Hybrid Type-II ARQ Schemes with Adaptive Modulation Systems for Wireless Channels Sorour Falahati and Arne Svensson Communication Systems Group, Department of Signals and Systems, Chalmers University of Technology, SE-412 96 Goteborg, Sweden phone: +46 31 772 1767, fax: +46 31 772 1748 email:fSorour.Falahati,
[email protected]
Abstract | In this paper, we proposed and analyzed a scheme for wireless channels which is a combination of a hybrid type-II Automatic Repeat reQuest (ARQ) scheme and an Adaptive Modulation System (AMS). In hybrid type-II ARQ schemes, the transmission of redundancy bits for error correction is adapted to the channel variations. Additionally, in the proposed AMS, the modulation is gradually changed from a large constellation to small constellations when the channel bit error probability is high. This is done without any knowledge of the channel at the transmitter. The proposed scheme can provide a signi cant gain in the throughput performance in an ecient and exible way. Simulation results are presented and they con rm that the proposed scheme considerably improves the performance.
I. Introduction
ARQ schemes can guarantee an almost error free reception which is strongly required in data communications. Hybrid type-II ARQ schemes are supplied by channel coding to further improve the performance in bad channel conditions. Additionally, the error correction capability in these schemes is adaptive which makes them suitable for time varying channels [1{7]. In our previous studies [6, 7], we have proposed a hybrid type-II ARQ scheme, referred to as Scheme 5, which performs the best compared to the other considered schemes, in all the channel conditions. The system performance is evaluated by the throughput which is de ned as the inverse of the total number of transmitted symbols per correctly received data bit. In our previous work, Scheme 5 used xed modulation, i.e. BPSK to transmit each coded bit. In this case the maximum throughput is one. The throughput can be improved by applying larger signaling constellations, such as QPSK, 8-PSK and 16-QAM. However there is a drawback by using large signaling constellation in poor channel conditions because of the increased noise sensitivity. Consequently, an adaptive modulation system (AMS) should be able to compensate this disadvantage in poor channel conditions. In the AMSs that are already presented in the literature (see e.g. [8, 9]), the modulation parameters such as symbol rate and constellation size, are controlled by a channel estimation. In this paper we propose an AMS combined with Scheme 5 which is completely blind and does not require any knowledge of the channel conditions. The transmission starts with the highest code rate and a large signaling constellation. When a NACK due to a failure of error free
reception is obtained, the transmitter simultaneously reduces the code rate and the constellation size in a prede ned way. An AMS assisted by the channel information provide better performance than our proposed system because more knowledge is available at the transmitter. But in this paper, we will show that our proposed blind system, performs almost equally well in most of channel conditions which makes it very interesting. In the following, Sections II and III describe the structure of Scheme 5 and the proposed AMS, respectively. The combination of Scheme 5 and AMS is explained in Section IV. The corresponding numerical results are shown and discussed in Section VI. Finally some conclusions are drawn in Section VII. II. Hybrid type-II ARQ scheme
Hybrid type-II ARQ schemes are based on an adaptive error correction technique. The amount of redundancy bits for protecting data bits against channel impairments are gradually increased during the retransmissions [1{7]. In our previous studies [6, 7], we have proposed a hybrid type-II ARQ scheme, referred as Scheme 5, which provides the best performance among all other considered schemes in all studied channel conditions. The structure of Scheme 5 is described in the following. We assume a Selective Repeat(SR) ARQ protocol with in nite bu ers at the transmitter and the receiver and an error free feedback channel. The data packet with length L is formed by n information bits which are concatenated by np parity bits for error detection and a tail of m zero bits, corresponding to the memory of the convolutional encoder. The data packet is denoted by C0 and is encoded by a convolutional encoder at the parent rate 1=3. The encoded bits are punctured periodically according to the optimum puncturing patterns to provide a set of rate compatible codes with corresponding code rates Rk where k 1 and Rk > Rk+1 . The incremental code word denoted by Ck , contains the coded bits in the code word of the rate Rk code which are not included in the code words of the higher rate codes. The incremental code words are interleaved and modulated for transmission over the channel. Figure 1 shows the relationship between the data packet C0 and the incremental code words Ck where 1 k 5. Furthermore, the puncturing pat-
Fig. 1. The diagram of the relationship between the data packet and the incremental code words in Scheme 5.
