A Near-Capacity MIMO Coded Modulation Scheme for ... - IEEE Xplore

IEEE TRANSACTIONS ON BROADCASTING, VOL. 61, NO. 3, SEPTEMBER 2015

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A Near-Capacity MIMO Coded Modulation Scheme for Digital Terrestrial Television Broadcasting Tao Cheng, Kewu Peng, Senior Member, IEEE, Fang Yang, Senior Member, IEEE, Jian Song, Senior Member, IEEE, and Zhixing Yang, Senior Member, IEEE

Abstract—Multiple-input multiple-output (MIMO), which can provide ultrahigh data transmission rate, is one of the key technologies for the next generation digital terrestrial television broadcasting (DTTB) standards. This paper proposes a nearcapacity MIMO bit-interleaved coded modulation scheme with either independent or iterative demapping (BICM/BICM-ID) for the DTTB system. First, the amplitude phase shift keying (APSK) constellation with Gray mapping is proposed to replace the conventional Gray quadrature amplitude modulation (QAM) counterpart. From the perspective of average mutual information analysis, Gray-APSK has certain shaping gain compared to Gray-QAM for both independent and iterative demapping schemes. Besides the APSK constellation, a novel bit interleaver named bit mapping, which takes into account the unequal error protection of both APSK constellations and low-density parity-check codes, is proposed to further improve the system performance. The tool of extrinsic information transfer chart is utilized to analyze and design the optimal bit mapping for the BICM/BICM-ID scheme. Bit error rate simulations are finally carried out to verify the superiority of the proposed MIMO coded modulation scheme. Index Terms—Multiple-input multiple-output (MIMO), amplitude phase shift keying (APSK), bit mapping, average mutual information (AMI), extrinsic information transfer (EXIT) chart.

I. I NTRODUCTION ULTIPLE-INPUT multiple-output (MIMO) are capable of providing significant higher transmission rate than single antenna systems without any additional bandwidth or increased transmission power [1]–[3]. Due to its potential gain, MIMO is deemed as one of the key technologies

M

Manuscript received December 3, 2014; revised February 18, 2015; accepted February 19, 2015. Date of publication July 23, 2015; date of current version September 2, 2015. This work was supported in part by the National Natural Science Foundation of China under Grant 61401248 and Grant 61471219, in part by the Research and Development Project of Science and Technology Innovation Commission of Shenzhen, China, under Grant JCYJ20140419122040614, and in part by the National Basic Research Program of China (973 Program) under Grant 2012CB316000. T. Cheng, K. Peng, F. Yang, and Z. Yang are with Research Institute Information Technology and Electronic Engineering, Department of Tsinghua University, Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China, and also with the National Engineering Laboratory for DTV, Beijing 100191, China. J. Song is with Research Institute Information Technology and Electronic Engineering, Department of Tsinghua University, Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China, also with the National Engineering Laboratory for DTV, Beijing 100191, China, and also with the Shenzhen City Key Laboratory of Digital TV System, Shenzhen 518057, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TBC.2015.2419177

and has been widely accepted by many communication standards, such as IEEE 802.11n for wireless local area network (WLAN) and 3GPP’s Long Term Evolution (LTE) for cellular networks [4], [5], etc. However, in the field of digital terrestrial television broadcasting (DTTB), MIMO is not so popular because of the consideration of backward compatibility to legacy infrastructure. The second generation Digital Video Broadcasting - Terrestrial (DVB-T2) [6] has only adopted multiple-input single-output (MISO) scheme, while Digital Video Broadcasting - Next Generation Handheld (DVB-NGH) [7] employs 2×2 MIMO scheme. MIMO techniques can exploit either diversity gain or multiplexing gain, or a tradeoff between them [8]. In this paper, we inspect MIMO schemes from the viewpoint of information theory. The Alamouti code [9] in DVB-T2 is optimal in that it is able to achieve the channel capacity for 2 × 1 MISO channel. However, it cannot be extended to MIMO channels with more transmitting or receiving antennas. To achieve the capacity of MIMO channels, the vertical Bell-lab layered space-time (V-BLAST) scheme was proposed [10], wherein the signals transmitted from different antennas are independent with each other. DVB-NGH is the first broadcasting standard that incorporates 2 × 2 MIMO as the key technology. On the other hand, the coding and modulation techniques have made a great progress in recent years. The utilization of low-density parity-check (LDPC) codes and bit-interleaved coded modulation (BICM) easily breaks the bound of cutoff rate, and pushes the signal-to-noise ratio (SNR) threshold towards theoretic-limit of single-input single-output (SISO) systems [11], [12]. The BICM with iterative demapping scheme (BICM-ID) uses the feedback of the decoder to the demapper as the a priori information, which helps to further improve the system performance [13]. With the emerging market of ultra high-definition television (UHDTV, also called 4K TV), which requires much higher transmission rate than standard definition television (SDTV) or HDTV, a near-capacity MIMO system is of great demand. Enlightened by the single antenna scheme, Hochwald et al proposed a MIMO BICM-ID system with quadrature amplitude modulation (QAM) and convolutional/Turbo codes, which aims at approaching the MIMO channel capacity [14]. However, take the 2 × 2 MIMO scheme with 64QAM on each transmitting antenna and rate-1/2 Turbo code as an example, the SNR threshold is still over 3 dB away from Shannon limit. Besides, the system is only optimized for the iterative demapping scheme, hence the performance

