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Figure from:Apsk Coded Modulation Schemes for Nonlinear Satellite Channels with High Power and Spectral Efficiency

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Fig. 2 Capacity surface for 4+12-PSK as function of p and y. The curves of channel capacity for the optimized 16- inner/outer ring phase offset ». Another interesting candi-

Figure 2 Capacity surface for 4+12-PSK as function of p and y. The curves of channel capacity for the optimized 16- inner/outer ring phase offset ». Another interesting candi-

Related Figures (10)

Fig. 1 Parametric description of double ring 16-APK con- stellation 4+12-PSK: N; = 4, No = 12, p = 2.7 and y = 15. expression in time domain is: Rp» are the number of points and corresponding radii of the
Fig. 1 Parametric description of double ring 16-APK con- stellation 4+12-PSK: N; = 4, No = 12, p = 2.7 and y = 15. expression in time domain is: Rp» are the number of points and corresponding radii of the
The curves of channel capacity for the optimized 16- APSK modulations are shown in Fig. 3, where it may be observed that the capacity bounds for 16-QAM, 4+12-PSK and 6+10-PSK are very close forthe AWGN linear channel. Taking into account the previous discussion, we can ex- pect that 4+12-PSK or 6+10-PSK modulation formats are likely to outperform 16-QAM over the nonlinear channel. For the sake of completeness, optimum’ hexagonal constel- lations (HEX-A, HEX-B) slightly outperforming 16-QAM are reported, even though they are clearly not suited for the nonlinear channel. Fig.3 Capacity for the two optimized 16-A PK signal constel- lations versus 16-QAM and 16-PSK. likely to outperform 16-QAM over the nonlinear channel. Despite the result of Fig. 3 showing a slight capacity
The curves of channel capacity for the optimized 16- APSK modulations are shown in Fig. 3, where it may be observed that the capacity bounds for 16-QAM, 4+12-PSK and 6+10-PSK are very close forthe AWGN linear channel. Taking into account the previous discussion, we can ex- pect that 4+12-PSK or 6+10-PSK modulation formats are likely to outperform 16-QAM over the nonlinear channel. For the sake of completeness, optimum’ hexagonal constel- lations (HEX-A, HEX-B) slightly outperforming 16-QAM are reported, even though they are clearly not suited for the nonlinear channel. Fig.3 Capacity for the two optimized 16-A PK signal constel- lations versus 16-QAM and 16-PSK. likely to outperform 16-QAM over the nonlinear channel. Despite the result of Fig. 3 showing a slight capacity
advantage for 6+10-PSK with respect to 4+12-PSK, con- sidering the nonlinear channel application, the latter con- stellation has been preferred as the presence of more points in the outer ring will allow to maximize the HPA DC effi- ciency. This is because the inner points will be transmitted at a lower power, to which corresponds a lower DC effi- ciency. Fig. 4 shows the distribution of the transmitted signal envelope for four constellations, namely, 16-QAM, 4+12-PSK, 6+10-PSK and 16-PSK. The shaping filter is a square-root raised cosine with a roll-off factor a = 0.35. Fig. 4 Simulated histogram of the transmitted signal enve- lope power: a) 16-QAM, b) 4+12-PSK, p = 2.7, » = 0,0 6+10-PSK, p = 2.21, y = 0, d) 16-PSK.
advantage for 6+10-PSK with respect to 4+12-PSK, con- sidering the nonlinear channel application, the latter con- stellation has been preferred as the presence of more points in the outer ring will allow to maximize the HPA DC effi- ciency. This is because the inner points will be transmitted at a lower power, to which corresponds a lower DC effi- ciency. Fig. 4 shows the distribution of the transmitted signal envelope for four constellations, namely, 16-QAM, 4+12-PSK, 6+10-PSK and 16-PSK. The shaping filter is a square-root raised cosine with a roll-off factor a = 0.35. Fig. 4 Simulated histogram of the transmitted signal enve- lope power: a) 16-QAM, b) 4+12-PSK, p = 2.7, » = 0,0 6+10-PSK, p = 2.21, y = 0, d) 16-PSK.