tern (PRk ) of the rate compatible punctured convolutional (RCPC) codes with period two at parent code rate 1=3 with generator polynomials (133; 165; 171) in octal form and constraint length 7 are given in Table I [10]. The transmission starts with the code at the highest rate (i.e. C1 at R1 = 1). The received word is decoded and if an error is detected, a retransmission is requested. Then, the transmitter sends the incremental code word of the next lower rate. At the receiver, the corresponding received word is combined with the previously received incremental code word(s), decoded and checked for the existence of a detectable error. If the received word at rate 1=3 still fails in correcting all the detectable errors, the procedure repeats by transmission of C1 , followed by C2 and so on. In other words, the codes at rates lower than 1=3, are provided by simple repetition. This procedure continues until an error free reception is achieved. III. Adaptive Modulation System (AMS)
Figure 2 shows the signaling constellation of 16QAM, 8-PSK, QPSK and BPSK modulations where Gray coding is used for mapping the bits to the symbols. With a constant average symbol energy and constant symbol rate (bandwidth), a large constellation such as 16-QAM provides a high bit rate at the expense of an increased noise sensitivity due to a smaller minimum Euclidean distance in the constellation as compared to a smaller constellation. Hence, in good channel conditions when most of the symbols are received correctly, a modulation with a large constellation, have the prospect to improve the system throughput. Besides, its drawback in the poor channel conditions, motivates the use of a modulation such as BPSK under these conditions. In this case, the symbols are farther apart in the constellation and more robust to the channel impairments. TABLE I
The RCPC codes at parent code rate 1=3 , K = 7 ,
(133 165 171) ;
P1 1 0 0 0 0 1
P2=3
1 1 0 0 0 1
;
P1=2
1 1 0 0 1 1
P2=5
1 1 0 1 1 1
Fig. 2. The signaling constellations diagram where (a), (b), (c) and (d) correspond to 16-QAM, 8-PSK, QPSK and BPSK constellations, respectively.
Hence, in a time varying channel, an adaptive modulation system (AMS) may improve the performance by taking advantage of the channel variations in an ecient way. In most of the proposed methods in the literature, the selection of modulation is based on a channel estimate which must be available at the transmitter (see e.g. [8,9]). We propose a blind AMS which does not utilize any knowledge of the channel condition. The adaptation of modulation is controlled by the retransmission requests. The rst transmission for a given packet, starts with a large signaling constellation. The size of signaling constellation is gradually reduced during retransmission. This procedure continues until successful transmission is achieved. In the next section, the description of a good combination of our previously proposed hybrid type-II ARQ scheme (Scheme 5 ) and AMS is given. IV. Hybrid type-II ARQ/AMS
Now we propose a hybrid type-II ARQ/AMS as a combination of Scheme 5 and the AMS as described in Section III. In this system, as the coding rate of Scheme 5 is reduced during retransmissions, the signaling constellation is simultaneously reduced in size. The main problem is to nd the appropriate modulation at each coding rate. An analytical solution to this problem seems to be complicated with large signaling constellations on a time varying Rayleigh fading channel. Moreover such an analysis has to rely on union bounds or other approximations of the bit error probability of convolutional codes which are known to be inaccurate at low signal to noise ratios. Therefore we question the usefulness of such an analysis. Instead we have used computer simulations to evaluate the throughput of various schemes and in this way, we have obtained good candidate schemes and their performances. One way of doing this is to simulate the whole system for di erent combinations of modulations and
3.5 3
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R7 R8
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10 Es / No dB
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Fig. 3. Simulated normalized throughput for the hybrid type-I ARQ/ xed modulation system for 144 bits data packets, 12 CRC bits and normalized Doppler frequency 0.001. Solid lines, dashed lines, dotted lines and dashed-dotted lines correspond to 16-QAM, 8-PSK, QPSK and BPSK modulations, respectively.
Fig. 4. Simulated normalized throughput for the hybrid type-I ARQ/ xed modulation system for 144 bits data packets, 12 CRC bits and normalized Doppler frequency 0.01. Solid lines, dashed lines, dotted lines and dashed-dotted lines correspond to 16-QAM, 8-PSK, QPSK and BPSK modulations, respectively.
coding rates. Eventually, the one with the best performance is found. Unfortunately, this method is time consuming due to the large number of combinations. Another approach for solving the problem, is to simulate the throughput of the hybrid type-I ARQ version ( xed code rate) of the system when a xed modulation is employed. In this way we are able to nd the best combination of code rate and signaling constellation for each signal to noise ratio and based on this we can reduce signi cantly the number of hybrid type-II ARQ/AMSs that should have been considered. More explanations and detail are given in Section VI.
