Digital video broadcasting-next generation handheld (DVB-NGH) is the first broadcasting standard that incorporates multiple-input multiple-output (MIMO) techniques to overcome the Shannon limit of single antenna systems. This paper contributes to analyze the performance of the DVB-NGH MIMO coded modulation system. The detailed performance degradation from information-theoretic limit to implementation by average mutual information and extrinsic information transfer analysis is presented, which provides an insight guideline for future system improvement. Finally, bit error rate simulations are carried out to verify the analysis.
Performance Analysis of DVB-NGH MIMO Coded Modulation System ∗ Research Tao Cheng∗, Kewu Peng∗, Fang Yang∗, and Zhixing Yang∗† Institute Information Technology & Electronic Engineering Department, Tsinghua University Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China † National Engineering Laboratory for DTV, Beijing 100191, China Email: chengt10@mails.tsinghua.edu.cn, {pengkewu, fangyang, yangzhx}@tsinghua.edu.cn Abstract—Digital video broadcasting-next generation handheld (DVB-NGH) is the first broadcasting standard that incorporates multiple-input multiple-output (MIMO) techniques to overcome the Shannon limit of single antenna systems This paper contributes to analyze the performance of the DVB-NGH MIMO coded modulation system The detailed performance degradation from information-theoretic limit to implementation by average mutual information and extrinsic information transfer analysis is presented, which provides an insight guideline for future system improvement Finally, bit error rate simulations are carried out to verify the analysis Keywords—DVB-NGH, multiple-input multiple-output (MIMO), average mutual information (AMI), extrinsic information transfer (EXIT) chart, Shannon limit I I NTRODUCTION Digital video broadcasting-next generation handheld (DVBNGH) [1] is the handheld evolution of the second generation digital video broadcasting - terrestrial (DVB-T2) standard It was developed with the aim of being the reference mobile multimedia broadcasting standard, outperforming existing first generation mobile TV terrestrial standard (DVB-H) in terms of capacity and coverage The first edition of DVB-NGH draft was released by European telecommunications standards institute (ETSI) in June 2013, which contains four profiles, including the base (sheer-terrestrial) profile, and the multipleinput multiple-output (MIMO) terrestrial profile, etc Bit-interleaved coded modulation (BICM) [2] is employed as the basic coded modulation architecture of DVB-NGH BICM consists of a forward error control (FEC) encoder, a bit-wise interleaver, and a symbol mapper As a typical paradigm, BICM is a simple yet efficient coded modulation scheme to combat deep fading in wireless environments The iterative demapping counterpart of BICM (BICM-ID) [3] is an improvement to BICM, which exploits the gain from the iterative operation between the demapper and the decoder, but with higher complexity So it is adopted as an optional receiver scheme in DVB-NGH, and the interleaver for the MIMO profile has been redesigned to reduce the implementation complexity of MIMO-BICM-ID systems [1] The utilization of low-density parity-check (LDPC) codes, as the FEC in BICM or BICM-ID, could achieve a performance close to the information-theoretic limits for a singleinput single-output (SISO) system The employment of MIMO 978-1-4799-0959-9/14/$31.00 ©2014 IEEE techniques [4]–[6] overcomes such limits of SISO systems without any additional bandwidth or increased transmission power There are two types of MIMO schemes in DVB-NGH The first type of schemes are MIMO rate-1 codes, which exploit the spatial diversity