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.
Trang 1Performance Analysis of DVB-NGH MIMO
Coded Modulation System
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, 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
con-tributes 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 INTRODUCTION Digital video broadcasting-next generation handheld
(DVB-NGH) [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
multiple-input 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
perfor-mance close to the information-theoretic limits for a
single-input single-output (SISO) system The employment of MIMO
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 en-hanced spatial multiplexing with phase hopping (eSM-PH), which is a variation of the vertical Bell-labs layered space-time (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
do not distinguish a random variable (r.v.) and a realization of the r.v., as they can be differentiated through the context
Trang 2II SYSTEMOVERVIEW
A MIMO Channel Model
Consider a MIMO channel with nT transmitting and nR
receiving antennas, the digital baseband equivalent channel can
be modeled as [9]
wherex∈Cn T ×1is the transmitting signal vector,y∈Cn R ×1
is the receiving signal vector, H ∈ Cn R ×n T is the channel
state information (CSI) matrix, andn∈Cn R ×1 is the additive
white Gaussian noise (AWGN) withni∼ CN(0, 1) The input
signal vector satisfies the power constraint thatE[x†x] = 1,
whereE[·] 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
B V-BLAST MIMO System
The MIMO rate-2 code of DVB-NGH is known as
eSM-PH 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 do 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 1
At the transmitter, the information bits are encoded by an
LDPC encoder and permuted by a bit interleaver Π After that,
everyNbpcu(= N1+ N2) consecutive bits are grouped into a
vectorb = [b0, b1, · · · , bN bpcu −1], where N1 and N2 bits are
mapped to the symbolx1and x2 from two constellation sets
X1 andX2, respectively The transmitted signal is therefore a
two-dimensional complex symbolx = [x1, x2]T from a large
constellation setX = X1× X2 In DVB-NGH, there are three
MIMO modulation modes: QPSK/16QAM, 16QAM/16QAM,
and 16QAM/64QAM, with correspondingNbpcu 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)
demap-ping algorithm [9] is applicable The extrinsic information of
thei-th bit of a symbol can be calculated as
Lei = log
x∈Xi(0)p(y|x, H)Pr(x|La
x∈Xi(1)p(y|x, H)Pr(x|La − La
whereXi(b) denotes the constellation subset with the i-th bit
beingb ∈ {0, 1}, and La = [La, · · · , LaNbpcu−1] is the a priori
information from the decoder, in the form of log-likelihood
Fig 1 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
p(y|x, H) ∝ exp(−y −√
The conditional probability Pr(x|La) can be decomposed into the product of the conditional probability of each bit bi as
i=0,··· ,N bpcu −1
Pr(bi|La
with the assumption that the elements inLaare independently
distributed due to sufficient bit interleaving And the condi-tional probability Pr(bi|La
i) can be further expressed as
Pr(bi|La
i) =
exp[(1− bi)Lai
1 + exp(Lai) , bi∈ {0, 1} (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
x∈Xi(0)p(y|x, H)
III AMI ANALYSIS OFMIMO SCHEMES
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†
where EH[·] denotes the expectation operator over H, det[·]
denotes the determinant, andI 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
Trang 3
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Fig 2 (a) The channel capacity (b) The AMI of coded modulation systems,
CM-AMI (c) The AMI of independent demapping systems, BICM-AMI.
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 = 2N bpcu, the
CM-AMI can be formulated as [12]
ICM= I(x; y|H)
log2
ˆx∈X p(y|ˆ x, H)
p(y|x, H)
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 outputLei forms an independent
chan-nel As shown in Fig 2(c), the overall AMI between bi and
Lei, called BICM-AMI, is calculated as [11], [13]
IBICM=
N bpcu −1
i=0
I(bi y|H) =
N bpcu −1 i=0
I(bi; Lei)
= Nbpcu−
N bpcu −1
i=0
Eb,y,H
log2
x∈X p(y|x, H)
i p(y|x, H)
(9)
BICM-AMI is the upper-bound of information rate for
inde-pendent demapping scheme According to the data processing
inequality [10], BIAMI must be less than or equal to
CM-AMI, 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
DVB-NGH, Gray mapping is adopted since it leads to the least
436.4$0
4$0
615DWHDFKUHFHLYLQJDQWHQQD G%
&KDQQHO&DSDFLW\
&0$0,
%,&0$0,
4$0
Fig 3 Numeric results of CM-AMI and BICM-AMI for the DVB-NGH MIMO system (N bpcu =6, 8, 10).
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 3 Consider the rate-2/3 LDPC code, the CM-AMI thresh-olds 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 constel-lation order, the shaping loss has the tendency of decreasing while the independent demapping loss is monotonously in-creasing In our previous work [14], the performance of DVB-T2 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 ANALYSIS OFMIMO SCHEMES 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
Trang 4?\ \
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V
`
V
Fig 4 EXIT analysis model for the MIMO system with LDPC codes.
