On Enhancing Hierarchical Modulations Shu Wang, Byung K. Yi and Soon Y. Kwon LG Electronics Mobile Research, USA
Introduction •
•
•
•
Hierarchical modulations are widely used in digital broadcast system design such as • Dedicated network: DVB-T, Media-FLO, UMB-BCMCS. • Hierarchical network: DVB Multiplexing. Hierarchical modulations can help • provide different QoS’s to users with different profiles, e.g. higher throughput for users with advanced receiver. • provide unequal protection on different contents, e.g., video, audio, text. • update system to provide better service to new users with advanced receiver with keeping existing users unchanged. The enhanced hierarchical modulation scheme by rotating enhancement layer(s) is investigated here for the next generation system in terms of an information theoretic perspective: achievable throughputs a signal-processing perspective: inter-layer interference, effective SNR, effective power, modulation efficiency. an implementation perspective: peak-to-average power ratio (PAPR) These criteria can be used for optimizing and evaluating layered/hierarchical transmissions in the future too.
Superposition Precoding and Hierarchical Modulation 01
00
0011
0000 0001
0010
b 1b 0
α
2β
0110
10
11
θ
0111
0100 0101
Base Layer: QPSK 1111
00 01
1100 1101
1110
β
θ
e 1e 0
10 11
Enhancement Layer: rotated QPSK
2α 1011 1010
1000 1001
QPSK/QPSK Hierarchical Modulation
Achievable rates, ( Bergmans and Cover, 1974 ).
•Optimal broadcast channel capacity is achievable by superposing two users’ signal together. •Superposition precoding with interference cancellation outperforms TDM and FDM schemes in most time.
•Hierarchical modulation is one of the popular implementations of superposition precoding.
b1e1b0e0
Hierarchical Modulation in Standards (1/2)
Media-FLO supports hierarchical
transmission of base/enhancement layers • Extends coverage with layered source coding • Provides a more graceful degradation of reception.
Hierarchical Modulation in Standards (2/2)
DVB-T -- QPSK/64QAM, 13.6/4.5Mbps with coding rate ¾ and ½.
•Besides using a dedicated DVB-H network, DVB-H service can also be embedded into DVB-T network using hierarchical modulation. • DVB-H service use the HP input while DVB-T services use LP. • The HP input can offer increased robustness in mobile environment over the LP input • The LP input can serve higher bit-rate for fixed reception service
Enhanced Hierarchical Signal Constellation 01
00
The key advantage: minimum 0011
b1b0
α
0111
c’
10
11
0001
0010
a 2β
0110
∆1
0000
θ
c b 0100
∆2
0101
δ
Base Layer: QPSK
complexity increase. The major gain: higher throughput on the base layer The extra benefit: lower bit-error rate on the enhancement layer
1111
00 01
a’
1101
β
θ
e1e0
10 11
Enhancement Layer: rotated QPSK
c” 1010
1100
b’
1110
2α
1011
1000 1001
Enhanced QPSK/QPSK Hierarchical Modulation
There are a couple of ways to find the best rotation angle: if the target SNR’s are known, maximizing the sum capacity of the two layers. if only the power splitting ratio is known, optimizing Euclid distance profile. another practical approach is to find the best angle by simulations.
