A Near-Capacity MIMO-BICM Scheme for Digital ... - IEEE Xplore

2015 IEEE Wireless Communications and Networking Conference (WCNC 2015) - Track 1: PHY and Fundamentals

A Near-Capacity MIMO-BICM Scheme for Digital Terrestrial Television Broadcasting Tao Cheng, Kewu Peng, Fang Yang, and Zhixing Yang Research Institute Information Technology & Electronic Engineering Department, Tsinghua University Tsinghua National Laboratory for Information Science and Technology (TNList), Beijing 100084, China National Engineering Laboratory for DTV, Beijing 100191, China Shenzhen City Key Lab of Digital TV System (Guangdong Province Key Lab of Digital TV System) Email: [email protected], {pengkewu, fangyang, yangzhx}@tsinghua.edu.cn Abstract—Multiple-input multiple-output (MIMO) is one of the key technologies for the next generation digital terrestrial television broadcasting (DTTB). This paper proposes a near-capacity MIMO bit-interleaved coded modulation (BICM) scheme for DTTB systems. The amplitude phase shift keying (APSK) constellation with Gray mapping is applied to the BICM scheme. From the perspective of average mutual information, APSK has the advantage of shaping gain compared to its quadrature amplitude modulation (QAM) counterpart. Moreover, a new kind of bit interleaver named bit mapping, which takes into account the unequal error protection of both APSK and low-density parity-check (LDPC) codes, is proposed to further improve the system performance. The tool of extrinsic information transfer chart is utilized to help analyze and design the optimal bit mapping. Bit error rate simulations are carried out to verify the superiority of the proposed MIMO system. Keywords—MIMO, bit-interleaved coded modulation (BICM), amplitude phase shift keying (APSK), bit mapping, extrinsic information transfer (EXIT) chart.

I.

I NTRODUCTION

Multiple-input multiple-output (MIMO) can provide ultra-high transmission rate without any additional bandwidth or increased transmission power compared to single antenna systems [1]. Due to its potential gain, MIMO has been widely accepted by many wireless communication standards, such as IEEE 802.11 and Long Term Evolution (LTE) [2]. But in the field of digital terrestrial television broadcasting (DTTB), MIMO is not popular due to the consideration of compatibility to legacy infrastructure. The second generation Digital Video Broadcasting - Terrestrial (DVB-T2) [3] has only adopted a multiple-input single-output (MISO) scheme, while Digital Video Broadcasting - Next Generation Handheld (DVB-NGH) [4] employs a 2×2 MIMO scheme.

978-1-4799-8406-0/15/$31.00 ©2015 IEEE

241

This paper contributes to propose a simple yet efficient MIMO bit-interleaved coded modulation (BICM) system that has the capacity-approaching performance. First, the Gray mapped amplitude phase shift keying (Gray-APSK) [5] is employed as the constellation mapping. Compared to its quadrature amplitude modulation (QAM) counterpart, Gray-APSK has certain shaping gain from the perspective of average mutual information (AMI) analysis. Second, considering the unequal error protection introduced by both APSK and irregular lowdensity parity check (LDPC) codes, a new kind of bit interleaver, called bit mapping [6], is applied to further improve the system performance. The tool of extrinsic information transfer (EXIT) chart [7] is employed to analyze and design the optimal bit mapping. Finally, as a representative of the next generation digital video broadcasting standard, DVB-NGH is deemed as a main reference in this paper. Bit error rate (BER) simulations have shown that the proposed system has considerable signal-to-noise ratio (SNR) gains over the DVB-NGH system at typical coded modulation mode. 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 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. Capitalized calligraphic symbols denote sets. The superscripts (·)T and (·)† denote the transpose and conjugate transpose, respectively. E(·) stands for the expectation operation.


LDPC Encoder

S / P

Symbol Mapping

Tx_1

Symbol Mapping

Tx_nT

symbol x can be calculated, in the form of log-likelihood ratio (LLR), as ∑ (0) x∈χ p(y|x, H) Li = log ∑ i , (2) x, H) ˆ ∈χ(1) p(y|ˆ x

x

H

i

Rx_1

LDPC Decoder

Fig. 1.