Fig. 5 I-O characteristics of the reference Ka-band TWT Amplifier. examples in the following we will consider the AM/AM and AM/PM characteristics shown in Fig. 5. We introduce here the parameter [Ey /Nolsat defined as the ratio between the transmitted energy per bit when the amplifieris driven at saturation by a continuous wave (CW) carrier and the noise power spectral density.? It is easy to find that the following general relation holds when a digital signal is passed through the HPA driven at a given input back-off (IBO):
Fig. 5 I-O characteristics of the reference Ka-band TWT Amplifier. examples in the following we will consider the AM/AM and AM/PM characteristics shown in Fig. 5. We introduce here the parameter [Ey /Nolsat defined as the ratio between the transmitted energy per bit when the amplifieris driven at saturation by a continuous wave (CW) carrier and the noise power spectral density.? It is easy to find that the following general relation holds when a digital signal is passed through the HPA driven at a given input back-off (IBO):
equalization becomes totally superfluous, reducing the nec- essary demodulator complexity.
equalization becomes totally superfluous, reducing the nec- essary demodulator complexity.
Fig. 7 Simulated BER for TCM in the nonlinear channel: r=3/4 code, IBO= 3 dB, roll-off factor=0.35. TURBO-CODED PERFORMANCE
Fig. 7 Simulated BER for TCM in the nonlinear channel: r=3/4 code, IBO= 3 dB, roll-off factor=0.35. TURBO-CODED PERFORMANCE
modulation symbols through Gray mapping (see Fig. 8). After this point, we discuss the selection of the binary code itself, based on lessons learned from the developments in turbo coding since their invention. The key point is the simple, yet fundamental, fact that a code which performs very well can be obtained from a not-too-complex good bi- nary code. The output of this code, taken as a block, is randomly permuted, and then passed through a simple ac- cumulator code.!® In!” it is shown that this procedure can improve the performance, and approach the ultimate Shan- non limit by adding a certain number of these permutation- accumulator blocks at the output of the first code. As a matter of fact, the first block could be as simple as a rep- etition code, although some decoder implementation prob- lems prevent us from choosing such a simple scheme. An high-level coder and decoder block diagram is shown in Fig. 8. After this point, we discuss the selection of the binary in which a good binary code is mapped onto the non-binary selection is clear, namely, we have chosen a BICM scheme, The road we have followed for the Coded Modulation
modulation symbols through Gray mapping (see Fig. 8). After this point, we discuss the selection of the binary code itself, based on lessons learned from the developments in turbo coding since their invention. The key point is the simple, yet fundamental, fact that a code which performs very well can be obtained from a not-too-complex good bi- nary code. The output of this code, taken as a block, is randomly permuted, and then passed through a simple ac- cumulator code.!® In!” it is shown that this procedure can improve the performance, and approach the ultimate Shan- non limit by adding a certain number of these permutation- accumulator blocks at the output of the first code. As a matter of fact, the first block could be as simple as a rep- etition code, although some decoder implementation prob- lems prevent us from choosing such a simple scheme. An high-level coder and decoder block diagram is shown in Fig. 8. After this point, we discuss the selection of the binary in which a good binary code is mapped onto the non-binary selection is clear, namely, we have chosen a BICM scheme, The road we have followed for the Coded Modulation
ee The following demodulator synchronizer settings have been adopted throughout this section: an AGC loop adap- tation step of y, = 10~%, the one-sided loop noise band- width of the symbol clock estimator, By, = 107° and the one-sided loop noise bandwidth of the carrier phase esti- mator Brg = 2-10-°. As for trellis coded modulatior we used a third-order timing interpolator. For the simu- lations the rate 3/4 turbo codec described previously has been adopted with an input frame block size of 16384 bits. When not specified, the number of decoder iterations has been set to 10. Results for the AWGN channel are pro- vided with and without channel estimation in Fig. 10. We observe that for QEF performance over the linear channel the turbo coding gain is about 1.65 dB with respect to the 16 state trellis code concatened with a trellis decoder and only 1.15 dB with respect to the 32-state trellis code.° Ad: ditionally, we should add the 0.35 dB loss due to the Reed Solomon concatenation for the TCM case, absent for the turbo as mentioned before. This amounts to a total gain of about 2.0 dB, for an increase in complexity of a factor 20-40. For the sake of comparison, the same figure shows the performance of 16-QAM with the same turbo code as well. The impact of the digital synchronizer described in a previous section has been verified by simulation and it has been found to be less than 0.1 dB in the waterfall BER region of the turbo decoder. This was considered a very satisfactory result considering the simplicity of the NDA scheme adopted. Considering the limited gain provided by the nonlinear equalizer for trellis-coded modulation, we abandoned the scheme for the turbo case. The IBO was optimized, as detailed in.