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for the independent demapping scheme is far from satisfying. Currently, most DTTB standards still recommend independent demapping scheme, although iterative demapping scheme is an option when the computing resources are available and the critical performance is required. Hence, the optimizations of both independent and iterative demapping schemes are of value. This paper contributes to propose a simple yet efficient MIMO BICM/BICM-ID system that has the capacity-approaching performance. First, we try to maximize the constellation constrained capacity. The Gray mapped amplitude phase shift keying (Gray-APSK) is employed as the constellation mapping. Compared to its QAM counterpart, Gray-APSK has certain shaping gain from the perspective of average mutual information (AMI) for both iterative and independent demapping schemes [15]. Moreover, to approach such constellation constrained capacity, a new kind of bit interleaver named bit mapping [16], [17], which takes into account the unequal error protection (UEP) of high-order APSKs and irregular LDPC codes, is employed. The tool of extrinsic information transfer (EXIT) chart [18]–[20] is utilized to analyze and design the optimal bit mapping. Finally, bit error rate (BER) simulations have shown that the performance of the proposed system surpasses that of the DVB-NGH system, which is the representative of the next generation DTTB standard and is deemed as a benchmark in this paper. The rest of this paper is organized as follows. Section II briefly introduces the MIMO channel and the system model. In Section III, Gray-APSK constellations are introduced and applied to the MIMO system, after which the AMI analysis is performed. In Section IV, the EXIT chart is employed to help analyze and design the optimal bit mapping. BER simulations of DVB-NGH and the proposed system are carried out in Section V. Section VI concludes this paper. Notations: The lowercase and uppercase boldface letters denote vectors and matrices, respectively. xi is the i-th entry of the vector x, and xi,j is the entry at the i-th row and j-th column of the matrix X. Capitalized calligraphic symbols denote sets. The superscripts (·)T and (·)† denote the transpose and conjugate transpose, respectively. Ex (·) stands for the expectation operation over the random vector x. II. MIMO BICM/BICM-ID S YSTEM M ODEL Consider a MIMO channel with nT transmitting and nR receiving antennas. Let x ∈ CnT ×1 be the transmitting vector, y ∈ CnR ×1 be the receiving vector, H ∈ CnR ×nT be the channel state information (CSI) matrix, and n ∈ CnR ×1 be the standard additive white Gaussian noise (AWGN) with ni ∼ CN (0, 1). The MIMO channel can be modeled as √ y = ρHx + n. (1) For simplicity, we consider the independent identical distributed (i.i.d.) Rayleigh fading channel only, i.e., each element of H satisfies the standard complex Gaussian distribution hi,j ∼ CN (0, 1). We further assume that the transmitting vector x satisfies the normalized power constraint E[x† x] = 1.

Fig. 1.

Block diagram of the MIMO BICM/BICM-ID scheme.

As the power of the transmitting vector and the channel gains are both normalized, ρ can be interpreted as the SNR at each receiving antenna. In this paper, we simply use channel coding combined with MIMO symbol mapper. This simple scheme can achieve capacity-approaching performance without any space-time coding. As shown in Fig. 1, the channel encoder, bit interleaver, MIMO symbol mapper, and corresponding decoder, de-interleaver, and demapper form a BICM or BICM-ID paradigm. Assume the transmitting vector x is composed of [x1 , · · · , xnT ]T , where xi is chosen from some complex constellation Xi with 2Ni points (i = 1, · · · , nT ). The vector x can thus be viewed as an nT -dimensional symbol from a large composite constellation X with 2N points, nT where X = X1 × · · · × XnT and N = i=1 Ni . At the transmitter, the information bit stream is LDPC coded, bit interleaved, and then converted to the symbol vector block by block. Every a bit T bits are grouped into N consecutive T = b0 , · · · , bN−1 , where vector b = b(1) , · · · , b(nT ) T i−1 b(i) = bki , · · · , bki +Ni −1 (ki = j=1 Nj ) is mapped to the symbol xi according to a labeling function. At the receiver, both independent and iterative demapping schemes are investigated in this paper. Since the number of the antennas is limited in terrestrial broadcasting (usually no more than two), the logarithmic maximum a posterior (log-MAP) demapping algorithm [14] is applicable. In the iterative demapping scheme, the output of the LDPC decoder is fed back to the joint MIMO demapper as the a priori information (represented by the dashed line in Fig. 1). Then the extrinsic information of the i-th bit of a symbol from the demapper can be calculated, in the form of log-likelihood ratio (LLR), as Liiter (b)

