IEEE ICC 2013 - Selected Areas in Communications Symposium
Coded Modulation with APSK Constellations for Power Line Communication Jian Song1 , Keqian Yan1 , Fang Yang1 , Qiuliang Xie2 , Fei Ren3 , and Jia Li3 1
Electronic Engineering Department, Tsinghua University Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, P. R. China 2 National Engineering Lab. for DTV (Beijing) 3 Sichuan Changhong Electronic Ltd. Co., Mianyang Sichuan 621000 Email:
[email protected]
Abstract—This paper proposes a novel coded-modulation scheme using amplitude phase shift keying (APSK) constellations with Gray mapping for the broadband power line communication systems for the first time. In this scheme, three key techniques including the Gray-APSK constellation design, the bit mapping technique, and the method of simplified soft APSK demapper are jointly employed to enhance the error-control performance while ensuring low complexity. Simulation results over AWGN and power line channels show that the proposed scheme provides a remarkable receiving performance gain, compared to its counterpart specified in the G.hn standard. Keywords—power line communication, APSK, bit mapping, simplified demapper.
I. I NTRODUCTION Due to the increasing demand for high data rate transmission, the broadband power line communication (PLC) has attracted the focus of attention of academic researches and practical applications. Operating in the wide frequency band, broadband PLC systems can support signal transmissions over electric power lines with rates up to a few hundred megabits per second. In recent years, several competing standards organizations have pushed forward specifications on broadband PLC, including the Recommendation G.hn [1] developed by ITU Telecommunication Standardization Sector (ITU-T) and IEEE 1901 [2] proposed by IEEE Communications Society. Since the power line was originally designed for electric power delivery rather than the telecommunication purpose, the measurement results of PLC channel show it presents a very harsh and hostile environment for the data transmission. The data transmitted by PLC faces several challenges: high attenuation, varying channel condition, considerably large noise, and severe frequency selectivity [3]. These issues seriously deteriorate the reception quality and impede the commercialization of PLC. Hence, the robust coded-modulation scheme with superior system performance becomes one of the key factors for the successful PLC deployment. As an emerging communication technology, PLC has employed the maturely developed coded-modulation techniques which have achieved striking success in other communication fields. These techniques include the low-density paritycheck (LDPC) code and the quadrature amplitude modulation (QAM). Owing to the capacity-approaching performance, LDPC code is commonly used as the forward error correction
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(FEC) code in wireless and satellite communications, and it is also proven to be suitable for PLC scenarios according to the previous work [4]. G.hn adopts the LDPC codes specified in worldwide interoperability for microwave access (WiMAX) [5] as its FEC code basis. IEEE 1901 also provides the LDPC code as an option for FEC besides the concatenation of Reed-Solomon (RS) and convolutional codes. As the most preferred modulation mechanism for highspeed digital communications, QAM has found its way into PLC. To achieve very high levels of spectral efficiency, dense QAM constellations are favored by broadband PLC standards. Both the G.hn and IEEE 1901 standards are capable of supporting numerous QAMs with the maximum number of constellation points of 4096. However, recent work shows that a well-designed amplitude phase shift keying (APSK) constellation with proper labeling can outperform its QAM counterpart over both additive white Gaussian noise (AWGN) and fading channels at code rates of interests [6], [7]. In this paper, an efficient and robust coded-modulation scheme is proposed for PLC systems, where the Gray-APSK constellations are employed instead of traditional Gray-QAM constellations and the G.hn LDPC codes are adopted. Furthermore, the bit mapping technique is applied to further improve the error-control performance, and the simplified demapper is employed, which can significantly reduce the computational complexity for hardware implementation. The remainder of this paper is organized as follows. The system model of the proposed coded-modulation scheme is briefly described in Section II, and the key technologies are detailed in Section III. The computer simulations are performed to verify the performance of the proposed scheme in Section IV. Finally, conclusions are drawn in Section V. II. S YSTEM M ODEL In the power network, the impedance mismatch at joints of the house service cables, connection boxes, and various connections of cables introduces numerous reflections, which displays as a multipath scenario in data transmission. Furthermore, the rapid variation of impedance with frequency also leads to a varying channel characteristic on the overall frequency band [8]. Hence, the PLC channel is usually characterized by multipath propagation models with severe
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Fig. 1. The system model of the proposed coded-modulation scheme assuming ideal synchronization, channel estimation, and equalization.
