Channel-encoded and SVD-assisted MIMO Multimode Transmission

Schemes with Iterative Detection

Sebastian Aust, Andreas Ahrens and Steffen Lochmann

Hochschule Wismar, University of Technology, Business and Design, Philipp-M¨uller-Straße 14, 23966 Wismar, Germany

Keywords:

Multiple-input Multiple-output (MIMO) System, Singular-value Decomposition (SVD), Bit Allocation,

Optical Fibre Transmission, Multimode Fiber (MMF), Bit-interleaved Coded Modulation (BICM).

Abstract:

In this contribution a coherent (2 × 2) MIMO (multiple input multiple output) transmission with iterative

detection over a measured multimode ﬁber channel at 1325 nm as well as at 1570 nm operating wavelength is

studied. For the channel measurements a ﬁbre length of 1,4 km were chosen. Extrinsic information transfer

(EXIT) charts are used for analyzing and optimizing the convergence behaviour of the iterative demapping

and decoding. Our results show that in order to achieve the best bit-error rate, not necessarily all MIMO layers

have to be activated.

1 INTRODUCTION

Energy consumption of telecom networks has been

identiﬁed as an important research topic throughout

the recent past since energy costs contribute signiﬁ-

cantly to network operator’s operational expenditures

(Baliga et al., 2009; Pickavet et al., 2008). Therefore

systems enabling energy-efﬁcient data transmission

are mandatory for next generation network equip-

ment.

In the recent past the concept of MIMO (multiple

input multiple output) transmission over multimode

ﬁbers has attracted increasing interest in the optical

ﬁber transmission community, e. g. (B¨ulow et al.,

2010; B¨ulow et al., 2011; Singer et al., 2008), target-

ing at increased ﬁber capacity. The concept of MIMO

transmission has been investigated since decades now

for both, twisted-pair copper cable transmission –

suffering from crosstalk between neighbouring wire

pairs – (Van Etten, 1975; Ahrens and Lange, 2006), as

well as for multi-antenna radio systems – where sig-

nal interference occurs on the radio interface (Telatar,

1999; Foschini, 1996).

A MIMO approach where modal dispersion is ex-

ploited, rather than avoided, is a promising solution.

Note that for a long time the multipath nature of wire-

less channels was viewed as a limiting factor to be

avoided. In recent years it has been realized that the

multipath nature of a channel can actually enhance

throughput and improve the quality of the data trans-

mission (i. e. minimize the bit-error rate) if it is prop-

erly exploited (Ahrens and Benavente-Peces, 2009b).

Bit-interleavedcoded modulation (BICM) was de-

signed for bandwidth efﬁcient transmission over fad-

ing channels (Caire et al., 1998; Chindapol, 2001).

Wireless MIMO-BICM transmission schemes for

both non-frequency and frequency selective MIMO

channels have attracted a lot of attention and reached

a state of maturity (K¨uhn, 2006; Ahrens and

Benavente-Peces, 2009a). By contrast, MIMO-aided

optical systems require substantial further research

(Shah et al., 2005; Hsu et al., 2006; Lenz et al.,

2004). That is why in addition to bit loading al-

gorithms in this contribution the beneﬁts of channel

coding are also investigated. The proposed iterative

decoder structures employ symbol-by-symbol soft-

output decoding based on the Bahl-Cocke-Jelinek-

Raviv (BCJR) algorithm and are analyzed under the

constraint of a ﬁxed data throughput (Bahl et al.,

1974).

Against this background, the novel contribution

of this paper is that we jointly optimize the num-

ber of activated MIMO layers and the number of bits

per symbol combined with powerful error correct-

ing codes under the constraint of a given ﬁxed data

throughput and integrity. The performance improve-

ments are exemplarily studied by computer simula-

tions at a measured 1,4 km multimode MIMO ﬁber

channel at 1325 nm and at 1570 nm operating wave-

length.

Since the ”design-space” is large, a two-stage op-

timization technique is considered. Firstly, the un-

353

Aust S., Ahrens A. and Lochmann S..

Channel-encoded and SVD-assisted MIMO Multimode Transmission Schemes with Iterative Detection.