= log

(0) xˆ ∈Xi

(1) x∈Xi

p y|ˆx, H Pr xˆ |La p( y|x, H)Pr(x|La )

− Lia ,

(2)

where Xi denotes the constellation subset with the i-th bit a ]T is the a priori being b ∈ {0, 1}, and La = [L0a , · · · , LN−1 information from the decoder, also in the form of LLR. With the noise being Gaussian distributed, the conditional

CHENG et al.: NEAR-CAPACITY MIMO CODED MODULATION SCHEME FOR DTTB

Fig. 2.

369

Gray-APSK constellations. (a) 8APSK. (b) 16APSK. (c) 32APSK.

probability density function of the received symbol has the form of √ −y − ρHx2 1 p( y|x, H) = exp , (3) π N0 N0 with N0 = 1. The conditional probability Pr(x|La ) can be decomposed into the product of the conditional probability of each bit as e(1−bi )Lia N−1 N−1 Pr x|La = Pr bi |Lia = a , 1 + eLi i=0 i=0

(4)

with the assumption that the elements in La are independently distributed due to sufficient bit interleaving. Substituting (3) and (4) into (2), we can get √ x)T La −y− ρHˆx2 (0) exp b(ˆ xˆ ∈Xi iter − Lia , (5) Li = log √ T a 2 exp b(x) L −y− ρHx (1) x∈X i

where b(x) denotes the column bit vector that corresponds to symbol x. If the a priori information is not available, as is the case for independent demapping scheme, the conditional probability of each symbol is assumed to be identical and (5) is therefore degenerated to √ ρHˆx2 (0) exp −y− ˆ x ∈ X . Liind = log i (6) √ ρHx2 (1) exp −y− x∈X i

The extrinsic information from the demapper’s output is deinterleaved and then sent to the LDPC decoder, which utilizes the standard sum-product algorithm (SPA) [21] to calculate the LLR of each bit. III. C ONSTELLATION O PTIMIZATION

MIMO modulation modes in DVB-NGH: QPSK×16QAM, 16QAM×16QAM, and 16QAM×64QAM, with corresponding N being 6, 8, and 10, respectively. From the view point of information theory, the capacity of the AWGN channel can be achieved only if the input satisfies Gaussian distribution [22]. Compared to the conventional squared uniform QAM, circularly distributed APSK is more Gaussian-like and can exploit some capacity gain, which is defined as the shaping gain [23]. However, conventional APSK does not have Gray mapping, which leads to high independent demapping loss and restricts its potential applications. Recently, a new kind of APSK constellation with Gary mapping is proposed [15]. A 2m -ary Gray-APSK is composed of 2m2 concentric rings with 2m1 points uniformly distributed on each ring, where m = m1 + m2 . For the m bits of a constellation symbol, the rightmost m1 bits determine the phase shift which forms a 2m1 -ary Gray-PSK, while the leftmost m2 bits determine the amplitude which forms a 2m2 -ary nonuniform Gray-PAM. Therefore, Gray mapping exists for such APSK constellations as illustrated in Fig. 2. In this paper, we first apply such Gray-APSK technique to the MIMO coded modulation system. The radii of the constellation rings, which are listed aside in Fig. 2, are carefully selected to maximize the AMI of the 2 × 2 MIMO system. There are two advantages for the MIMO system to use GrayAPSK replacing conventional Gray-QAM constellations. First, the AMI of Gray-APSK is greater than that of Gray-QAM in both iterative and independent demapping schemes, as will be illustrated in the next subsection. Second, for some modulation mode with N not being a multiple of 4, saying N = 10 for example, DVB-NGH must use imbalanced constellations on different antennas, like 16QAM×64QAM, but the proposed system can use balanced constellations 32APSK×32APSK instead.