frequency-selective fading [8], [9]. Considering the hostile characteristics of PLC channel, an efficient coded-modulation scheme, wherein APSK constellations are employed for the outstanding performance over fading channels, is proposed. Fig. 1 shows the system block diagram of the proposed coded-modulation scheme. The transmitter consists of the FEC encoder, the bit interleaver, the bit permutation, the constellation mapper, and the inverse fast Fourier transform (IFFT). In this scheme, we adopt the irregular quasi-cyclic (QC) LDPC codes with code rates of 1/2 and 2/3 specified in ITU Recommendation G.9960 [1], the physical layer specification of G.hn standard, as the FEC codes. After encoding, the bit mapping is performed by the bit interleaver concatenated with the bit permutation. The function of the bit mapping is to selectively map coded bits to distinct modulation levels, thus achieving a proper match between the decoder and the demapper [10], [11], and it can provide considerable coding diversity under fading channels as well. The output binary sequence of bit mapping will be converted to the complex symbol stream by the constellation mapper. The Gray-APSK which can provide significant shaping gain compared with squared uniform QAM for its Gaussian-like distribution is adopted as the mapping constellation. In this paper, we focus on 256-APSK and 1024APSK constellations for the performance evaluation on the high data rate transmission. Finally, the symbol stream is modulated to the time domain via IFFT operation. The receiver includes the functional blocks corresponding to their counterparts in the transmitter, while the synchronization, the channel estimation, and the equalization are considered to be perfect with their blocks omitted in Fig. 1. The received signal is converted to the frequency domain via fast Fourier transform (FFT) operation, and then sent to the simplified APSK soft demapper. The output of demapper, expressed in the log-likelihood ratio (LLR) form, is re-arranged via the bit de-permutation and bit de-interleaving. Finally, the binary information is recovered after LDPC decoding. III. C ODED M ODULATION WITH APSK C ONSTELLATIONS In this section, we detail the proposed coded-modulation scheme with the following three features: the Gray-APSK constellation, the bit mapping technique, and the simplified demapper. A. Gray-APSK Constellation An APSK constellation is composed of R concentric rings containing signal points uniformly distributed on each ring.
The M -APSK constellation set X can be expressed as [12] ⎧ 2π ⎪ r exp j i + θ i = 0, . . . , n1 − 1 ⎪ 1 1 ⎪ ⎪ n1 ⎪ ⎪ 2π ⎨ r2 exp j i = 0, . . . , n2 − 1 n2 i + θ2 X= (1) . ⎪ .. ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ rR exp j n2πR i + θR i = 0, . . . , nR − 1 where nl , rl , and θl denote the number of points, the radius, and the phase offset,of the l-th ring (l = 1, √. . . , R), respecR tively, and we have l=1 nl = M and j = −1. The APSK constellation is first proposed by Thomas in [13]. From the information theoretical point of view, the nonuniformly spaced APSK can achieve certain shaping gain as it is more likely to be Gaussian-distributed comparing to QAM [6]. However, for most conventional APSK constellations, the absence of Gray labeling leads to a relatively large independent demapping loss. Furthermore, the APSK soft demapping requires very high complexity. Hence, in most communication systems such as the second generation digital video broadcasting-terrestrial (DVB-T2) [14], WiMAX, and G.hn, the APSK is usually not preferred compared with the Gray-QAM [15]. Recently, a method to design APSK constellations with Gray labeling is addressed in [7], wherein each ring possesses both the same number of points and phase offset. For a 2m -ary APSK designed in this way, each ring contains 2m1 points, and the number of rings is R = 2m2 , where m1 + m2 = m, and both m1 and m2 are positive integers. In this paper, we denote such an APSK as (2m1 ×2m2 )2m -APSK. The recommended radius of each ring is determined as rl = − ln[1 − (l − 12 ) · 2−m2 ], 1 ≤ l ≤ R . (2) The labeling of the constellation maps a bit-vector b with the length of m to the constellation symbol x ∈ X . We assume the leftmost m1 bits in this bit-vector are only relevant to the phases, and the rest m2 bits are only relevant to the amplitudes of the APSK constellation. Hence, the (2m1 ×2m2 )2m -APSK can be viewed as the product of a 2m1 -ary phase shift keying (PSK) and a pseudo 2m2 -ary pulse amplitude modulation (PAM). The Gray labeling of APSK constellation is thus achieved when both the 2m1 -PSK and the 2m2 -PAM are Gray labeled. It is verified by average mutual information (AMI) analysis and bit error rate (BER) simulations that the GrayAPSK can provide better performance in both independent and iterative demapping scenarios [7]. In the Gray-APSK design, the parameters m1 and m2 should be deliberately selected to ensure good error-control performance, whereby the criterion is to maximize the AMI of coded modulation (CM-AMI) [16] for iterative demapping or the AMI of bit-interleaved coded modulation (BICMAMI) [16] for independent demapping. In this paper, we will focus on the independent demapping scenario. Fig. 2 gives the gaps between the BICM-AMI and the channel capacity for 256-APSK and 1024-APSK with different pairs of (m1 , m2 )
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1.6
Gap to channel capacity (dB)
1.2
1.4
1
Fig. 3.