QPSK/16QAM Hierarchical Modulation
Channel Capacity using N-ary Modulation •The capacity of a general N-ary modulation can be written by Signal Constellation and Euclid Distances Profile
⎧⎪ ⎡ N −1 ⎛ 1 C N = log 2 ( N ) − N ∑ E ⎨log 2 ⎢∑ exp⎜⎜ − j =0 ⎪⎩ ⎢⎣ i =0 ⎝ N −1
s j + n − si
2
2σ 2
−n
2
⎞⎤ ⎫⎪ ⎟⎥ ⎬ ⎟ ⎠⎥⎦ ⎪⎭
n denotes normally distributed complexvalued noise with variance σ2
Achievable Gains (1/2) Achiievable Capacity Gain (bits/symbol)
0.16
QPSK/QPSK, ER=2 QPSK/QPSK, ER=3.5 QPSK/QPSK, ER=3.75 QPSK/QPSK, ER=4
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0 0
5
10
15
SNR (dB)
20
25
30
Achievable Gains (2/2) 45
QPSK/QPSK, ER=2 QPSK/QPSK, ER=3.5 QPSK/QPSK, ER=3.75 QPSK/QPSK, ER=4
Optimial Rotation Angle (degree)
40 35 30 25 20 15 10 5 0 0
5
10
15
SNR (dB)
20
25
30
Achievable Rates: 16QAM/QPSK 7
rate in crease b y ro tatin g en h an cem en t-layer sym b o l
Achievable Rate R, bit/symbol
6
5
cap acity lo ss d u e to th e in terferen ce fro m en h an cem en t layer 4
3
2
R 1 6 Q A M/Q P S K of th e reg u lar h ierarch ical m od u lation R 1 6 Q A M/Q P S K of th e en h an ced h ierarch ical m od u lation B
R 1 6 Q A M/Q P S K of th e reg u lar h ierarch ical m od u lation
1
B
R 1 6 Q A M/Q P S K of th e en h an ced h ierarch ical m od u lation E
R 1 6 Q A M/Q P S K , th e Q P S K en h an cem en t-layer rate 0 0
10%
20%
30%
40%
50%
60%
B ase-L ay er P o w er R atio β
70%
80%
90%
P/σ2=(P1+P2)/σ2= 23dB
100%
Constrained Throughput of Hierarchical Modulations 6
Spectral Efficiency in Good Channel (|h 2| =0.0dB), bit/symbol
5.7
the total rate in good reception condition
2
5
4
SPC Bound Shannon Bound TDM Bound Base Layer / 16QAM Enhancement Layer / QPSK Total Rate, 16QAM/QPSK Optimized Base Layer Optimized Enhancement Layer Optimized Total Rate
inter-layer interference
3
2
1
0
the base layer with good reception condition the enhancement layer with good reception condition 0
0.5
1
1.5
2
2.5
2
3
3.5
Base-Layer/16QAM Spectral Efficiency in Bad Channel (|h1| =-6.0dB), bit/symbol
3.75
4
Inter-Layer Interference Enhancement Layers 10
-1
10
-1
Base Layers 10
-2
10
-2
the regular hierarchical modulation and its base layer & enhancement layer
16QAM
BER p
e
QPSK
10
-3
10
-3
the optimized hierarchical modulation and its base layer & enhancement layer
QPSK 10
10
10
-4
10
QPSK 16QAM QPSK/QPSK ζ =-6.0dB Optimized QPSK/QPSK ζ =-6.0dB Base-Layer QPSK Optimized Base Layer Enhancement-Layer QPSK Optimized Enhancement Layer
-5
-6
0
2
4
6
8
10
12
SNR (dB)
10
-5
-6
14
16
18
16QAM
-4
10 20 0
QPSK 16QAM QPSK/QPSK ζ =-1.9dB Optimized QPSK/QPSK ζ =-1.9dB Base-Layer QPSK Optimized Base Layer Enhancement-Layer QPSK Optimized Enhancement Layer 2
4
6
8
10
12
SNR (dB)
14
16
18
20
Effective Signal-to-Noise Ratio •Effective SNR γeff is defined as the SNR necessitated when the base
layer signal is sent alone with the same power. • Effective SNR always is less than the actual SNR. • The required symbol energy for achieving the same BER is called effective power, which is smaller than actual base-layer signal power. • For example, For QPSK/QPSK hierarchical modulation, the effective SNR of base-layer BER pe is given by 2 ( ) ε σ ε base eff 2 −1 = PQPSK ( pe ) ≤ γ = 2 γ eff (σ ) = 2 σ σ Due to inter-layer interference, effective SNR or effective power is less than actual SNR or power. Stronger inter-layer interference is and smaller effective SNR/power becomes
Modulation Efficiency (1/2)
η = γ eff
σ 2 ε eff (σ 2 ) = ε base ε base
η ∞ = lim η σ 2 →0
•Modulation efficiency of a modulated signal is defined by the ratio between effective SNR and actual SNR. •Modulation efficiency is not greater than 1. •Modulation efficiency, as well as effective SNR and effective power, is the parameter proposed by us for evaluating the performance of the whole transceiver chain, including modulation and demodulation. •Asymptotic modulation efficiency is the ratio when the SNR becomes very large and interference becomes dominant. •Asymptotic modulation efficiency is proposed by us for evaluating the interference resistance capability of both hierarchical modulation scheme and demodulation scheme.