DOI: 10.5220/0004018203530360

In Proceedings of the International Conference on Data Communication Networking, e-Business and Optical Communication Systems (OPTICS-2012),

pages 353-360

ISBN: 978-989-8565-23-5

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

10µm

Figure 1: Forming the optical MIMO channel (left: light

launch positions at the transmitter side with a given eccen-

tricity δ, right: spatial conﬁguration at the receiver side as a

function of the mask radius r).

coded MIMO scheme is analyzed, investigating the

allocation of both the number of bits per modulated

symbol and the number of activated MIMO layers at

a ﬁxed data rate. Secondly, the optimized uncoded

system is extended by incorporating bit-interleaved

coded modulation using iterative detection (BICM-

ID), whereby both the uncoded as well as the coded

systems are required to supportthe same user data rate

within the same bandwidth.

The remaining part of this contribution is orga-

nized as follows: Section 2 introduces our system

model, while the proposed uncoded solutions are dis-

cussed in section 3. In section 4 the channel encoded

MIMO system is introduced. The associated perfor-

mance results are presented and interpreted in section

5. Finally, section 6 provides our concluding remarks.

2 CHANNEL MEASUREMENTS

AND MIMO SYSTEM MODEL

Forming the MIMO (multiple input multiple output)

system, the corresponding optical transmitter as well

as receiver side conﬁguration is depicted in Fig. 1. At

the receiverside different spatial ﬁlters have been pro-

duced by depositing a metal layer at ﬁber end-faces

and subsequent ion milling (Pankow et al., 2011).

Details on the transmission model, which has been

determined by channel measurements, are given in

(Pankow et al., 2011).

2.1 MIMO Channel Measurements

For the investigated optical MIMO channel an eccen-

tricity δ of 10µm and a mask radius r of 15µm were

chosen (Fig. 1). The arising electrical (2× 2) MIMO

channel is highlighted in Fig. 2.

The obtained MIMO channel impulse responses

at 1325 nm and 1570 nm operating wavelength are

depicted in Fig. 3 and Fig. 4, respectively and show

the expected dependency from the operating wave-

s 1

(t)

s 2

(t)

k 1

(t)

k 2

(t)

Figure 2: Electrical (2× 2) MIMO system model.

length. The measured MIMO channel impulse re-

sponses at 1325 nm operating wavelength are high-

lighted in Fig. 3 and illustrate the activation of dif-

ferent mode groups according to the transmitter side

light launch conditions (Fig. 1). The individual mode

groups are clearly separated since almost no chro-

matic dispersion is imminent at the wavelength of

1325 nm. At a higher operating wavelength, i. e. 1570

nm, the separation of the different mode groups disap-

pears based on the additional effect of the chromatic

dispersion (Fig. 4).

0 2 4

0.2

0.4

0 2 4

0.2

0.4

t (inns) →t (inns) →

1 1

(t) →

1 2

(t) →

2 1

(t) →

2 2

(t) →

Figure 3: Measured electrical MIMO impulse responses

with respect to the pulse frequency f

= 1/T

= 5,12 GHz

at 1325 nm operating wavelength.

2.2 MIMO Channel Parameters

In MMF two different sources of dispersion take

place, i. e. modal and chromatic dispersion. The

modal dispersion can be approximated by a weighted

Dirac delta impulse response

(νµ)

(t) =

N−1

∑

κ=0

(νµ)

mκ

δ(t − τ

− τ

) . (1)

Therein, N is the number of propagating modes (i.e.

mode groups), g

(νµ)

mκ

describes the attenuation of the

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354

0 2 4

0.1

0.2

0 2 4

0.05

0.1

0 2 4

0.1

0.2

0 2 4

0.05

0.1

t (inns) →t (inns) →

1 1

(t) →

1 2

(t) →

2 1

(t) →

2 2

(t) →

Figure 4: Measured electrical MIMO impulse responses

with respect to the pulse frequency f

= 1/T

= 5,12 GHz

at 1570 nm operating wavelength.

κth propagation mode (i. e. mode group) between

the µth input and the νth output, τ

is the differential

modal delay with respect to the overall baseline delay

of τ

. In the presence of modal coupling, the attenua-

tion factor g

(νµ)

mκ

would become time-varying. Taking

the different SISO (single input single output) chan-

nels into consideration, the value g

(νµ)

mκ

expresses the

different contributions of the individual mode groups

to the SISO channels within the MIMO system. Since

almost no chromatic dispersion is imminent at the

wavelength of 1325 nm, the individual mode groups

are clearly separated as highlighted in Fig. 3.

