constellation points doesn't provide the highest BICM capacity so a degree of non uniformity .... and delay specified in the DVB-T2 standard. The performance in ...
1
Combining Advanced Constellations and SSD Techniques for Optimal BICM Capacity J. Barrueco1, C. Regueiro1, J. Montalban1, M. Velez1, P. Angueira1, Heung-Mook Kim2, Sung-Ik Park2, Jae-Young Lee2 1
Dept. of Communications Engineering, University of the Basque Country (UPV/EHU), Alda.Urquijo s/n, 48013 Bilbao, Spain Email: { jon.barrueco, cristina.regueiro, jon.montalban, manuel.velez,pablo.angueira }@ehu.es 2 Broadcasting Syst. Res. Dept., Electron.&Telecommun. Res. Inst., Daejeon, South Korea Email: { hmkim, psi76,jaeyl}@etri.re.kr
provide signal robustness under difficult fading conditions. Abstract — Uniform quadrature amplitude modulation (QAM) has been widely used in terrestrial broadcasting systems because it provides a high data rate although it is less resilient to noise and interference. However, the uniform pattern of the constellation points doesn’t provide the highest BICM capacity so a degree of non uniformity is needed so as to improve the BICM capacity of the system. On the other hand, due to the propagation scenario in broadcasting applications is really tough, a signal space diversity (SSD) technique should be applied to face it. The goal of this paper is to present and show the performance of advanced constellation schemes and signal space diversity techniques. Index Terms — Modulation, Non Uniform Constellation, Rotated Constellation, Signal Processing for Transmission, Terrestrial Broadcasting, Making Better Use of the Spectrum
I. INTRODUCTION n digital video broadcasting (DVB) terrestrial systems, uniform quadrature amplitude modulation (QAM) has been one of the most widely used constellation schemes. Its main advantage is that it provides a higher data rate than other constellations such as phase shift keying (PSK) but is less robust. Recently, a new way of QAM constellations called non uniform constellations (NUC) has been proposed in [1] in order to maximize the BICM capacity [2] and reduce the existing gap from Shannon’s capacity [3]. These constellations are optimized with respect to one of the axis (dividing the QAM in two pulse amplitude modulations and optimizing one of them) and so, they are called one dimension non uniform constellations (1D-NUC). Recently, an additional degree of freedom has been given to the design of NUC in order to overcome their shortcoming below a signal to noise ratio (SNR) of 11 dB as shown in [4] obtaining two dimension non uniform constellations (2D-NUC). Moreover, the capacity gain of 2D-NUC is bigger than for 1D-NUC. On the other hand, rotated constellation (RC) [5], which is an specific signal space diversity (SSD) technique, is used to
I
This paper has the main goal of evaluating the performance of non uniform and rotated constellations when used together. For reaching that objective three steps are taken: −
Compare the performance of non uniform constellations versus the uniform ones. − Study the gain in terms of bit error rate (BER) and frame error rate (FER) versus signal to noise ratio (SNR) of using rotated constellations. − Compare the performance of using jointly non uniform and rotated constellations versus uniform and non rotated constellations. The paper is organized as follows: Section II includes a detailed description of the non uniform constellations and simulation results comparing the performance between uniform and non uniform constellations. Section III shows the performance of rotated constellations under a fading channel. Section IV includes a study of the performance of using jointly non uniform and rotated constellations. Finally, the main conclusions are included in section V. II. NON UNIFORM CONSTELLATIONS A. Definition Uniform constellations are characterized by their square shape and uniform symbol distribution and have been used in communication systems for a very long time. Recently, NUC have been proposed [6] – [7] for broadcasting systems which provide better performance than the uniform one. Indeed, it has been demonstrated that the capacity of a communication system can be increased if all the constellation points are adapted to the SNR range in which the system is working. This means that for each SNR value, there is one location for each constellation symbol which maximizes the system capacity i.e. with an equal system capacity, this technique supplies higher SNR value than the one obtained with a uniform constellation. Bearing in mind all these issues, the first approach consists in maximizing BICM capacity with