of the MIMO channel without the requirement of multiple antennas at the receiver side They can be applied across the transmitter sites of single frequency networks (SFNs) as the Alamouti code [4] in DVB-T2, or to an individual multiple-antenna transmitter site The second type is the MIMO rate-2 code, which fully exploits both the diversity and multiplexing capabilities of the MIMO channel However, it requires two antennas at both the transmitting and the receiving sides In this sense, DVB-NGH is the first broadcasting standard that incorporates pure MIMO as one of the key technologies The MIMO rate-2 code of DVB-NGH is known as enhanced spatial multiplexing with phase hopping (eSM-PH), which is a variation of the vertical Bell-labs layered spacetime (V-BLAST) [6] scheme to improve the robustness in presence of spatial correlation between multiple antennas In this paper, we mainly focus on the basic model of V-BLAST MIMO scheme under the independent identical distributed (i.i.d.) Rayleigh fading channel The detailed performance loss from MIMO Shannon limit to implementation by average mutual information (AMI) and extrinsic information transfer (EXIT) analysis [7], [8] is presented, which provides an insight guideline for future system improvement The rest of this paper is organized as follows In Section II, a brief overview of the MIMO channel model and the DVB-NGH MIMO system are presented Section III gives a theoretical analysis of the MIMO scheme from the AMI point of view, especially under the constraint of constellations In Section IV, EXIT-chart analysis of the MIMO scheme is carried out, where the issue of interleaver design is addressed Bit error rate (BER) simulations are presented in Section V, and finally conclusions are drawn in Section VI For the sake of clarity, the following notations are adopted throughout this paper Symbols in boldface denote vectors or matrices, e.g., x denotes the transmitting symbol vector and H denotes the channel state matrix Capitalized calligraphic symbols denote sets, e.g X denotes the constellation set We not distinguish a random variable (r.v.) and a realization of the r.v., as they can be differentiated through the context 190 II S YSTEM OVERVIEW A MIMO Channel Model /'3& (QFRGHU Consider a MIMO channel with nT transmitting and nR receiving antennas, the digital baseband equivalent channel can be modeled as [9] √ y = ρHx + n, (1) nT ×1 B V-BLAST MIMO System The MIMO rate-2 code of DVB-NGH is known as eSMPH It is in fact a variation of the regular V-BLAST scheme followed by a MIMO precoding matrix and the periodic constellation rotation, which increases the robustness against spatial correlation However, in this paper, we not study the effect of the precoding and phase hopping, and only focus on the basic model of V-BLAST MIMO scheme under i.i.d Rayleigh fading channels The 2×2 V-BLAST MIMO system is depicted in Fig At the transmitter, the information bits are encoded by an LDPC encoder and permuted by a bit interleaver Π After that, every Nbpcu (= N1 + N2 ) consecutive bits are grouped into a vector b = [b0 , b1 , · · · , bNbpcu −1 ], where N1 and N2 bits are mapped to the symbol x1 and x2 from two constellation sets X1 and X2 , respectively The transmitted signal is therefore a two-dimensional complex symbol x = [x1 , x2 ]T from a large constellation set X = X1 × X2 In DVB-NGH, there are three MIMO modulation modes: QPSK/16QAM, 16QAM/16QAM, and 16QAM/64QAM, with corresponding Nbpcu being 6, 8, and 10, respectively At the receiver, either independent or iterative demapping scheme is adopted depending on the application scenarios In the iterative demapping scheme, the output of the LDPC decoder is fed back to the joint MIMO demapper as the a priori