VI. Numerical Results and Discussion
V. System Configuration
The constraints on the simulation are follows. We have assumed in nite bu ers at the transmitter and the receiver and an error free feedback channel. Scheme 5 is based on the RCPC codes given in Table I. The receiver with soft decisions and perfect CSI uses the Viterbi decoder at the rate 1=3. Each simulation is continued until 1000 packets are received correctly. The results are plotted for 144 bit data packets where each data packet consists of 12 CRC bits and a tail of 6 zero bits. The throughput is displayed versus average symbol energy Es per noise spectral density No . We have assumed that Es is equal for all signaling constellations which corresponds to a transmitter with control average power.
A block of data is fed to a CRC encoder, followed by a punctured convolutional encoder to provide the (incremental) code words. The selected (incremental) code word for transmission is interleaved and packed into the channel block(s) with the size of Lc bits. The channel block(s) are modulated and transmitted over the Rayleigh fading channel. Additionally, the choice of the coding rate and the modulation at each transmission attempt is based on the feedback signal (ACK/NACK). The fading process is generated by the Jakes model which means that there is correlation between the symbols within a channel block [11]. However, we assume that fading is independent between the blocks. The receiver is assumed to have complete knowledge of the channel condition. The received symbols which are scaled by the conjugate of the fading process, together with perfect CSI are used to evaluate the soft bits based on the maximum likelihood function [12]. The soft bits are deinterleaved and fed to a Viterbi decoder, followed by a CRC decoder which determines the type of feedback signal (ACK/NACK).
A. Results of the search for a good hybrid type-II ARQ (Scheme 5) with AMS As explained in Section IV, the performance of a hybrid type-I ARQ scheme with xed modulation, can be helpful in order to nd out a suitable correspondence between the modulations and the coding rates. For this purpose, Scheme 5 is modi ed as the follows. The data packet C0 is encoded at a xed rate Rk . The resultant code word which is denoted by CWk , is the union of the previously de ned incremental code words Ci for 1 i k , i.e. [ki=1 Ci = CWk . CWk is interleaved, modulated and transmitted over the channel. If an error is detected at the receiver, the erroneously received code word is discarded and CWk is retransmitted. This system is simulated for the coding rates R1 to R10 (1; 2=3; 1=2; 2=5; 1=3; 1=4; 2=9; 1=5; 2=11; 1=6) and all the modulations schemes shown in Figure 2. The simulated throughput for normalized Doppler frequencies 0.001 and 0.01 corresponding to the slow and fast fading environments, are plotted in Figures 3 and 4, respectively. However in order to have a clear and
3.5
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Normalized throughput
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Fig. 5. Simulated normalized throughput for the hybrid type-I ARQ/AMS for 144 bits information blocks, 12 CRC bits and normalized Doppler frequency 0.001.
Fig. 6. Simulated normalized throughput for the hybrid type-I ARQ/AMS for 144 bits information blocks, 12 CRC bits and normalized Doppler frequency 0.01.
understandable picture, just the important results are selected and shown here. The upper envelope of these graphs can be a hint to a suitable combination of the modulations and the coding rates. Three hybrid type-II ARQ/AMS are selected among the di erent combinations and they are introduced in Table II as Systems A, B and C. Simulations are carried out for these systems, together with other combinations which are not described in Table II. The results show that System A provides very good performance in comparison with the others in most of the channel conditions.