2 optimized 1D-NUC. In this sort of constellations, each symbol is optimized with respect to only one axis, which simplifies the calculation complexity. This constellation is demapped using a simple one dimension demapper, which calculates the log-likelihood ratio (LLR) values independently. The disadvantage of this mode is the existing worsening in the SNR value range below 11dB. Next, with the goal of getting over this limitation, BICM capacity is maximized using 2DNUC. For 2D-NUC, each symbol is optimized with respect to both of the axis, resulting in circular shaped constellations. The complexity of the calculation and processing of this type of constellations is higher than in 1D-NUC case due to the high number of variables involved and, besides, a 2D-demapper is needed because both of the axis are dependent. B. Performance All the simulations have been made for a threshold of BER = 10^-6 and the code rates (CR) selected have been 4/15, 8/15 and 12/15 to show all representative cases. Fig.1 shows the performance of 64 non uniform and uniform constellations for an Additive White Gaussian Noise (AWGN) and Rayleigh i.i.d. channels. In the x axis the SNR value is displayed in dBs and in the y axis the BER/FER value. Data displayed in Fig.1 shows that non uniform constellations greatly outperforms the uniform ones, because the constellation points are optimized for each SNR value. What is more, for all the possible combinations of modulation and coding, NUC always outperform non uniform constellations.
10
10
BER/FER
10
10
10
10
0
10
-1
10
-2
10
-3
10
BER/FER
10
-4
-5
10
10
-6
10
0
-1
-2
-3
-4
-5
-6
BER 64-NUQAM CR=12/15
BER 64-NUQAM CR=12/15
10
-7
FER 64-NUQAM CR=12/15
10
-7
FER 64-NUQAM CR=12/15
BER 64-QAM CR=12/15
BER 64-QAM CR=12/15
FER 64-QAM CR=12/15
FER 64-QAM CR=12/15
-8
10 14.5
15
15.5 SNR [dB]
16
16.5
10
-8
18.5
19 19.5 SNR [dB]
20
can be optimized. Moreover, no matter the type of channel (AWGN or Rayleigh i.i.d.), there is always gain for non uniform constellation with respect to uniform ones. Another interesting point is that in this case, gains for AWGN channel are greater than for Rayleigh i.i.d. because NUC have been optimized for such (AWGN) channel. TABLE I NON UNIFORM VS UNIFORM CONSTELLATIONS GAIN FOR 4/15, 8/15 AND 12/15 CODE RATES IN AWGN AND RAYLEIGH I.I.D. CHANNELS 16 points gain [dB] CR
64 points gain [dB]
AWGN
RAYLEIGH I.I.D.
AWGN
RAYLEIGH I.I.D.
4/15
0.2
0.1
0.9
0.6
8/15
0.1
0.1
0.5
0.4
12/15
0.1
0.1
0.3
0.4
III. SSD TECHNIQUE Signal space diversity technique is based on spreading the different I/Q components of the signal through the available space in order to each of the components experiment a different channel fading. The SSD technique analyzed in this paper is rotated constellation, which is explained below. A. Rotated Constellations One of the most known SSD techniques is rotated constellation (RC) added with an inphase and quadrature (I/Q) interleaving to spread both components over the signal space. There are two different RC techniques, one defined for second generation terrestrial digital video broadcasting (DVBT2) standard [8] and another for next generation handheld digital video broadcasting (DVB-NGH) standard proposal. Two steps are defined in the rotation process for both of the techniques defined above. First of all, the constellation symbols are rotated with a defined angle which maximizes the performance in fading channels. After the rotation is done, a I/Q interleaving process is carried out in order to spread the components of each symbol through the entire constellation space. This provides space diversity to the I/Q components sent by the transmitter and, in case one of the components is received incorrectly, the other one remains correct due to it has experimented a different fading and the symbol could be recovered. When rotated constellations are used, the demapper must be two dimensional because I/Q components of each symbol are dependent.