The structure of bit permutation.
0.8 0.6 0.4 0.2 0
TABLE I PARAMETERS OF BIT PERMUTATION
(128×8)1024−APSK (64×16)1024−APSK (32×32)1024−APSK (64×4)256−APSK (32×8)256−APSK (16×16)256−APSK 2
3
4
5 6 AMI (bits/channel use)
N
Rate
Permutated indices Π
256-APSK
8
1/2 2/3
{2,5,4,3,0,1,6,7} {0,1,3,4,6,5,2,7}
1024-APSK
10
1/2 2/3
{1,3,5,4,0,6,2,7,8,9} {1,3,4,5,6,7,0,2,8,9}
Constellation
7
8
9
Fig. 2. Gaps between the BICM-AMI and the channel capacity for 256APSK and 1024-APSK over AWGN channel.
over AWGN channel. It is shown that the (64×16)1024-APSK is slightly inferior to (32×32)1024-APSK about 0.12 dB at the code rate of 1/2, while it provides obvious advantages at rate 2/3 or higher rates. Meanwhile, the (32×8)256-APSK is superior to other 256-APSK counterparts when the code rate exceeds 1/2. Taking the overall performance at code rates of usual interests into consideration, we select the (64×16)1024APSK and (32×8)256-APSK as the constellations, which is also in accord with the recommendation in [15] to choose m1 = m/2 + 1 and m2 = m/2 − 1 for an even m. B. Bit Mapping The irregular LDPC code is characterized with unequal variable node degree, which implies that the nodes with different degrees show different reliabilities at the receiver. Similarly, for high-order modulations, the bits mapped to one complex symbol also exhibit different bitwise sub-channel capacities, expressed as the AMI between each bit and the channel output. According to the unequal error protection (UEP) property inherent from both the irregular LDPC code and the high-order modulation, it is noted that the bit mapping distribution {λk,v }, i.e., the proportion of the variable nodes of degree k mapped to the v-th modulation sub-channel, affects the system error-control performance [17]. Hence, the bit mapping is proposed to optimize the bit mapping distribution and achieve a good match between the LDPC decoding and constellation demapping. Considering the low-complexity implementation requirement in practical applications, a bit interleaver concatenated with a bit permutation is used to implement the bit mapping. This technique has already been adopted in DVB-T2 standard due to its ingenious structure. The bit interleaver, aiming at roughly scrambling the bit mapping distribution and achieving the coding diversity, is usually selected for the purpose of low complexity. Here we adopt the simple block bit interleaver, where the elements are written in column into the interleaved
matrix and read out in row. The interleaving depth is set to m for 2m -APSK. After bit interleaving, the bit permutation is performed to further optimize the bit mapping distribution. Fig. 3 shows the structure of bit permutation, wherein the input bits are divided into N streams with sequential indices from 0 to N − 1, and then permuted with the new indices Π = {π(0), π(1), . . . , π(N − 1)}, which implies that the original i-th stream gi is read out in the order of π(i). For simplicity, we perform the bit permutation within one constellation symbol, that is, N = m for 2m -APSK. An extrinsic information transfer (EXIT)-aided bit mapping design method is proposed in our previous work [10] which contains two steps. First, the EXIT curve-fitting is performed on all the effective bit permutation patterns to obtain the coarse searching results with the lowest convergence threshold, which is defined as the lowest SNR value required for a well-matched EXIT chart. Then the optimal pattern is determined among the patterns selected above according to BER simulations. We apply this method in search of the proper bit permutation patterns for the proposed coded-modulation scheme using the proposed APSK constellations and LDPC codes specified in G.hn, and also consider the trade-off between AWGN and PLC multipath fading channels modeled in [8]. The parameters of the designed patterns are listed in Table I. C. Simplified Demapper In the past, the high complexity of APSK soft demapping is an important factor that impedes the applications of APSK constellations. Assume the modulator maps a bit-vector b with the length of m onto a complex symbol x at the transmitter, and the received and phase-equalized symbol is y after x passing through the channel characterized by the channel gain h and AWGN n with the variance of N0 . In a traditional Max-Log-MAP demapper without a priori information, the soft information of the i-th bit can be expressed as
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Lei ≈ log
max max
x∈X x∈X
(0) p(y|x) i (1) p(y|x) i
,
0≤i