Modulation Efficiency (2/2) 1
Base Layer ζ =-6.0dB Optimized Base Layer ζ =-6.0dB Enhancement Layer ζ =-6.0dB Optimized Enhancement Layer ζ =-6.0dB Base Layer ζ =-1.9dB Optimized Base Layer ζ =-1.9dB Enhancement Layer ζ =-1.9dB Optimized Enhancement Layer ζ =-1.9dB QPSK
0.9
Modulation Efficiency η
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
SNR (dB)
12
14
16
18
20
PEP and Minimum Euclid Distance •A upper bound for
pairwise error probability (PEP) can be derived with
assuming • The Hamming distance is d << K: two codeword c and c’ differ in d bits. • Perfect interleaving. Minimum Euclid distance
pairwise error probability
⎛ Pr{c → c' | c} = Q⎜ ⎝
d
1 2σ
∑s i =1
ki
− s'k
2 i
⎞ ⎟ ≤ ∏e ⎠ i =1 d
−
1 4σ 2
s i − s 'i
Observation: PEP is dominated by the terms with the smallest squared Euclid distance in high SNR region
2
≤e
−
d 4σ 2
Δ2min
Minimum Euclid Distance: QPSK/16QAM
0.9 P 2/P1=0.08 P 2/P1=0.09 P 2/P1=0.10
Minimum Euclid Distance Δ = min{|a-c|,|b-c|}
0.8
P 2/P1=0.11 P 2/P1=0.12 P 2/P1=0.13 P 2/P1=0.14
0.7
P 2/P1=0.15
0.6
0.5
0.4
0.3
0.2
0.1
0
0
5
10
15
20
25
Rotation Angle θ (degree)
30
35
40
45
PAPR of OFDM E s (t )
2
0.25
≈ O (L ) Probability Density Function
PAPR =
max s (t )
2
2
Imaginary Part of OFDM Signal
1.5
3.01dB
1
0.5
0
-0.5
0.2
0.15
0.1
0.05
-1
-1.5
-2 -2
0 2
6.53dB -1.5
-1
-0.5
0
0.5
Real Part of OFDM Signal
1
1.5
4
2
8PSK, L=128
6
8
10
12
Peak-to-Average-Power Ratio (dB)
14
16
Hierarchical Modulation with Rotation 0
10
-1
CCDF
10
10
10
10
-2
-3
-4
0
Gaussian Approximation, L=128 Regular QPSK/QPSK, P 2 /P 1 =0.01, L=128 Regular QPSK/QPSK, P 2 /P 1 =0.09, L=128 Regular QPSK/QPSK, P 2 /P 1 =0.25, L=128 Enhanced QPSK/QPSK, P 2 /P 1 =0.01, L=128 Enhanced QPSK/QPSK, P 2 /P 1 =0.04, L=128 Enhanced QPSK/QPSK, P 2 /P 1 =0.09, L=128 Enhanced QPSK/QPSK, P 2 /P 1 =0.16, L=128 Enhanced QPSK/QPSK, P 2 /P 1 =0.25, L=128 2
4
6
8
Peak-to-Average Power Ratio (dB)
10
12
PAPR Reduction with Group-Based Cyclic Delay (1/2)
The input layeredmodulated symbols are divided into multiple smaller groups of layeredmodulated symbols
Cyclic Delay Combining and PAPR calculation
Cyclic Delay
PAPR Reduction with Group-Based Cyclic Delay (2/2) 0
10
-1
CCDF
10
10
-2
Gaussian Approximation, L=128 Regular QPSK/QPSK, P 2 /P 1 =0.01, L=128 Regular QPSK/QPSK, P 2 /P 1 =0.09, L=128
10
-3
Regular QPSK/QPSK, P 2 /P 1 =0.25, L=128 with PAPR Reduction, P 2 /P 1 =0.01, L=128, G=2 with PAPR Reduction, P 2 /P 1 =0.04, L=128,G=2 with PAPR Reduction, P 2 /P 1 =0.09, L=128, G=2 with PAPR Reduction, P 2 /P 1 =0.16, L=128, G=2
10
-4
0
with PAPR Reduction, P 2 /P 1 =0.25, L=128, G=2
2
4
6
8
Peak-to-Average Power Ratio (dB)
10
12
Conclusions • •
•
•
