requested via the NACK signal, discrete spectra to be bed back is chosen from s˜f , and the spectra are distributed on whole the system band with an equal frequency space. This operation is performed by using a spectrum masking and mapping matrix M with its size of K × K. For example, when K is set at 8, β is set at 1/2 and, 1st, 2nd, 3rd and 8th spectrum components are mapped onto 1st, 3rd, 5th and 7th frequency positions, M is given by 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (1) M= 0 0 1 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 The relay node re-transmits the created partial spectrum signal sfRelay , which is represented by a relay signal vector in the frequency domain with its size of K × 1 as (2)
Using M, the time interval of the re-transmitted waveform is shortened thereby increasing the system throughput. For example, when all the bandwidth is used for half of the spectrum component re-transmission (β = 1/2), its re-transmission time duration becomes a half. Frequency domain received signal vector from relay to desf with its size of K × 1 is obtained as tination nodes rRD f f = ΞRD sfRelay + νRD rRD
Initial re-transmission rate β selection No
β=1 ?
(3)
Yes
Mutual information I E calculaiton I E > IthE ?
No
Higher rate β selection
Yes
End
Re-transmission scheme by the relay node
sf . sfRelay = M˜
Start
End
Figure 2: Mutual information based re-transmission rate detection algorithm where ΞRD is a diagonal matrix with its size of K × K and it’s diagonal components represents the frequency transfer funcf is frequency domain tion from relay to destination nodes, νRD noise vector with its size of K ×1, which is subject to Gaussian process with its mean value of zero and variance of N0:RD . In the destination node, when the transposed matrix of M is f , we can obtain the re-transmitted spectrum multiplied to rRD f with size of K × 1 as components vector rRD:demask f f rRD:demask = MT rRD f = MT ΞRD M˜ sf + MT νRD .
(4)
After the reception of this signal, this signal and already ref are combined using MRC in order to compensate ceived rSD for deterioration spectra. C Re-transmission rate detection algorithm based on mutual information In the destination node, re-transmission rate is determined based on the expected mutual information at the output of equalizer after the re-transmission. In [10], if Turbo coding is applied to a channel coding and equalizer output mutual information I E (0 ≤ I E ≤ 1) is more than 0.6, decoder output mutual information I D (0 ≤ I D ≤ 1) can reach 1.0 with probability of 99%. Therefore, it is desirable to determine the re-transmission rate in order that I E after the re-transmission will be more than 0.6. Figure 2 shows the re-transmission rate detection algorithm based on mutual information. Before the destination node returns the NACK signal, it calculates expected I E after retransmission using J function. Firstly, β is set at 1/4, and I E is E calculated. If I E is more than the threshold Ith , the destination node requests the re-transmission set as β (= 1/4). Otherwise, β is set at 1/2, and the destination node calculates the expected I E again. This process is repeated until β is expected to satisfy I E of more than 0.6 or β reaches 1. When β of 1/2 or less is chosen, re-transmission frame length can be shortened, thereby radio resource can be saved in the CSMA/CA employed systems.
The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’07)
Source node
Destination node 1st Transmission
NACK 1st Transmission Re- transmission
Relay node (a) Re-transmission with relay terminal 1st Transmission
Source node
Destination node NACK Re- transmission
Table 1: Simulation parameters Modulation (Coding rate) Bit interleaved QPSK (1/2) Turbo code (4 iterations) Channel coding (Constraint length 4) Max-Log-MAP Decoder with correction factor Data symbol length 2048 symbols Cyclic prefix length 64 symbols Interleaver Random Equal gain Path model 24-spike Rayleigh model Num. of Tx antennas 1 Num. of Rx antennas 1 Re-transmission rate β 1, 1/2, 1/4 Channel estimation Perfect
(b) Re-transmission without relay terminal
Source node 1st Transmission
2nd Transmission
Relay node
E
(c) 2-hop transmission
I (C.D.F. = 10 %)
Destination node
Figure 3: Simulation models IV A
S IMULATION RESULTS
w/ Relay node w/o Relay node 2−hop Transmission
1
2
Simulation parameters
The performances of the proposed re-transmission scheme based on Fig. 3 are evaluated by the computer simulation. Three models are evaluated; the proposed re-transmission with relay node (model (a)), conventional re-transmission without relay node (model (b)) and conventional 2-hop transmission (model (c)). Table 1 shows simulation parameters. In this simulation, the number of re-transmissions is limited to one. In this simulation, (Es /N0 )SD means the received Es /N0 between source and destination nodes. The average Es /N0 between source and relay nodes as well as relay and destination nodes are assumed to be 6 dB higher than (Es /N0 )SD . All the nodes employ an MMSE based FDE for equalization process. A destination node calculates the expected I E after the re-transmission using J function and it also calculates a necessary re-transmission rate according to the algorithm shown in E is set at 0.65. Fig. 2. In Fig. 2, Ith B
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
Simulation results