As the SNR decreases, System A gradually performs better than System B which shows that employing 8-PSK at third and forth code rates is a good choice. However at very low SNRs, System B is better than System A. This is due to the fact that System B adapts more quickly to the modulations of lower constellations, i.e. QPSK and BPSK, than System A. Furthermore, by decreasing the SNR, System C merges to System A. However the results in Figure 6 show that it even continues to beat the other two systems in fast fading environments. The reason is that System C changes the modulation to QPSK and BPSK with the least delay compared to the two other systems and obviously, QPSK and BPSK are the most suitable modulations among the others, at poor channel conditions. Figures 7 and 8, show the throughput performance of the hybrid type-II ARQ scheme (Scheme 5 ) when combined with the proposed AMS (System A) and xed modulation systems for slow and fast fading environments, respectively.Please note that in these two plots, the label Adap. Mod. corresponds to System A which is described in Section VI-A. Here we see a nice property of System A. At high SNRs we obtain almost the throughput of Scheme 5 combined with 16-QAM. For intermediate SNRs we obtain the throughput of Scheme 5 with 8-PSK. Therefore we draw the conclusion that System A performs very good for high SNRs (high throughput). However, below Es =No = 5dB , System A starts to loose performance compared to Scheme 5 with QPSK and eventually compared to BPSK. The reason is that System A is not rate compatible in the sense that the transmitted information at e.g. rates R5 to R7 is not equivalent to transmitting QPSK at same corresponding rate already from the beginning. With xed modulation, the scheme is rate compatible which means that we do not loose any throughput due to the adaptation of the scheme.
B. The performance of hybrid type-II ARQ/AMS In Figures 5 and 6, the throughput performance of System A, B and C are depicted for normalized Doppler frequencies 0.001 and 0.01, respectively. As it is shown, System A outperforms the other systems except at very low SNRs. It can also be seen that Systems A and B provide almost same throughput for high SNRs, but there is a considerable reduction in the throughput of System C in that range of SNRs. This behavior is due to the fact that both Systems A and B gain in performance by using 16-QAM at the rst two code rates as it is recommended by the results in Figures 3 and 4, whereas in System C the modulation is switched faster to 8-PSK compared to the two others systems. TABLE II
The relationship between the modulations and the code rates in three different systems
Modulation 16-QAM 8-PSK QPSK BPSK
System A System B System C R1 ,R2 R1 ,R2 R1 R3 ,R4 R3 R2 R5 ,R6 ,R7 R4 R3 ,R4 Rk ,k 8 Rk ,k 5 Rk ,k 5
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2.5
3
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Normalized throughput
3
3.5 16−QAM 8−PSK QPSK BPSK Adap. Mod.
2 1.5 1 0.5 0 0
2.5
16−QAM 8−PSK QPSK BPSK Adap. Mod.
2 1.5 1 0.5
5
10
15
20
Es / No dB
0 0
5
10
15
20
Es / No dB
Fig. 7. Simulated normalized throughput of Scheme 5 for 144 bits information blocks and normalized Doppler frequency 0.001. The solid lines and dashed-dotted line correspond to the performance of Scheme 5 with xed modulation and adaptive modulations, respectively.
Fig. 8. Simulated normalized throughput of Scheme 5 for 144 bits information blocks and normalized Doppler frequency 0.01. The solid lines and dashed-dotted line correspond to the performance of Scheme 5 with xed modulation and adaptive modulations, respectively.
However with AMS, once we used e.g. 16-QAM at high rates, we have to live with its higher noise sensitivity also at lower rates. This is a disadvantage, but so far we have not been able to nd a rate compatible ARQ/AMS scheme. It is important to note that no knowledge of the channel condition is utilized in System A and the adaptation of the coding rates and the modulations in this system is only based on the ACK/NACK feedback signal. But very good performance in most of the channel conditions is still provided by the proposed System A.
signaling constellation, the throughput will increase as will the delay. This will be further studied.
VII. Conclusion
In this paper we propose a hybrid type-II ARQ scheme combined with an AMS that achieves high throughput on a wireless channel. The proposed system takes advantage of the channel variations in a clever way to increase the performance. This system starts the transmission with a high rate channel code and a modulation with a large signaling constellation. For each new retransmission request, codes with lower rates and modulations with smaller constellations are employed. The simulation results show that this system can improve the throughput performance considerably, in most of the channel conditions. The proposed system does not utilize any knowledge of the channel at the transmitter which makes it less complex compared to the AMS based on the channel estimation. Therefore this system can be quite suitable for the applications where there is not any channel information available at the transmitter. In order to have better understanding of this system, one can analyze the hybrid type-II ARQ/AMS. However it is too complicated to evaluate, but maybe some reasonable approximations can be found out. It is also clear that the performance can be improved by using channel state information at the transmitter, specially at low SNRs. By starting with a smaller
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