As a result of the modal dispersion at the receiver

side, a single transmitted pulse may spread into a

number of adjacent symbol periods, depending on

the data rate, distance traveled, and ﬁber properties

(Singer et al., 2008). Practically, the weighted Dirac

delta pulses can be approximated by Gaussian pulses.

Fig. 5 shows the obtained impulse responses by using

Matlabs



curve ﬁtting tool.

Another limit for MMF is given by the chromatic

dispersion, based on the frequency-dependenceof the

phase velocity of a wave. The transfer function of the

chromatic dispersion is given by

( f) = e

(π f τ

)

. (2)

Therein, the spectral width affecting parameter τ

re-

sults in

= D

· δ

· ℓ , (3)

with the parameter ℓ describing the ﬁbre length. The

parameter δ

represents the spectral width of the

source and D

is the group delay dispersion param-

eter, which depend on the refractive index n and the

operating wavelength λ, and is described as

= −

dλ

. (4)

0 2 4

0.2

0.4

0 2 4

0.2

0.4

t (inns) →t (inns) →

1 1

(t) →

1 2

(t) →

2 1

(t) →

2 2

(t) →

Figure 5: Approximated electrical MIMO impulse re-

sponses with respect to the pulse frequency f

= 1/T

5,12 GHz at 1325 nm operating wavelength by using

Matlabs



curve ﬁtting tool.

In this work a ﬁbre length of ℓ = 1,4 km is chosen.

The spectral width of the source is δ

= 11 nm and

the group delay dispersion parameter is assumed to

be D

= 18 ps/(nm·km). The impulse response of

the chromatic dispersion g

(t) can be obtained by the

inverse Fourier transform of (2).

Finally, the multi-mode channel impulse response

between the µth input and the νth output can be ob-

tained as

νµ

(t) = g

(νµ)

(t) ∗ g

(t) . (5)

Fig. 6 shows the obtained SISO impulse responses

with modal and chromatic dispersion within the

MIMO system by using Matlabs



curve ﬁtting tool.

0 2 4

0.1

0.2

0 2 4

0.05

0.1

0 2 4

0.1

0.2

0 2 4

0.05

0.1

t (inns) →t (inns) →

1 1

(t) →

1 2

(t) →

2 1

(t) →

2 2

(t) →

Figure 6: Approximated electrical MIMO impulse re-

sponses with respect to the pulse frequency f

= 1/T

5,12 GHz at 1570 nm operating wavelength by using

Matlabs



curve ﬁtting tool.

Channel-encodedandSVD-assistedMIMOMultimodeTransmissionSchemeswithIterativeDetection

355

replacements

q µ

(t)

νµ

(t)

e ν

(k)

Figure 7: Mathematical representation of the MIMO related

single input single output (SISO) channels.

2.3 MIMO System Model

Fig. 7 illustrates the MIMO related single input sin-

gle output (SISO) channels. Rectangular pulses are

used for transmit and receive ﬁltering. The baseband

ﬁnite-length impulse response of the MIMO channel

between the µth input and the νth output is given by

νµ

(t) = g

(t) ∗ g

νµ

(t) ∗ g

(t) . (6)

The impulse responses of the transmit and receive ﬁl-

tering are described by g

(t) and g

(t).

The block diagram of the transmission model is

shown in Fig. 8: Coherent transmission and detec-

tion is assumed together with the modulation format

QAM (quadrature amplitude modulation) per MIMO

transmission mode. The block-oriented system for

frequency selective channels is modelled by:

u = H· c+ w . (7)

In (7), the transmitted signal vector c is mapped by

the channel matrix H onto the received vector u.

Finally, the vector of the additive, white Gaussian

noise (AWGN) is deﬁned by w (Pankow et al., 2011;

Raleigh and Ciofﬁ, 1998). Details on the transmission

model are given in (Pankow et al., 2011).

transmit vector

receive vector

noise vector

Figure 8: Transmission system model.