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 degreedi that is mapped to thej-th protection level,
its individual EXIT curve is
IEIND IA; di, σj2
= J
(di− 1)[J−1(IA)]2+ σj2
, (10) where the expression of J-function is given in [7], and σj2
denotes the equivalent noise variance of thej-th modulation
level Under the fading channel with CSI known to the
receiver, the equivalentσj2 can be calculated by
σj2=
J−1(I(bj;y|H))2, j = 0, · · · , Nbpcu− 1, (11)
wherebj belongs to thej-th modulation level If an irregular
LDPC code has the variable node degrees of (d1, · · · , dV),
there areV kinds of modulation level since the variable node
with degree di corresponds to a rate-1/di repetition code.
As a result, there areV × 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
IEeVND(IA;P, σ2) =
V
i=1
N bpcu−1 j=0 pi,jdiIIND
E (IA; di, σj2)
V
i=1
N bpcu −1 j=0 pi,jdi , (12) wherepi,j denotes the proportion of the variable nodes with
degreedi that mapped to thej-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
, (
, $
,$H91',(&1'
&1'FXUYH
H91'FXUYHZLWKXQLIRUPELWPDSSLQJ
H91'FXUYHZLWKRSWLPL]HGELWPDSSLQJ
Fig 5 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 inter-leaver The interleaving pattern is optimized for each coded modulation mode to improve the system performance We called it optimized bit mapping Take 16QAM/64QAM (rate-2/3) as an example, the variable node degree isdv= (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
Pun= 101
⎡
⎢
1
3 13 13 13 13 13 13 13 13 13 3
5 35 35 35 35 35 35 35 35 35 1
15 151 151 151 151 151 151 151 151 151
⎤
⎥
⎦ (13) and
Pop= 101
⎡
⎢
3
9 49 49 39 19 39 49 49 39 19 6
9 59 39 59 89 69 59 39 59 89
⎤
⎥
⎦ , (14)
respectively The corresponding EXIT curves for the CND and eVND are depicted in Fig 5 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 SIMULATIONRESULTS
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 rate-2/3 LDPC code Both the iterative and independent demap-ping schemes are simulated In the independent demapdemap-ping
Trang 5
615 G%
,WHUDWLYHGHPDSSLQJZLWKELOY
,QGHSHQGHQWGHPDSSLQJZLWKELOY
,QGHSHQGHQWGHPDSSLQJZLWKQRELOY
YW^<ͬ
ϭϲYD
ϭϲYDͬ
ϭϲYD
ϭϲYDͬ
ϲϰYD
Fig 6 BER simulation results at the code rate of 2/3 for QPSK/16QAM,
16QAM/16QAM, 16QAM/64QAM.
TABLE I SNR T HRESHOLDS FOR THE DVB-NGH MIMO S YSTEM
Rate-2/3 LDPC Code QPSK/
16QAM
16QAM/
16QAM
16QAM/
64QAM AMI
No ID, no bilv 9.70 12.55 15.55
Simu-lation
No ID, no bilv 10.29 13.78 16.28
* The SNR thresholds for simulations were measured at BER = 3×10 −5.
scheme, the LDPC decoder takes a maximum of 50 iterations
using sum-product algorithm [18] In the iterative demapping
scheme, the maximum iterative number for the LDPC decoder
is set 100, and the output of the decoder is fed back to
the demapper every 20 decoding iterations The simulation
results are shown in Fig 6 Take 16QAM/64QAM mode as
an example, the simulated SNR threshold at BER=3×10−5for
the iterative demapping scheme is 15.03dB, which is 1.95dB
away from CM-AMI The independent demapping threshold
with/without the bit interleaver is 16.00dB/16.28dB, which is
about 1.24dB/1.52dB away from BICM-AMI The actual gain
introduced by the bit interleaver is about 0.28dB, fitting the
EXIT prediction very well In summary, the SNR thresholds
for all the three modes at each step are listed in Table I
VI CONCLUSION The performance of the DVB-NGH 2×2 MIMO system
was evaluated through the AMI and EXIT chart analysis
In the AMI analysis, both CM-AMI and BICM-AMI were
considered, which correspond to the theoretical upper limit
of the iterative and independent demapping schemes In the
EXIT analysis, the UEPs of LDPC codes and high-order
modulations were taken into consideration, and the effect of
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 perfor-mance in the future
ACKNOWLEDGEMENT This work was supported by National Key Basic Research Program of China (No 2013CB329203) and China Electric Power Research Institute (CEPRI) (No.TX71-13-007)
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...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...
VI CONCLUSION The performance of the DVB-NGH 2×2 MIMO system
was evaluated through the AMI and EXIT chart analysis
In the AMI analysis, both CM-AMI and BICM-AMI...
Fig (a) The channel capacity (b) The AMI of coded modulation systems,
CM-AMI (c) The AMI of independent demapping systems, BICM-AMI.
not Gaussian distributed