20.5
Fig. 1. 64 NUQAM vs 64 QAM Performance for CR=12/15 and AWGN (Left) and Rayleigh i.i.d. (Left) Channels
In Table I, simulation results are extended for 4/15, 8/15 and 12/15 code rates, showing the SNR gain of NUC over uniform constellations for BER=10^-6. As depicted in Table I, the gain for high CR values is lower than for low values because the shape of the constellation is uniform alike. Besides, the bigger the number of points of the constellation, the higher the gain achieved due to there are more points that
B. Rotated Constellations Performance The performance of rotated constellation has been carried out simulating uniform QAM constellations with the rotation and delay specified in the DVB-T2 standard. The performance in terms of BER/FER (y axis) versus SNR (x axis) is shown in Fig.2 for QPSK and 12/15 code rate. In this case, the gain in SNR is 1.2dB but this is one of the best gains obtained with the rotation technique. What this means is that rotated constellation presents gain only for low constellation orders and high code rates. Indeed, for high order
3 constellations (from 256 constellation points) there are losses for all the possible code rates.
channel (using BICM with OFDM chain). However, the tendency is the same in both cases. TABLE II ROTATED VS NON ROTATED CONSTELLATION GAIN FOR 4/15, 8/15 AND 12/15 CODE RATES IN RAYLEIGH I.I.D. CHANNEL
0
10
-1
10
-3
10
BER/FER
4/15
QPSK Gain [dB] -0.2
16-QAM Gain [dB] -0.2
64-QAM Gain [dB] -0.1
8/15
0.2
-0.1
-0.1
12/15
1.2
0.5
0.2
CR
-2
10
-4
10
IV. OVERALL PERFORMANCE
-5
10
-6
10
BER QPSK NRC CR=12/15 FER QPSK NRC CR=12/15 BER QPSK RC CR=12/15 FER QPSK RC CR=12/15
-7
10
-8
10
7
7.5
8 8.5 SNR [dB]
9
9.5
In this chapter, the performance of using jointly the techniques described above (non uniform and rotated constellations) is presented. Fig.4 shows the performance in terms of BER/FER vs SNR when using both of the techniques and neither of them for 64 constellation points and 12/15 code rate. Indeed, there is only gain for 12/15 code rate in case rotation and non uniform constellation is used. This is a consequence of the losses produced by applying rotation to low code rates. 0
10
Fig. 2. QPSK RC vs QPSK NRC Performance for CR=12/15and Rayleigh i.i.d. Channel
-1
10
-2
10
-3
10
BER/FER
Fig.3 shows that when applying rotated constellations there is only gain (up to 2 dBs for QPSK and 13/15 code rate) for low order constellations and high code rates. What is more, for low code rates and high order constellations (even for QPSK and 16-QAM) there are losses in the performance. Besides, it is necessary to bear in mind that rotated constellations only provide gain in fading channels so all the simulation and results are for the DVBT-P1 channel. In AWGN channels, there is no difference between using or not rotated constellations in terms of BER/FER vs SNR performance because there is no fading.
-4
10
-5
10
-6
10
BER 64-QAM & NRC CR=12/15 FER 64-QAM & NRC CR=12/15 BER 64-NUQAM & RC CR=12/15 FER 64-NUQAM & RC CR=12/15
-7
10
-8
10
18.5
19
19.5 SNR [dB]
20
Fig. 4. 64-NUQAM & RC vs 64-QAM & NRC Performance for CR=12/15and Rayleigh i.i.d. Channel
Fig. 3. Rotated constellation performance gain for QPSK, 16-QAM and 64QAM using DVB-T2 rotation
In Table II, it is detailed the gain of rotated constellations for a Rayleigh i.i.d. channel (using BICM block). Results are slightly different from the ones obtained using the DVBT-P1
Table III shows that if the results are compared with the ones in Table I (gain of non uniform constellations), the results are worse for all the cases except for code rate 12/15 when applying both techniques. This is due to the losses of rotated constellations for low code rates, apart from the rotation angles defined in DVB-T2 are not the optimum for the non uniform constellations used. Moreover, if the results of Table III and Table II (gain of rotated constellations) are compared, there is only gain for code rate 12/15and 64 constellation points. This is a consequence of using non uniform constellations.