information Since there are only two transmitting and receiving antennas, the maximum a posterior (MAP) demapping algorithm [9] is applicable The extrinsic information of the i-th bit of a symbol can be calculated as Lei = log (b) (0) x∈Xi (1) x∈Xi p(y|x, H)Pr(x|La ) p(y|x, H)Pr(x|La ) − Lai , (2) where Xi denotes the constellation subset with the i-th bit being b ∈ {0, 1}, and La = [La1 , · · · , LaNbpcu −1 ] is the a priori information from the decoder, in the form of log-likelihood 6\PERO 0DSSLQJ 7[ 6\PERO 0DSSLQJ 7[ [ + 5[ /'3& 'HFRGHU nR ×1 where x ∈ C is the transmitting signal vector, y ∈ C is the receiving signal vector, H ∈ CnR ×nT is the channel state information (CSI) matrix, and n ∈ CnR ×1 is the additive white Gaussian noise (AWGN) with ni ∼ CN(0, 1) The input signal vector satisfies the power constraint that E[x† x] = 1, where E[·] denotes the expectation operation, and x† denotes the conjugate transpose of x To simplify the analysis, we consider the i.i.d Rayleigh fading channel, i.e., each element of H satisfies the standard complex Gaussian distribution hi,j ∼ CN(0, 1) As the power of the input signal vector and the channel gains are normalized, ρ can be interpreted as the signal-to-noise ratio (SNR) at each receiving antenna 3 -RLQW 6\PERO 'HPDSSLQJ \ 5[ Fig V-BLAST MIMO coded modulation system of DVB-NGH ratio (LLR) With the noise being Gaussian distributed, the conditional probability density function (PDF) of the received symbol given the transmitted symbol and CSI matrix is √ (3) p(y|x, H) ∝ exp(− y − ρHx ) The conditional probability Pr(x|La ) can be decomposed into the product of the conditional probability of each bit bi as a Pr(bi |Lai ), Pr(x|L ) = (4) i=0,··· ,Nbpcu −1 with the assumption that the elements in La are independently distributed due to sufficient bit interleaving And the conditional probability Pr(bi |Lai ) can be further expressed as Pr(bi |Lai ) = exp[(1 − bi )Lai ] , bi ∈ {0, 1} + exp(Lai ) (5) by the definition of LLR 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 (2) is therefore degenerated into the form of Lei = log (0) p(y|x, H) (1) p(y|x, H) x∈Xi x∈Xi III AMI A NALYSIS OF (6) MIMO S CHEMES As shown in Fig 2(a), the channel capacity is defined as the maximum AMI between the input and output of the channel, where the maximum operation is taken over all possible input distributions According to Shannon’s information theory [10], the ergodic channel capacity of the fading channel with Gaussian noise is C = EH log2 det I + ρHH† , (7) where EH [·] denotes the expectation operator over H, det[·] denotes the determinant, and I represents the unit matrix The capacity can only be achieved if the input satisfy Gaussian distribution In practical systems, the coded bits are modulated by the symbol mapper before transmission The input of the channel is therefore constrained by the constellation set, and is clearly 191 [ FDQ EH DUELWUDU\ GLVWULEXWLRQ [ \ &KDQQHO S \_[ & 'HFRGHU PD[ , [ \ S [ D (QFRGHU 6\PERO 0DSSHU )(& (QFRGHU [ LV FRQVWUDLQHG E\ WKH FRQVWHOODWLRQ VHW [ \ &KDQQHO S \_[ , &0 'HFRGHU , [ \ (QFRGHU 'HFRGHU [ 436.4$0 615 DW HDFK UHFHLYLQJ DQWHQQD G% F ICM = I(x; y|H) p(y|ˆ x, H) p(y|x, H) ˆ ∈X x = Nbpcu − Ex,y,H log2 (8) The CM-AMI could be achieved by joint optimized demapping and decoding method, such as iterative demapping scheme For independent demapping scheme, each bit bi and the independent demapping output Lei forms an independent channel As shown in Fig 2(c), the overall AMI between bi and Lei , called BICM-AMI, is calculated as [11], [13] Nbpcu −1 Nbpcu −1 I(bi ; Lei ) I(bi ; y|H) = i=0 Nbpcu −1 Eb,y,H log2 i=0 Fig Numeric results of CM-AMI and BICM-AMI for the DVB-NGH MIMO system (Nbpcu =6, 8, 10) , E /H not Gaussian distributed