In MIMO communication, singular-value decom-

position (SVD) has been established as an efﬁcient

concept to compensate the interferences between the

different data streams transmitted over a dispersive

channel: SVD is able to transfer the whole sys-

tem into independent, non-interfering layers exhibit-

ing unequal gains per layer as highlighted in Fig. 9.

The singular-value decomposition (SVD)

(Haykin, 2002) of the system matrix H results in:

H = S · V · D

, where S and D

are unitary matrices

and V is a real-valued diagonal matrix of the positive

square roots of the eigenvalues of the matrix H

sorted in descending order

The transpose and conjugate transpose (Hermitian) of

D are denoted by D

and D

, respectively.

The MIMO data vector c is now multiplied by the

matrix D before transmission. In turn, the receiver

multiplies the received vector u by the matrix S

. In

doing so, neither the transmit power budget nor the

noise power characteristic is changed. The overall

transmission relationship is deﬁned as

y = S

(H· D· c+ w) = V· c+ ˜w. (8)

The unequal gains per layer, i. e., the diagonalelement

and

of the matrix V at the time instant k,

are deﬁned by the positive square roots of the eigen-

values of the matrix H

H (Fig. 9).

1 k

2 k

˜w

1 k

˜w

2 k

1 k

2 k

1 k

2 k

Figure 9: SVD-based layer-speciﬁc transmission model.

3 OPTIMIZATION APPROACH

By taking the different layer-speciﬁc weighting, in-

troduced by the positive square roots of the eigenval-

ues of the matrix H

H, into account (Fig. 9), bit- and

power loading per layer can be used to balance the bit-

error probabilities and thus optimize the performance

of the whole transmission system. Given a ﬁxed trans-

mission bit rate, the optimization target is a minimum

BER: Therefore the bit loading to the different trans-

mission modes is optimized according to the options

shown in Table 1.

Table 1: Parameters for bitloading: investigated QAM

transmission modes for ﬁxed transmission bit rate.

throughput layer 1 layer 2

4 bit/s/Hz 16 0

4 bit/s/Hz 4 4

2 bit/s/Hz 4 0

2 bit/s/Hz 2 2

4 CHANNEL-ENCODED MIMO

SYSTEM

BICM is constituted by the concatenation of an en-

coder, an interleaver and a mapper, which is extended

here to a BICM-MIMO scheme, where different sig-

nal constellations are mapped appropriately to differ-

ent layers.

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356

1 k

2 k

encoder

∏

Mapper

MUX and Buffer

Figure 10: The channel-encoded MIMO transmitter struc-

ture.

The channel-encoded transmitter structure is de-

picted in Fig. 10. The encoder employs a

half-rate non-systematic, non-recursive convolutional

(NSNRC) code using the generator polynomials (7,5)

in octal notation. The uncoded information is orga-

nized in blocks of N

bits, consisting of at least 3000

bits, depending on the speciﬁc QAM constellation

used. Each data block i is encoded and results in the

block b consisting of N

= 2N

+ 4 encoded bits, in-

cluding 2 termination bits. The encoded bits are in-

terleaved using a random interleaver and stored in the

vector

b. The encoded and interleaved bits are then

mapped to the MIMO layers. The task of the multi-

plexer and buffer block of Fig. 10 is to divide the vec-

tor of encoded and interleaved information bits, i.e.

b, into subvectors according to the chosen transmis-

sion mode (Table 1). The individual binary data vec-

tors are then mapped to the QAM symbols c

and

according to the speciﬁc mapper used (Fig. 9 and

Fig. 10).

1 k

2 k

Soft Demapper

(ν)

(

∏

−1

∏

(ν)

a,1

(b)

decoder

(ν)

(i)

(ν)

(b)

(ν−1)

e,1

(b)

(ν)

a,2

(

Figure 11: Iterative demodulator structure.

The iterative demodulator structure is shown in

Fig. 11 (Ahrens et al., 2008).