A. Gray-APSK Constellations In this paper, we mainly focus on the 2 × 2 MIMO scheme. We use ‘×’ to connect the two constellations used at different antennas. For example, the notation ‘16QAM×64QAM’ stands for a 2 × 2 MIMO scheme with one transmitting antenna using 16QAM constellation and the other using 64QAM constellation. There are three

B. Average Mutual Information Analysis As shown in Fig. 3(a), the channel capacity is defined as the maximum AMI between the inputs and outputs of the channel, where the maximum is taken over all possible input distributions. According to Shannon’s information theory, the ergodic

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Fig. 3. (a) Channel capacity. (b) AMI of coded modulation systems, CM-AMI. (c) AMI of independent demapping systems, BICM-AMI.

channel capacity of the fading channel with Gaussian noise is [22]

, (7) C = EH log2 det I + ρHH† where det [ · ] denotes the determinant and I represents the identity matrix. The channel capacity can be achieved only if input satisfies Gaussian distribution. In practical systems, the coded bits are modulated by the constellation mapper before transmission. The input of the channel is therefore constrained by the constellation set, which is clearly not Gaussian distributed. As shown in Fig. 3(b), the AMI between the constellation constrained input and output, named CM-AMI, becomes the new highest transmission rate under such modulation. For an equiprobable constellation X with its cardinality being M = 2N , the CM-AMI can be formulated as [24] ICM = I(x; y|H)

= N − Ex,y,H log2

p y|ˆx, H . p( y|x, H)

xˆ ∈X

(8)

The CM-AMI could be reached by joint demapping and decoding method, such as iterative demapping paradigm like BICM-ID. In the independent demapping scheme like BICM, each bit bi and the independent demapping output Lie form parallel independent channels [11]. As shown in Fig. 3(c), the overall AMI between bi and Liind within one symbol, called BICM-AMI, is calculated as [25] IBICM =

N−1 i=0

N−1 I bi ; Liind = I(bi ; y|H), i=0

(9)

Fig. 4. SNR gaps between the CM-/BICM-AMI and Shannon limit over the 2 × 2 MIMO i.i.d. Rayleigh channel. N = 6 stands for QPSK × 16QAM and 8APSK × 8APSK. N = 8 stands for 16QAM × 16QAM and 16APSK × 16APSK. N = 10 stands for 16QAM × 64QAM and 32APSK × 32APSK.

where I(bi ; y|H) = 1−Eb,y,H

x, H xˆ ∈X p y|ˆ log2 . (10) (b) p( y|x, H) x∈X i

BICM-AMI is the upper-bound of information rate for an independent demapping scheme. According to the data processing inequality [22], BICM-AMI must be less than or equal to CM-AMI, i.e., IBICM ≤ ICM . The performance degradation caused by independent demapping is therefore called independent demapping loss. Moreover, it can be observed from (9) that the BICM-AMI is closely related to the mapping function from the bit vector to the symbol. That is why Gray mapping is always chosen since it leads to the least independent demapping loss. C. Numeric Results of CM- and BICM-AMI We propose to use 8APSK×8APSK, 16APSK×16APSK and 32APSK×32APSK to replace their QAM counterparts in DVB-NGH. Using (7)-(9), we can calculate the Gaussianinput channel capacity, as well as the CM- and BICM-AMI constrained by Gray-APSKs and Gray-QAMs. The SNR gaps between the CM-/BICM-AMI and Shannon limit over the 2×2 MIMO Rayleigh fading channel are illustrated in Fig. 4.


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It is shown that for low order modulation (N = 6), APSK and QAM have almost the same CM-/BICM-AMI. But for high order modulations (N = 8, 10), APSKs are clearly superior to their QAM counterparts at typical code rates, e.g., 1/2 or 2/3 around, from the perspective of both CM- and BICM-AMI. Taking 32APSK×32APSK as an example, it has about 0.25 dB CM-AMI gain and 0.20 dB BICM-AMI gain over 16QAM×64QAM at the code rate from 1/2 to 2/3. IV. EXIT-A IDED B IT M APPING D ESIGN In Section III, Gray-APSK is used in the MIMO system to provide potential shaping gain compared to Gray-QAM. But to exploit such shaping gain in practical systems, the forward error control (FEC) code and the bit interleaver need to be carefully designed for the BICM/BICM-ID scheme. The LDPC codes of DVB-NGH have excellent performance and are widely accepted, so we will focus on the bit interleaver design in this subsection. A. Practical Bit Mapping Structure Conventional bit interleaving just tries to randomize the bit positions, and treats all the bits equally. However, the bits at different positions have unequal error protections (UEPs) due to inherent properties of irregular LDPC codes and high-order modulations [11], [19]. Hence, when combining the encoder and the modulator, we face the problem of how to map different coded bits to different modulation levels, which is called bit mapping [16], [17]. In the DVB-NGH MIMO system, the bit interleaver is composed of the parity interleaver, the quasi-cyclic block (QB) interleaver and the section interleaver [7]. The interleaving pattern is optimized for each coded modulation mode. It has been demonstrated in our previous work that the interleaver could bring in about 0.28 dB gain for the 16QAM×64QAM rate-2/3 mode [26]. However, to the best of our knowledge, no public literature has revealed the design process of the interleaver in the DVB-NGH system. Moreover, the bit interleaver of DVB-NGH is composed of three parts and specified by many parameters, which is often too complicated to optimize and implement in practical systems. So in this paper, we propose to use a much simpler bit mapping instead, which is just a row-column interleaving combined with inner-row permutation. The row-column interleaver has NLDPC /N rows and N columns, where NLDPC is the length of the LDPC code. As shown in Fig. 5, the coded bits are written into the interleaver column-wise and read out row-wise. But before they are read out of the interleaver, the bits within a row shall be reordered according to an inner-row permutation pattern q = (q0 , · · · , qN−1 ). Specifically, if the bits within a row are sequentially labeled from 0 to N − 1, then the i-th bit in a row is mapped to bqi which denotes the qi -th bit position of a constellation symbol.