° The E, /No was selected in the Because of the simplified four-quadrant decision ap- proach its implementation is easier than a truly DD scheme for 4+12-PSK and decisions are insensitive to possible sig- nal amplitude estimation errors. The main scheme draw- back is related the so called pattern noise or irreducible phase jitter floor due to the phase error signal averaging for the four constellation points belonging to the same quad- rant. This floor is not present with QPSK modulation, where the exact Decision- Directed, and this simplified ver- sion are identical. Simulation results indicate that the per- formance is degraded with respect to the TC-DD scheme but remains acceptable even at low SNR. It was found that a phase jitter standard deviation of about 1 degree can be achieved at E;/No = 5 dB for loop bandwidth!” BreTs;(oo) =5-1075. Because of the simplified four-quadrant decision ap-
ee The following demodulator synchronizer settings have been adopted throughout this section: an AGC loop adap- tation step of y, = 10~%, the one-sided loop noise band- width of the symbol clock estimator, By, = 107° and the one-sided loop noise bandwidth of the carrier phase esti- mator Brg = 2-10-°. As for trellis coded modulatior we used a third-order timing interpolator. For the simu- lations the rate 3/4 turbo codec described previously has been adopted with an input frame block size of 16384 bits. When not specified, the number of decoder iterations has been set to 10. Results for the AWGN channel are pro- vided with and without channel estimation in Fig. 10. We observe that for QEF performance over the linear channel the turbo coding gain is about 1.65 dB with respect to the 16 state trellis code concatened with a trellis decoder and only 1.15 dB with respect to the 32-state trellis code.° Ad: ditionally, we should add the 0.35 dB loss due to the Reed Solomon concatenation for the TCM case, absent for the turbo as mentioned before. This amounts to a total gain of about 2.0 dB, for an increase in complexity of a factor 20-40. For the sake of comparison, the same figure shows the performance of 16-QAM with the same turbo code as well. The impact of the digital synchronizer described in a previous section has been verified by simulation and it has been found to be less than 0.1 dB in the waterfall BER region of the turbo decoder. This was considered a very satisfactory result considering the simplicity of the NDA scheme adopted. Considering the limited gain provided by the nonlinear equalizer for trellis-coded modulation, we abandoned the scheme for the turbo case. The IBO was optimized, as detailed in.° The E, /No was selected in the Because of the simplified four-quadrant decision ap- proach its implementation is easier than a truly DD scheme for 4+12-PSK and decisions are insensitive to possible sig- nal amplitude estimation errors. The main scheme draw- back is related the so called pattern noise or irreducible phase jitter floor due to the phase error signal averaging for the four constellation points belonging to the same quad- rant. This floor is not present with QPSK modulation, where the exact Decision- Directed, and this simplified ver- sion are identical. Simulation results indicate that the per- formance is degraded with respect to the TC-DD scheme but remains acceptable even at low SNR. It was found that a phase jitter standard deviation of about 1 degree can be achieved at E;/No = 5 dB for loop bandwidth!” BreTs;(oo) =5-1075. Because of the simplified four-quadrant decision ap-
Fig. 11 Simulated BER for turbo coded 4+12-PSK in the non- linear channel: r=3/4 code, IBO = 2 GB, roll-off factor=0.35. middle of the waterfall BER region to allow for capturing the BER variation. Clearly, optimization cannot be per. formed at P,; = 10~*° but the current working point hardly differs from the QEF in terms of SNR. The decoder input SNR was computed based on the effective demodulator in- put F;/No previously defined (see eqn. (6)) [E5/Noler. For the optimum IBO of 2 dB the BER over the nonlinear channel was then simulated and the results are collected in Fig. 11. We can see that due to the optimal combination of Fig. 11. We can see that due to the optimal combination of
Fig. 11 Simulated BER for turbo coded 4+12-PSK in the non- linear channel: r=3/4 code, IBO = 2 GB, roll-off factor=0.35. middle of the waterfall BER region to allow for capturing the BER variation. Clearly, optimization cannot be per. formed at P,; = 10~*° but the current working point hardly differs from the QEF in terms of SNR. The decoder input SNR was computed based on the effective demodulator in- put F;/No previously defined (see eqn. (6)) [E5/Noler. For the optimum IBO of 2 dB the BER over the nonlinear channel was then simulated and the results are collected in Fig. 11. We can see that due to the optimal combination of Fig. 11. We can see that due to the optimal combination of