As shown in Fig 2(b), the AMI between the constrained input and output symbol, named CM-AMI [11], becomes the highest transmission rate under such modulation And the gap between the CM-AMI and the capacity is the so-called shaping loss For the equiprobable constellation X with its cardinality being M = 2Nbpcu , the CM-AMI can be formulated as [12] = Nbpcu − 4$0 6\PERO / )(& 'HPDS 'HFRGHU Fig (a) The channel capacity (b) The AMI of coded modulation systems, CM-AMI (c) The AMI of independent demapping systems, BICM-AMI IBICM = H \ &KDQQHO S \_[ , %,&0 [ LV FRQVWUDLQHG E\ DQG LQGHSHQGHQW GHPDSSLQJ 4$0 E E 6\PERO )(& 0DSSHU (QFRGHU &KDQQHO &DSDFLW\ &0$0, %,&0$0, $0, ELWVFKDQQHO XVH (QFRGHU i=0 x∈X p(y|x, H) (b) p(y|x, H) x∈X (9) independent demapping loss To summarize, from Shannon limit to CM-AMI, the SNR loss is caused by the shape of the constellation set, while from CM-AMI to BICM-AMI, the SNR loss is caused by independent demapping Numeric results of the CM-AMI and BICM-AMI versus SNR for the DVB-NGH 2×2 MIMO system are depicted in Fig Consider the rate-2/3 LDPC code, the CM-AMI thresholds for QPSK/16QAM, 16QAM/16QAM, 16QAM/64QAM (Nbpcu = 6, 8, 10) are 8.03dB, 10.30dB, 13.08dB, with shaping loss being 1.35dB, 0.72dB, 0.93dB, respectively, while the BICM-AMI thresholds are 8.96dB, 11.79dB, 14.76dB, with independent demapping loss being 0.93dB, 1.49dB, 1.68dB, respectively As we can see, with the increasing of constellation order, the shaping loss has the tendency of decreasing while the independent demapping loss is monotonously increasing In our previous work [14], the performance of DVBT2 256QAM rate-2/3 mode is evaluated, where the shaping loss and the independent demapping loss are 1.08dB and 0.31dB Compared to the 16QAM/16QAM MIMO system, which has the same spectral efficiency, the SISO system has greater shaping loss but less independent demapping loss This is because multi-dimensional signals tend to be more aggregated to zero than QAMs with the same power level [15], but have more severe mutual interference between antennas that cannot be easily overcome by independent demapping IV EXIT A NALYSIS i BICM-AMI is the upper-bound of information rate for independent demapping scheme According to the data processing inequality [10], BICM-AMI must be less than or equal to CMAMI, i.e., IBICM ≤ ICM The performance degradation cause 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 (i.e labeling) from the bit vector to the symbol In DVBNGH, Gray mapping is adopted since it leads to the least OF MIMO S CHEMES The CM-AMI or BICM-AMI is the highest information rate that can be achieved under ideal coding techniques However, the performance will be degraded due to the non-ideal LDPC code and interleaver in actual systems As the LDPC decoding can be viewed as an iteration process between the variable node decoder (VND) and check node decoder (CND), the EXIT chart [7], [8] is employed to predict the SNR threshold Due to the unequal error protection (UEP) introduced by high-order QAMs and irregular LDPC codes [2], [7], the mapping strategy from LDPC’s variable nodes to different bit 192 V \ V 0,02 6\PERO 'HPDSSHU # V , H91' ( , &1' ( , &1' $ 91' ESFX &1' , H91' $ ,$ H91' EXIT analysis model for the MIMO system with LDPC codes ,( Fig &1' H91' &1' FXUYH H91' FXUYH ZLWK XQLIRUP ELW PDSSLQJ H91' FXUYH ZLWK RSWLPL]HG ELW PDSSLQJ FXUYH FXUYH # G% FXUYH FXUYH # G% positions of a constellation symbol (i.e., modulation level), which is called bit mapping [16], [17], will affect the system performance In order to analyze such system, the concept of enhanced VND (eVND) that combines the demapper and the VND is proposed in [16] As shown in Fig 4, there is no feed back from the VND to the demapper, so