Fig. 5. Bit mapping consisting of row–column interleaving and inner-row permutation.

matrix is defined as the variable node and the check node, respectively. Then the decoding algorithm can be viewed as an iterative process between the variable node decoder (VND) and the check node decoder (CND) [21], which can be analyzed via the tool of EXIT chart. To calculate the EXIT curves, both the VND and CND are assumed to be a module that produces a new sequence of extrinsic LLRs using the input a priori LLRs. Then the AMI between the input/output LLRs and the transmitted bits is calculated to represent the information transferred between VND and CND. For each input AMI IA , there is a corresponding output IE , which forms an EXIT curve. The iterative decoding process can thus be visualized by a trajectory between the two curves. And the essential condition of successful decoding is that the VND’s EXIT curve should lie above the CND’s curve before they reach the point (1, 1). However, conventional EXIT curves of VND do not take into account the UEP property. So a new concept of enhanced VND (eVND), which can model the UEP of LDPC’s irregular column weight and high-order modulation, is addressed for both independent and iterative demapping schemes in this paper. In the eVND, the variable nodes with the same degree are classified into a group that has the same protection level, and the bits (after interleaving and before constellation mapping) at the same position within a constellation symbol are considered to have the same modulation level. If we use Gaussian approximation [18] to model the output LLR of the demapper, each bit position corresponds to an equivalent noise variance σj2 , as shown in Fig. 6. For a variable node of degree di and mapped to the j-th modulation level, its individual EXIT curve can be calculated as

2 (di − 1) J −1 IAeVND + σj2 , IEVND IAeVND ; di , σj2 = J (11) wherein the J(·) function is defined as [19] J(σ ) = 1 −

B. Extrinsic Information Transfer Analysis EXIT chart is a powerful tool to analyze iterative systems. For the LDPC code, the column and the row of a parity check

∞

−∞

e−

2 ξ −σ 2 /2 /2σ 2

√

2π σ 2

· log2 1+e−ξ dξ. (12)

The J(·) function dose not have a closed form, but it is monotonic increasing, so the inversion function J −1 (·) exists.

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If an irregular LDPC code has the variable node degrees of (d1 , · · · , dV ), there are V×N combinations from different variable nodes to distinct modulation levels. Given the mapping distribution P = [pi,j ]V×N , where pi,j denotes the proportion of the variable nodes with degree di that mapped to the j-th modulation level, the total EXIT curve of the eVND can be expressed as

V N−1 VND I eVND ; d , σ 2

p d I i,j i i i=1 j=0 j E A IEeVND IAeVND ; P, σ 2 = . V N−1 i=1 j=0 pi,j di (19) Fig. 6. Independent/iterative demapping and decoding model of the coded modulation system for EXIT chart analysis.

Literature [27] gives a good approximation of the J(·) and J −1 (·) functions as

2H2 H3 I = J(σ ) ≈ 1 − 2−H1 σ , (13) 1 2H2 1 1 σ = J −1 (I) ≈ − log2 1 − I H3 , (14) H1 in which H1 = 0.3073, H2 = 0.8935, and H3 = 1.1064. Then we need to derive the expression of σj2 . For the independent demapping scheme, the equivalent σj2 can be evaluated by

2

σj2 = J −1 I bj ; Ljind

2 = J −1 I(bj ; y|H) , (15) where the formula of I(bj ; y|H) is given in (10). Similarly, for the iterative demapping scheme, σj2 has the form of

2

. (16) σj2 = J −1 I bj ; Ljiter However, it is not easy to calculate I(bj , Ljiter ), because the demapper has extra information IADEMAP fed back from the CND, as is represented by the dashed line in Fig. 6. So we resort to Monte Carlo simulation. A sequence of Gaussian distributed LLRs with the variance of [J −1 (IADEMAP )]2 are generated as the a priori information of the demapper. After that we use (5) to calculate Ljiter and then measure the AMI between bj and Ljiter using the histogram method. As a result, σj2 is a function of IADEMAP with σ 2 as a parameter, i.e.,