Figure 4 shows 10 % value of I E vs. the (Es /N0 )SD . As shown in Fig. 4, the 10% value of the proposed scheme is controlled to be higher than 0.6 at lower (Es /N0 )SD from 0.0 dB to 3.0 dB, because the relay node re-transmits the frame that enables I E after re-transmission to be more than 0.6, as described in section III-C. On the other hand, in a model (b) and a
3 4 5 6 7 (E /N )SD [dB] s
8
9 10
0
Figure 4: I E (C.D.F. = 10 %) vs. (Es /N0 )SD model (c), I E is increasing at lower (Es /N0 )SD , because only the received signal level is increased in these models without consideration of the cause of performance degradation. Figure 5 shows the C.D.F. of throughput efficiency η when (Es /N0 )SD is 0 dB, where η is defined as η=
Ngood frame
,
Nretry frame
Ntransmit frame +
(5)
βk
k=1
Ngood frame is the total number of error free frames, Ntransmit frame is the total number of transmitted frames, Nretry frame is the total number of re-transmission and βk is the k-th β. As shown in Fig. 5, η for the proposed re-transmission scheme is improved by 15 % compared to the 2-hop transmission at the C.D.F. of 10 %. Figure 6 also shows C.D.F. of throughput efficiency when (Es /N0 )SD is 3 dB. In this case, the proposed re-transmission scheme can improve η by 35 % compared to the conventional re-transmission and the 2-hop transmission cases at the C.D.F. of 10 %. The reasons why the proposed scheme can largely improve
The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’07)
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R EFERENCES
Figure 5: C.D.F. vs. throughput efficiency when (Es /N0 )SD is 0 dB 0
10
[1] K. Higuchi, H.Kawai, N.Maeda, H.Taoka and M. Sawahashi, “Adaptive control of surviving symbol replica candidates in QRM-MLD for OFDM MIMO multiplexing,” IEEE J. Sel. Areas Commun., vol. 24, June 2006. [2] S. M. Faccin, C. Wijiting, J. Kenckt and A. Damle, “Mesh WLAN networks : concept and design,” IEEE Wireless Commun., vol.13, Apr. 2006.
Ret. from Relay Ret. from Source 2 − hop Trans.
[3] D. Chase, “Code combining – a maximum-likelihood decoding approach for combining an arbitrary number of noisy packets,” IEEE Trans. Commun., vol. 33, no. 5, May 1985.
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C.D.F. @ (E /N )SD = 3 dB
C ONCLUSIONS
This paper proposed a relay assisted re-transmission control scheme in which re-transmission is conducted not by the source node but by a relay node that locates almost in the mid point between source and destination nodes. Because reduction of the re-transmission time period is a direct way to improve throughput efficiency in CSMA/CA introduced wireless access systems, only deeply faded spectrum components in the first transmission are re-transmitted in a shorter time period, and the number of spectrum components to be fed back is determined based on expected mutual information after re-transmission. The results confirm that throughput efficiency of the proposed scheme can achieve much higher throughput efficiency than the conventional two-hop transmission schemes.
0
C.D.F. @ (E /N )SD = 0 dB
10
−1
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[4] J. Hagenauer, “Rate-compatible punctured convolutional codes (RCPC Codes) and their applications, ” IEEE Trans. Commun., vol. 36, no. 4, Apr. 1988. [5] T. M. Cover and J. A. Thomas, Elements of Information Theory 2nd Edition. John Wiley & Sons, inc., 2006.
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Throughput efficiency Figure 6: C.D.F. vs. throughput efficiency when (Es /N0 )SD is 3 dB
throughput can be explained as follow. In the proposed scheme, deeply faded spectra that cause low mutual information at the equalizer output is transmitted via a better channel, thereby the huge performance improvement after equalization can be obtained. On the other hand, when we just re-transmit the same signal, bad quality of spectrum components are still in bad conditions in the re-transmission; the only improvement is the average received signal level improvement. In the case of two hop case, because the transmitted signal is hopped anytime regardless of the channel quality, its throughput efficiency is upperlimited to 0.5. Therefore, the proposed scheme can enlarge the wireless mesh network scale and keep the high throughput efficiency even if (Es /N0 )SD is much lower. Another important advantage for the proposed scheme is that time period for re-transmission is controlled according to the necessary number of re-transmitted spectra, thereby the average time period for re-transmission can be reduced.
[6] N. Miki, H. Atarashi, S. Abeta and M.Sawahashi, “Comparison of throughput employing hybrid ARQ packet combining in forward link OFCDM broadband packet wireless access,” IEICE Trans. Commun., vol. E88-B, no. 2, Feb. 2005. [7] K. Mashima and S. Sampei, “Broadband single carrier transmission technique using dynamic spectrum control, ” Technical Report of IEICE, RCS2006 - 233, Jan. 2007. [8] S. ten Brink, “Convergence behavior of iteratively decoded parallel concatenated codes,” IEEE Trans. Commun., vol. 49, no. 10, pp 1727-1737, Oct. 2001. [9] F. Brannstrom, Convergence analysis and design of multiple concatenated codes, Ph.D. Thesis, Chalmers University of Technology, 2004. [10] S. Ibi, S. Sampei and N. Morinaga, “Comparison study of MIMO transmissions for single and multi carrier turbo equalization,” Technical Report of IEICE, RCS2006 - 62, July 2006.