4 Another issue to take into account in the case of applying rotated constellations is that the performance for the same throughput value of a higher modulation and lower coding without rotation is better than the one for a lower modulation and higher code rate with rotation i.e. a combination of QPSK and 10/15 code rate with rotation (throughput of 1.33 bits/symbol) performs worse than 16-NUQAM and 5/15 code rate without rotation for a Rayleigh channel. In this case, the losses are 0.85 dB in terms of SNR. In another example, for 16-NUQAM and 12/15 code rate with rotation (throughput of 3.2 bits/symbol) the performance degradation with respect to 64-NUQAM and 8/15 code rate without rotation is 1.5 dB. TABLE III NON UNIFORM & ROTATED VS UNIFORM & NON ROTATED CONSTELLATION GAIN FOR 4/15, 8/15 AND 12/15 CODE RATES IN RAYLEIGH I.I.D. CHANNEL CR 4/15
16 Points Gain [dB] 0
64 Points Gain [dB] -0.3
8/15
-0.1
-0.1
12/15
0.5
0.5
V. CONCLUSIONS
In this paper, the performance of two different techniques to approach Shannon’s capacity limits has been presented. Besides, results of combining both of the techniques have been shown in order to check jointly their performance. It has been presented that non uniform constellations present better performance than the uniform ones for all the possible combinations of modulation and coding. Moreover, in the case of rotated constellations, it has been checked that they provide gain when they are used for low order constellations and high code rates. Finally, when applying both of the techniques, the results are not as good as when using each technique separately. ACKNOWLEDGMENT This work has been financially supported in part by the University of the Basque Country UPV/EHU (UFI 11/30), by the Basque Government (IT-683-13 and SAIOTEK), by the Spanish Ministry of Science and Innovation under the project NG-RADIATE (TEC2009-14201), by the Spanish Ministry of Economy and Competitiveness under the project HEDYTGBB (TEC2012-33302) and the European Regional Development Fund (ERDF). REFERENCES [1] Stott, J H, 2012. CM and BICM limits for rectangular constellations. Where they come from, how to calculate them – and how to maximize them by optimizing the constellation. Report produced under contract to BBC R&D, document JSC/BBC 022, August 2012. Submitted to DVB as document TM-MIMO0007. [2] G. Caire, G. Taricco and E. Biglieri, “Capacity of bit-interleaved channels,” IEE Electronic Letters., vol. 32, no. 12, Jun. 1996 [3] C. E. Shannon, “A mathematical theory of communication”, Bell Labs System Journal, vol. 27, Jul., Oct. 1948
[4] J. Zöllner and N. Loghin, “Optimization of high-order non-uniform QAM constellations”, IEEE International Symposium on Broadband Multimedia Systems and Broadcasting (BMSB), 2013 [5] C. A. Nour and C. Douillard, “Rotated QAM constellations to improve BICM performance for DVB-T2,” in Proc. IEEE Int. Symp. Spread Spectrum Tech. Appl., Bologna, Italy, Aug. 2008, pp. 354–359. [6] Stott, J H, 2014. Beyond NUQAM & ConQAM – overcoming their limitations, especially at lower SNRs. Report produced under contract to BBC R&D, document JSC/BBC 034. Submitted to DVB as document TM-T0007. [7] J. Zöllner and N. Loghin, 2014. High order Non-Uniform Constellations. Submitted to DVB as document TM-MIMO0010 [8] Digital Video Broadcasting (DVB); Frame structure channel coding and modulation for a second generation digital terrestrial television broadcasting system (DVB-T2), ETSI EN 302 755, V1.1.1, 2008