2

σj2 = J −1 I bj , Ljiter IADEMAP ; σ 2 . (17) Besides, IADEMAP and IAeVND are not independent with each other. Assuming d¯v to be the average column weight of the LDPC code, it is easy to derive that 2 . (18) d¯v − 1 J −1 IAeVND IADEMAP = J Substitute (18) into (17), we can get the relationship between σj2 and IAeVND , and finally obtain the transfer function of the VND for a specific bit position bj and variable node degree di in the iterative demapping scheme.

After we have obtained the EXIT curve of eVND, we still need to get the EXIT curve of CND, which is relatively simple to calculate using the method in [19]. Then, the SNR threshold of successful decoding can be predicted by the SNR level at which the two curves are critically tangent [20]. C. Optimization of Bit Mapping As the parameters of the row-column interleaver is fixed, the only freedom left is the inner-row permutation pattern. There are in total N! permutations, from which we would like to choose a best one. Theoretically, N! is usually a very large number even for a moderate value of N. But in fact, many different permutations have the same bit mapping distribution matrix P, which indicates that they have the same performance from the viewpoint of EXIT analysis. So we can first classify the permutations with the same mapping distribution into a group, and then perform the searching by choose only one permutation from each group, which greatly reduces the searching space. Take 32APSK×32APSK (N = 10) as an example, the LDPC code adopted here is the rate-2/3 16200-bit code of DVB-NGH [7]. There are originally 10! = 3, 628, 800 permutations, but after classification, the searching space is decreased to 5, 040, which is only 1/720 the size of the original searching space. For the aforementioned example, there are 3 kinds of variable node degrees dv = (2, 3, 13) (there is only one variable node with degree 1, which is ignored here), and 10 modulation levels. If no bit mapping is employed, the variable nodes are consecutively mapped to different modulation levels, which is called uniform bit mapping with the distribution being ⎡ 1 1 1 1 1 1 1 1 1 1 ⎤ Pun =

⎢ 3 1 ⎢ 3 5 10 ⎢ ⎣ 1 15

3 3 5 1 15

3 3 5 1 15

3 3 5 1 15

3 3 5 1 15

3 3 5 1 15

3 3 5 1 15

3 3 5 1 15

3 3 5 1 15

3 3 5 1 15

⎥ ⎥ ⎥. (20) ⎦

In this paper, the optimized bit mapping is obtained by searching through all the 5, 040 groups. The search result shows that the optimized permutation patterns for the independent and iterative demapping schemes are qind = (1, 2, 4, 5, 6, 9, 8, 0, 3, 7) and qiter = (8, 2, 3, 5, 7, 9, 0, 1, 4, 6), respectively, with corresponding mapping distributions being ⎡ ⎤ 3 0 0 3 0 0 0 3 1 0 1⎣ 0 1 3 0 3 3 3 0 2 3 ⎦, (21) Pind opt = 30 0 2 0 0 0 0 0 0 0 0


Fig. 7.

and Piter opt

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EXIT analysis of the 32APSK × 32APSK mode with DVB-NGH rate-2/3 LDPC code. (a) Independent demapping. (b) Iterative demapping.

⎡

1 1⎣ 2 = 30 0

3 0 0

0 3 0

0 3 0

3 0 0

0 3 0

3 0 0

0 3 0

0 1 2

⎤ 0 3 ⎦. (22) 0

TABLE I BER S IMULATION R ESULTS OF THE DVB-NGH S YSTEM AND THE P ROPOSED S YSTEM

The EXIT curves of eVND and CND are depicted in Fig. 7. In order to show the EXIT tunnel clearly, the difference between the two curves is magnified by 10 times and also plotted in the figure. In the independent demapping scheme, the SNR thresholds with uniform bit mapping and optimized bit mapping are 15.45 dB and 15.05 dB, respectively, with 0.40 dB potential gain. And in the iterative demapping scheme, the corresponding SNR thresholds are 13.35 dB and 12.95dB, also with 0.40 dB potential gain. The same analysis could be applied to other coded modulation modes, which are omitted here due to the limited space constraint. V. S IMULATION R ESULTS In this section, BER simulations are carried out for the DVB-NGH MIMO system and the proposed system. There are three modulation modes - QPSK×16QAM, 16QAM×16QAM, and 16QAM×64QAM - in the DVB-NGH MIMO system. The LDPC codes and the bit interleaver are specified in the second part of the standard draft [7]. DVBNGH has only one code length of 16200 bits for the MIMO system, but has various code rates, from which rate-2/3 code is chosen as a representative. The proposed MIMO system employs 8APSK×8APSK, 16APSK×16APSK, and 32APSK×32APSK to replaces their QAM counterparts, and the LDPC code employed is the same as that of DVB-NGH. Besides, the inner-row permutation patterns of the bit mapping for the proposed BICM/BICM-ID system are listed in Table I. At the receiver, the demapper uses the log-MAP algorithm mentioned in Section II, and the LDPC decoder uses SPA [21]. The maximum iteration number is set 100 for both iterative and independent damapping schemes.