P / S

Joint Symbol Demapping

(b) χi

where denotes the constellation subset with the ith bit being b ∈ {0, 1}, and p(·|·, ·) is the conditional probability density function (PDF) of the received symbol given the transmitted symbol and CSI matrix. The output of the demapper is de-interleaved and then sent to the LDPC decoder, which utilizes the sum-product algorithm (SPA) [10] to calculate the LLR of each bit.

y Rx_nR

The block diagram of the V-BLAST BICM scheme.

II.

MIMO BICM S YSTEM M ODEL

Consider an nR × nT dimensional MIMO channel. 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 input-output relation of the MIMO transmission system is √ (1) y = ρHx + n. The transmitting vector x satisfies the normalized power constraint E[x† x] = 1. For simplicity, we consider the Rayleigh fading channel only, i.e., each element of H satisfies the standard complex Gaussian distribution hi,j ∼ CN (0, 1). 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 use the simple V-BLAST MIMO scheme [8], since the proposed BICM system can approach the channel capacity without any space-time codes. The block diagram of the system model is depicted in Fig. 1. Assume the transmitting vector x is composed of [x1 , · · · , xnT ]T , where xi is chosen from some complex constellation Xi with 2Ni points. The vector x can thus be viewed as an nT -dimensional symbol from a large constellation ∑ X with 2N points, where T X = X1 × · · · × XnT and N = ni=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 N consecutive bits are grouped into a bit [ ]T vector b = [b1 , · · · , bN ]T = b(1) , · · · , b(nT ) , where ∑ b(i) = [bki +1 , · · · , bki +Ni ]T (ki = i−1 j=1 Nj ) is mapped to the symbol xi according to a labeling function. At the receiver, since the number of the antennas is limited in DTTB standards (usually no more than two), the maximum a posterior (MAP) demapping algorithm [9] is applicable. The output of the i-th bit of a

242

III.

C ONSTELLATION O PTIMIZATION

A. Gray-APSK Constellations There are three 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 [11], the capacity of the AWGN channel can be achieved only if the input satisfies Gaussian distribution. Compared to the conventional squared uniform QAM, circularly distributed APSK is more Gaussian-like and can exploit some capacity gain, which is defined as shaping gain [12]. 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 [5]. 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 Gray-PAM. Therefore, Gray mappings exist for such APSK constellations as illustrated in Fig. 2. In this paper, we are the first to apply such GrayAPSK technique to the MIMO system. There are two main advantages for the MIMO system to use GrayAPSK instead of conventional Gray-QAM constellations. First, the AMI of Gray-APSK is greater than that of Gray-QAM, as will be illustrated in the next subsection. Second, for some modulation mode with N not being a multiple of 4, say 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.


2.5

2

2

1.5

1.5

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4

9

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1

1

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6 U U

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30

16

1

2

22

13U

U

15

0

1

(a)

2

-2

-1

U U 21 U U

29

0

1

-2

2

-1

0

(b)

28 20

23

1

2

(c)

Gray-APSK constellations, (a) 8APSK, (b) 16APSK, (c) 32APSK. 4.0

B. Average Mutual Information Analysis The channel capacity is defined as the maximum AMI between the input and output of the channel, where the maximum is taken over all possible input distributions [11]. The channel capacity can be achieved only if the input satisfies Gaussian distribution. Practically, the channel input is constrained by the constellation set, which is clearly not Gaussian distributed. In the BICM scheme, each bit bi and the independent demapping output Li forms parallel independent channels [9]. The overall AMI between bi and Li of a symbol, called BICM-AMI, is calculated as [13] IBICM =

N −1 ∑

N −1 ∑

i=0

i=0

I(bi ; y|H) =

= N−

N −1 ∑

Eb,y,H

i=0

[

BICM-AMI QAM BICM-AMI APSK 3.5

1

Gap to Shannon limit (dB)

Fig. 2.

-1

24

13

31

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1

1

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3

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7

8

BICM-AMI (bits/channel use)

Fig. 3. The SNR gaps between the BICM-AMI and Shannon limit over the 2×2 MIMO i.i.d. Rayleigh channel.

I(bi ; Li )

] ∑ x∈X p(y|x, H) . log2 ∑ (b) x∈Xi p(y|x, H) (3)

We propose to use 8APSK×8APSK, 16APSK×16APSK and 32APSK×32APSK to replace the QAM counterparts in DVB-NGH. In order to adapt the MIMO system, the radii of the constellation rings, which are listed aside in Fig. 2, are finely tuned to provide larger AMI. We can calculate the BICM-AMI constrained by Gray-APSKs and Gray-QAMs using (3). The SNR gaps between the BICM-AMI and Shannon limit over the 2×2 MIMO Rayleigh fading channel are illustrated in Fig. 3. It is shown that for low order modulation (N = 6), APSK and QAM have almost the same 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. Taking 32APSK×32APSK as an example, it has about

243

0.20 dB BICM-AMI gain over 16QAM×64QAM at the code rate of both 1/2 and 2/3. IV.