Hierarchical modulation has been adopted in various standards including MediaFLO, DVB-H and UMB. The enhance hierarchical modulation is adopted in UMB, the salient features of which include • minimum modulation/demodulation complexity increase. • high bps: channel capacity gain on lower layer(s) • lower BER: signal processing gain. The enhanced hierarchical modulation is investigated in terms of achievable throughputs inter-layer interference asymptotic modulation efficiency peak-to-average power ratio The enhanced hierarchical modulation is recommended for the nextgeneration standards.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
T. Cover, Broadcast channels, IEEE Trans. Information Theory, Vol. 18, pp. 2-14, Janurary 1972. G. Ungerbock, Channel coding with multilevel/phase signals, IEEE Trans. On Information Theory, Vol. 28, No. 1, January 1982, pp. 55-67 H. Jiang and P. A. Wilford, A hierarchical modulation for upgrading digital broadcast systems, IEEE Trans. Broadcasting, 2005 T. W. Sun, R. D. Wesel, Superposition turbo TCM for multirate broadcast, IEEE Trans. Communications, Vol. 52, No. 3, March 2004 Qualcomm Incorporation., FLO Air Interface Specification , 80-T0314-1 Rev. D 3GPP2, Ultra Mobile Broad Physical Layer, C.P0084-001, February 13, 2007 D. Gomez-Barquero and A. Bria, Feasibility of DVB-H Deployment on Existing Wireless Infrastructure, IWCT 2005 T. Cover and J. Thomas, Elements of information theory, John Wiley & Sons, 1991 P. P. Bergmans and T. M. Cover, Cooperative broadcasting, IEEE Trans. Information Theory, Vol. 20, pp. 317-324, May 1974. C.-E. W. Sundberg, W. C. Wong and R. Steele, Logarithmic PCM weighted QAM transmission over Gaussian and Rayleigh fading channels, Proc. IEE, Vol. 134, No. 6, pp. 557-570, October 1987 L.-F. Wei, Coded modulation with unequal error protection, IEEE Trans. Communication, Vol. 41, pp.1439-1449, October. 1993. LMQS, BCMCS in LBC, C30-20070131-001 LGE, Enhanced Hierarchical Modulation, C30-20070201-003, C30-2007-0206-004. LGE, Zone-based BCMCS for HRPD, C30-20050214-014, Feb 2006.
Appendix
4
Achievable Rates (bits/symbol)
3.5
QPSK/QPSK; ER=2 QPSK/QPSK, Enhanced; ER=2 Shannon Bound Achievable Capacity Gain
3
2.5
2
1.5
1
0.5
0 0
5
10
15
SNR (dB)
20
25
30
Achievable Rates for QPSK/QPSK, ER=3.5 4
Achievable Rates (bits/symbol)
3.5
QPSK/QPSK, ER=3.5 QPSK/QPSK, Enhanced; ER=3.5 Shannon Bound Achievable Gain
3
2.5
2
1.5
1
0.5
0 0
5
10
15
SNR (dB)
20
25
30
Achievable Rates for QPSK/QPSK: ER=3.75 4
Achievable Rates (bits/symbol)
3.5
QPSK/QPSK; ER=3.75 QPSK/QPSK, Enhanced; ER=3.75 Shannon Bound Achievable Gain
3
2.5
2
1.5
1
0.5
0 0
5
10
15
SNR (dB)
20
25
30
Achievable Rates for QPSK/QPSK, ER=4 4
QPSK/QPSK, 16QAM; ER=4 QPSK/QPSK, Enhanced; ER=4 Shannon Bound Achievable Capacity Gain
Achiavable Rates (bits/Symbol)
3.5
3
2.5
2
1.5
1
0.5
0 0
5
10
15
SNR (dB)
20
25
30