The difference is in that for the independent demapping, the iteration is only between VND and CND, while for the iterative demapping, the output of CND is also fed back to the demapper in every iteration. Let us first compare the 16QAM×64QAM and 32APSK×32APSK modes, both of which have N = 10 bits per constellation symbol. The BER simulation results are shown in Fig. 8. For the independent demapping scheme, the SNR threshold (@BER=10−5 ) of the QAM system with uniform bit mapping is 16.38 dB, and the SNR threshold of the APSK system with uniform bit mapping is 16.19 dB, which brings in 0.19 dB shaping gain. If we applied the optimized

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Fig. 8. BER simulation results for the N = 10 and rate-2/3 mode. QAM system with uniform bit mapping, APSK system with both uniform and optimized bit mapping, both independent and iterative demapping schemes.


the gap between the proposed APSK-BICM system (with optimized bit mapping) and the QAM-BICM (with DVB-NGH bit interleaver) shrinks, but we still have gains. Furthermore, if we apply iterative demapping to the APSK system, i.e., APSK-BICM-ID, up to 2.0 dB SNR gain can be achieved compared to the standard QAM-BICM system of DVB-NGH, which is a striking result in the coded modulation field. One more thing to be noted, the aforementioned bit mappings are designed with the assumption of optimal demapping and decoding algorithms. In practical systems, the complexity of optimal demapping and decoding algorithms is quite high for implementation, so the investigation of simplified demapping like max-log-MAP and simplified decoding like min-sum algorithm is also of great value. However, the simplified demapping and decoding algorithms will affect the shape of the EXIT curves, the well-designed bit mappings for optimal demapping and decoding algorithms are often not well-matched for simplified algorithms. Therefore, the bit mapping optimization for simplified demapping and decoding algorithms needs further investigation. VI. C ONCLUSION

Fig. 9. BER simulation results for the N = 6, 8, 10 and rate-2/3 mode. DVB-NGH system (BICM) and the proposed APSK system (both BICM and BICM-ID).

bit mapping to the APSK system, an extra 0.40 dB gain can be further achieved. As for the iterative demapping scheme, the APSK constellation and the optimized bit mapping could bring in 0.18 dB and 0.35 dB gain, respectively. As we can see, the BER results match the AMI and EXIT analyzes in Section IV quite well, which validates the effectiveness of our analysis and design. The BER simulation results of all the three modes (N = 6, 8, 10) for the DVB-NGH system and the proposed system are depicted in Fig. 9. The detailed SNR thresholds and SNR gains for each mode are listed in Table I. Also take the N = 10 mode as an example, the performance of the proposed APSK-BICM system exhibits 0.30 dB SNR gain compared to the QAM-BICM system specified in DVB-NGH. The SNR gain here is not as large as mentioned in previous paragraph. This is because DVB-NGH has already optimized its bit interleaver for each coded modulation mode. As a result,