B IT M APPING D ESIGN

Besides the constellation mapping, the forward error control (FEC) code and the interleaver are two other key factors that will affect the system performance. The LDPC codes of DVB series have excellent performance and are widely accepted, so we will focus on the bit interleaver design in this subsection. A. 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 (UEP) due to inherent properties of irregular LDPC codes and high-order modulations [9], [14]. Hence, when combining the encoder and the modulator, we face the


successful decoding is that the VND’s EXIT curve should lie above the CND’s curve before they reach the point (1, 1) [7].

Bit Mapping c0

bq0

ci

...

... Row-Column Interleaver

Inner-Row Permutation

...

... cN 1

bqi bqN 1

Fig. 4. Bit mapping consisting of row-column interleaving and innerrow permutation.

problem of how to map different coded bits to different modulation levels, which is called bit mapping [6], [15]. 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. The interleaving pattern is optimized for each coded modulation system. To the best of our knowledge, no public literature has revealed the design process of the interleaver in the DVB-NGH system. But it has been demonstrated the interleaver could bring in about 0.28 dB gain for the 16QAM×64QAM rate-2/3 mode in our previous work [16]. However, the bit interleaver of DVB-NGH is too complicated to optimize and implement in practical systems. So in this paper, we propose to use a rowcolumn interleaving combined with an inner-row permutation instead, which is much simpler. The row-column interleaver has NLDPC /N rows and N columns, where NLDPC is the length of the LDPC code. As shown in Fig. 4, 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 ci is mapped to the qi -th bit position of a constellation symbol bqi . B. Extrinsic Information Transfer Analysis For the LDPC code, the column and the row of a parity check matrix are 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) [10]. And the essential condition of

244

However, conventional EXIT curves of VND do not take into account the UEP. 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 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 transmitting symbol are considered to have the same modulation level. For a variable node of degree di and mapped to the j -th modulation level, its individual EXIT curve is (√ ) ( ) 2 VND 2 2 −1 IE IA ; d i , σ j = J (di −1)[J (IA )] + σj , (4) where σj2 denotes the equivalent noise variance of the j -th modulation level, and the expression of J -function is given by [14] ∫ ∞ −(ξ−σ2 /2)2 /2σ2 [ ] e √ J(σ) = 1 − · log2 1+e−ξ dξ. (5) 2πσ 2 −∞ Under the flat fading channel with CSI known to the receiver, the equivalent σj2 can be calculated by [ ]2 σj2 = J −1 (I(bj ; y|H)) , j = 0, · · · , N − 1. (6) If an irregular LDPC code has the variable node degrees of (d1 , · · · , dV ), there are V × N combinations from variable nodes to 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 ∑

IEeVND (IA ; P, σ 2 ) =

i=1 j=0

pi,j di IEVND (IA ; di , σj2 )

∑V i=1

∑N −1 j=0

pi,j di

. (7)

The calculation of CND’s EXIT curve is relatively simple and can be found in any related references [14]. With the obtained EXIT curves of eVND and CND, the SNR threshold of successful decoding is the SNR level at which the two curves are critically tangent [7]. C. Optimization of Bit Mapping As the parameters of the row-column interleaver are fixed, the only freedom left is the inner-row permutation


1.0

10-1

10-2

10-3

1 10-4

IE

eVND

0.4

BER

CND curve0 eVND curve1 with uniform bit mapping eVND curve2 with optimized bit mapping 10*(curve1 - curve0) @ 15.45dB 10*(curve2 - curve0) @ 15.05dB

0.6

/ IA

CND

0.8

DVB-NGH System APSK without Bit Mapping (i.e. uniform) APSK with Bit Mapping (i.e. optimized)

1 1

0.2

10

-5

0.0 0.0

0.2

0.4 eVND

IA

0.6

0.8

9.5

1.0

10.0

CND

/ IE

Fig. 5. EXIT analysis of the 32APSK×32APSK mode with DVBT2’s rate-2/3, 64800-bit LDPC code.