this model can be only used to analyze the independent demapping schemes The bit interleaver will change the bit mapping strategy, and thus affect the system performance Considering a variable node of degree di that is mapped to the j-th protection level, its individual EXIT curve is IEIND IA ; di , σj2 = J (di − 1)[J −1 (IA )] + σj2 , (10) where the expression of J-function is given in [7], and σj2 denotes the equivalent noise variance of the j-th modulation level Under the fading channel with CSI known to the receiver, the equivalent σj2 can be calculated by σj2 = J −1 (I(bj ; y|H)) , j = 0, · · · , Nbpcu − 1, (11) where bj belongs to the j-th modulation level If an irregular LDPC code has the variable node degrees of (d1 , · · · , dV ), there are V kinds of modulation level since the variable node with degree di corresponds to a rate-1/di repetition code As a result, there are V × Nbpcu combinations from variable nodes to modulation levels Given the mapping distribution P = [pi,j ]V ×Nbpcu , the total EXIT curve of the eVND can be expressed as V Nbpcu −1 IEeVND (IA ; P, σ ) = i=1 pi,j di IEIND (IA ; di , σj2 ) j=0 V i=1 Nbpcu −1 j=0 pi,j di , (12) where pi,j denotes the proportion of the variable nodes with degree di that mapped to the j-th modulation level After we have obtained the EXIT curves of eVND and CND, the SNR threshold for successful decoding can be predicted by the SNR level at which the two curves are critically tangent [8] From BICM-AMI to the EXIT chart prediction, the SNR loss is mainly caused by the variable node degree distribution of the LDPC code Furthermore, the bit interleaver would change the value of the mapping distribution P and thus affect the SNR threshold If there is no bit interleaver (bilv) between the encoder and symbol mapper, the variable nodes are consecutively mapped to different modulation levels, which is called uniform bit mapping In the DVB-NGH MIMO Fig ,$ H91' ,( &1' EXIT analysis results for the 16QAM/64QAM rate-2/3 mode profile, 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 mode to improve the system performance We called it optimized bit mapping Take 16QAM/64QAM (rate2/3) as an example, the variable node degree is dv = (2, 3, 13) (there is only one variable node with degree 1, so it is ignored), and there are 10 modulation levels The mapping distributions for the uniform bit mapping and optimized bit mapping are ⎡ 1 1 1 1 1 ⎤ Pun = 10 and Pop = ⎢ ⎣ ⎡ 10 ⎢ ⎣ 3 15 3 15 3 15 3 15 3 15 3 15 3 15 3 15 3 15 3 15 9 9 9 9 0 9 9 9 9 9 9 9 9 ⎥ ⎦ (13) ⎤ ⎥ ⎦ , (14) respectively The corresponding EXIT curves for the CND and eVND are depicted in Fig In order to show the EXIT tunnel clearly, the difference of the two 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 15.55dB and 15.30dB, respectively, and the potential gain is 0.25dB Furthermore, the potential gains for QPSK/16QAM and 16QAM/16QAM are about 0.15dB and 0.10dB, respectively, but the EXIT charts are not given due to the limited space V S IMULATION R ESULTS In this section, BER simulations are carried out for the DVB-NGH MIMO system We choose the QPSK/16QAM, 16QAM/16QAM, 16QAM/64QAM modulations with the rate2/3 LDPC code Both the iterative and independent demapping schemes are simulated In the independent demapping 193 the bit interleaver on the system performance was addressed Finally, BER simulations for both iterative and independent demapping schemes were carried out to verify the previous analysis This paper contributes to give a detailed analysis of the system performance deterioration from Shannon limit to implementation, which helps to improve the system performance in the future ,WHUDWLYH GHPDSSLQJ ZLWK ELOY ,QGHSHQGHQW GHPDSSLQJ ZLWK ELOY ,QGHSHQGHQW GHPDSSLQJ ZLWK QR ELOY %(5 YW^