In this paper, we have proposed a near-capacity MIMO-BICM/-BICM-ID scheme for the DTTB systems. The Gray-APSK constellation, which is more Gaussian-like and has larger CM-/BICM-AMI, is used to replace the Gray-QAM in the MIMO system. Moreover, simple rowcolumn interleaver and inner-row permutation are employed to approach the optimal bit mapping. And EXIT chart analysis is adopted to help optimize the inner-row permutation pattern for both independent and iterative demapping schemes. BER simulations are carried out to demonstrate the effectiveness of our proposed system. With the requirement of higher transmission rate and spectral efficiency, the proposed MIMO-BICM/-BICM-ID scheme expects a wide application in the future broadcasting systems. R EFERENCES [1] G. L. Stuber et al., “Broadband MIMO-OFDM wireless communications,” Proc. IEEE, vol. 92, no. 2, pp. 271–294, Feb. 2004. [2] J.-S. Han, J.-S. Baek, and J.-S. Seo, “MIMO-OFDM transceivers with dual-polarized division multiplexing and diversity for multimedia broadcasting services,” IEEE Trans. Broadcast., vol. 59, no. 1, pp. 174–182, Mar. 2013. [3] S. X. Ng and L. Hanzo, “On the MIMO channel capacity of multidimensional signal sets,” IEEE Trans. Veh. Technol., vol. 55, no. 2, pp. 528–536, Mar. 2006. [4] J. Ketonen, M. Juntti, and J. R. Cavallaro, “Performance-complexity comparison of receivers for a LTE MIMO-OFDM system,” IEEE Trans. Signal Process., vol. 58, no. 6, pp. 3360–3372, Jun. 2010. [5] K. Peppas, F. Lazarakis, C. Skianis, A. Alexandridis, and K. Dangakis, “Impact of MIMO techniques on the interoperability between UMTS-HSDPA and WLAN wireless systems,” IEEE Commun. Surv. Tuts., vol. 13, no. 4, pp. 708–720, Sep. 2010. [6] Digital Video Broadcasting (DVB); Frame Structure Channel Coding and Modulation for a Second Generation Digital Terrestrial Television Broadcasting System (DVB-T2), ETSI Standard EN 302 755, Nov. 2011. [7] Digital Video Broadcasting (DVB); Next Generation Broadcasting System to Handheld, Physical Layer Specification (DVB-NGH), ETSI Standard EN 303 105, Jun. 2013. [8] L. Zheng and D. N. C. Tse, “Diversity and multiplexing: A fundamental tradeoff in multiple-antenna channels,” IEEE Trans. Inf. Theory, vol. 49, no. 5, pp. 1073–1096, May 2003.


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Tao Cheng received the B.S.E. degree from the Department of Electronic Engineering, Tsinghua University, Beijing, China, in 2010. He is currently pursuing the Ph.D. degree with the Research Institute Information Technology and Electronic Engineering, Department of Tsinghua University, Tsinghua National Laboratory for Information Science and Technology. His research interests lie in the physical layer of digital terrestrial television broadcasting systems, especially in the field of channel coding and modulation.

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Kewu Peng was born in Hefei, China. He received the B.E. degree in electronics engineering from the Hefei University of Technology, the M.E. degree in electronics engineering from Tsinghua University, and the Ph.D. degree in electrical engineering from the University of Minnesota, Minneapolis, in 1993, 1996, and 2003, respectively. He was a Researcher and a Lecturer with the Department of Electronics Engineering, Tsinghua University from 1996 to 1999. Since 2005, he has been a Research Staff with the Digital Television Research Center, Tsinghua University, an Assistant Researcher since 2006, and an Associate Professor since 2009. His research interests include mobile/wireless communications, digital terrestrial/television broadcasting, and embedded image/video transmission. He has published over 70 journal and conference papers and holds over 50 China patents.

Fang Yang received the B.S.E. and Ph.D. degrees from the Department of Electronic Engineering, Tsinghua University, Beijing, China, in 2005 and 2009, respectively. He is currently working as an Associate Professor with the DTV Technology Research and Development Center, Tsinghua University. His research interests lie in the field of channel estimation and interference cancelation for digital wireless communication system, space-time coding and diversity techniques, as well as the training sequence design.

Jian Song received the B.Eng. and Ph.D. degrees in electrical engineering from Tsinghua University, Beijing, China, in 1990 and 1995, respectively, and worked for the same university upon his graduation. He has worked with the Chinese University of Hong Kong and the University of Waterloo, Canada, in 1996 and 1997, respectively. He has been with Hughes Network Systems in USA for seven years. He was a Professor with the faculty team of Tsinghua University in 2005. He is currently the Director of Tsinghua’s DTV Technology Research and Development Center. He has been working in quite different areas of fiber-optic, satellite and wireless communications, as well as the power line communications. His current research interest is in the area of digital TV broadcasting. He has published over 110 peer-reviewed journal and conference papers and holds two U.S. and over 20 Chinese patents. He is a fellow of IET.

Zhixing Yang received the B.Eng. degree in electrical engineering from Tsinghua University, Beijing, China, in 1970. He is the Deputy Director of the State Key Laboratory on Microwave and Digital Communications, Tsinghua University, where he is also the Director of the Digital TV (DTV) Transmission Technology Research and Development Center. He is currently the Chairman of Zhongguancun DTV Industry Alliance. He is the First Draftsman of the Chinese Digital Television Terrestrial Broadcasting Standard known as DTMB (GB20600-2006). His research interests focus on the various transmission technologies for both telecommunications and broadcasting areas. He was a recipient of the National Technological Invention Award thrice and several other awards. He is a member of the Special Committee of National DTV Standardization, the Group Leader of the Coordinating Working Group for DTV Standardization of the Ministry of Industry and Information, and an Invited Committee Member of the Science and Technology Committee, State Administration of Radio Film and Television.