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 code of DVB-T2 [3]. There are originally N ! = 3628800 permutations, but after classification, the searching space is decreased to 5040, which is only 1/720 the size of the original search space. For the aforementioned example, there are 3 kinds of variable node degrees dv = (2, 3, 13), and 10 modulation levels. The optimized bit mapping is obtained by searching through all the 5040 groups. By contrast, if no bit mapping is employed, the variable nodes are consecutively mapped to different modulation levels, which is called uniform bit mapping. The corresponding EXIT curves are depicted in Fig. 5. In order to show the EXIT tunnel clearly, the difference between the eVND and CND’s EXIT curves is magnified by 10 times and also plotted in the figure. As we can see, the SNR thresholds with uniform bit mapping and optimized bit mapping are 15.45 dB and 15.05 dB, respectively, which indicates 0.40 dB potential gain. The same analysis can also be applied to other coded modulation modes, which

245

10.5

12.5

13.0 13.5 SNR (dB)

15.5

16.0

16.5

Fig. 6. BER simulation results at the code rate of 2/3 for N = 6, 8, 10.

are omitted here because of limited space. 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 DVBNGH MIMO system. The LDPC codes and the bit interleaver are specified in the second part of the standard draft [4]. DVB-NGH 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 DVB-T2’s LDPC codes with the code length of 16200 bits are adopted for the proposed system. We use DVB-T2’s codes instead of DVB-NGH’s codes, because DVB-T2 also has long codes of 64800 bits, and the bit mapping optimized for the short codes can be directly extended to the long codes. Besides, the inner-row permutation pattern of the bit mapping for each coded modulation mode is listed in Table I. At the receiver, the demapper uses the MAP algorithm [9] mentioned in Section II, and the decoder uses SPA [10] with a maximum of 100 iterations. The BER versus SNR curves are shown in Fig. 6. The detailed SNR thresholds (@BER=10−5 ) and SNR gains for each mode are listed in Table I. Take the 32APSK×32APSK mode as an example, the performance of the APSK system without bit mapping is even poorer than that of the DVB-NGH system. This


TABLE I.

I NNER - ROW P ERMUTATION PATTERNS AND SNR T HRESHOLDS FOR THE P ROPOSED S YSTEM

Modulation

Permutation Pattern

SNRth1 (dB)

SNR Gain2

SNR Gain3

64-ary (N = 6)

(0, 1, 2, 3, 4, 5)

10.12

0

0.18

256-ary (N = 8)

(3, 0, 1, 2, 7, 6, 4, 5)

12.90

0.18

0.30

1024-ary (N = 10)

(1, 4, 6, 7, 8, 9, 5, 0, 2, 3)

15.78

0.20

0.41

R EFERENCES [1]

[2]

[3]

1

The SNR thresholds for the proposed APSK system with optimized bit mapping (@BER = 10−5 ). 2 The SNR gain of the proposed APSK system over the DVB-NGH system (both with optimized bit mapping). 3 The SNR gain for the APSK system with and without bit mapping.

[4]

[5]

is because DVB-NGH has already optimized its bit interleaver for each coded modulation mode. If we also apply the optimized bit mapping to the APSK system, which brings in about 0.41 dB gain, the proposed APSK system can achieve 0.20 dB gain over the DVB-NGH system. It can be deemed as the shaping gain, since both of the two systems have adopted the optimized bit mapping. As we can see, the BER results match the AMI and EXIT analysis in Section IV quite well, which validates the effectiveness of our analysis and design. VI.

[6]

[7]

[8]

C ONCLUSION [9]

In this paper, we have proposed a near-capacity MIMO-BICM scheme for the DTTB applications. The Gray-APSK constellation, which is more Gaussian-like and has larger BICM-AMI, is used to replace the GrayQAM in the MIMO system. Moreover, simple rowcolumn interleaver and inner-row permutation are employed to approach the optimal bit mapping, in which EXIT analysis is adopted to help optimize the permutation pattern. 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 system expects a wide application in future broadcasting systems. ACKNOWLEDGEMENT

[10]

[11] [12]

[13]

[14]

[15]

This work was supported by the National Natural Science Foundation of China (Grant No. 61401248, 61471219), Standardization Administration of the People’s Republic of China with AQSIQ Project DTV001, and the R&D Project of Science and Technology Innovation Commission of Shenzhen, China (No. JCYJ20140419122040614).

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[16]

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