When using the iteration index ν, the ﬁrst iteration

of ν = 1 commences with the soft-demapper deliver-

ing the N

log-likelihood ratios (LLRs) L

(ν=1)

(

b) of

the encoded and interleaved information bits, whose

de-interleaved version L

(ν=1)

a,1

(b) represents the input

of the convolutional decoder as depicted in Fig. 11

(Bahl et al., 1974; K¨uhn, 2006). This channel de-

coder provides the estimates L

(ν=1)

(i) of the original

uncoded information bits as well as the LLRs of the

NSNRC-encoded bits in the form of

(ν=1)

(b) = L

(ν=1)

a,1

(b) + L

(ν=1)

e,1

(b) . (9)

As seen in Fig. 11 and (9), the LLRs of the NSNRC-

encoded bits consist of the receiver’s input signal it-

self plus the extrinsic information L

(ν=1)

e,1

(b), which

is generated by subtracting L

(ν=1)

a,1

(b) from L

(ν=1)

(b).

The appropriately ordered, i.e. interleaved extrinsic

LLRs are fed back as a priori information L

(ν=2)

a,2

(

to the soft demapper of Fig. 11 for the second itera-

tion.

Following the detailed structure of the soft-

demapper in Fig. 12, the N

LLRs L

(ν)

(

b) are com-

posed of sub-blocks (L

(ν)

(

),L

(ν)

(

)). Each vec-

tor L

(ν)

(

ℓ

) (with ℓ = 1,2) is generated by the soft

demapper from the MIMO channels’ output y

ℓ,k

and

the a priori information L

(ν)

a,2

(

ℓ

) (with ℓ = 1,2) pro-

vided by the channel decoder. After the ﬁrst iteration,

this a priori information emerges from the N

LLRs

(ν)

a,2

(

b).

MUXandBuffer

DEMUXandBuffer

(k)

Soft-

Demapper

(ν)

(

)

(ν)

(

)

(ν)

a,2

(

)

(ν)

a,2

(

)

(ν)

(

(ν)

a,2

(

Figure 12: Detailed soft demapper demodulator structure.

5 RESULTS

The numerical analysis targets at BER results. For

this purpose it is assumed, that each optical input

within the multimode ﬁber is fed by a system with

identical mean properties with respect to transmit ﬁl-

ter and pulse frequency f

= 1/T

. For numerical as-

sessment within this paper,the pulse frequencyis cho-

sen to be f

= 5,12 GHz, the average transmit power

is supposed to be P

= 1V

– this equals 1 W at a lin-

ear and constant resistance of 1Ω – and as an external

disturbance a white Gaussian noise with power spec-

tral density N

is assumed (Pankow et al., 2011). In

order to transmit at a ﬁxed data rate while maintain-

ing the best possible integrity, i. e., bit-error rate, an

appropriate number of MIMO layers has to be used,

which depends on the speciﬁc transmission mode, as

detailed in Tab. 1.

5.1 Uncoded MIMO System

The optimization results, obtained by computer simu-

lation at an overall data rate of 20,48 Gbps, are shown

Channel-encodedandSVD-assistedMIMOMultimodeTransmissionSchemeswithIterativeDetection

357

in Fig. 13 for different operating wavelength: The

BER becomes minimal in case of an optimized bit

loading (Fig. 13) with highest bit loading in the layer

with largest singular values. The optimized MIMO

transmission exhibits an improvement with respect to

SISO transmission, but a non-optimized MIMO trans-

mission leads to a signiﬁcant degradation of the sys-

tem performance. Furthermore, the simulation results

show that in order to minimize the overall BER at a

ﬁxed data rate, not necessarily all MIMO layer should

be activated. Instead, only the strongest MIMO layers

should be used with appropriate modulation levels in

the considered example.

Furthermore, as obtained by the channel measure-

ments (Fig. 3 and Fig. 4), at a higher operating wave-

length, i. e. 1570 nm, the separation of the differ-

ent mode groups disappears based on the effect of

the chromatic dispersion. Since the chromatic disper-

sion affects all mode groups almost equally, MIMO

isn’t able to generate an additional diversity gain

(in comparison to wireless channels, where delay-

spread isn’t any longer a limiting parameter (Ahrens

and Benavente-Peces, 2009b; Ahrens and Benavente-

Peces, 2011)). The advantage of a higher signal-to-

noise-ratio due to lower attenuation in the third op-

tical window is diminished by the chromatic disper-

sion. Therefore, the obtained bit-error rate results

are higher at 1570 nm compared to 1325 nm. How-

ever, dispersion compensation schemes are well es-

tablished in optical communications and they are not

considered as a practical limitation.

However, uncoded systems have reached a state

of maturity. By contrast coded MIMO conﬁgurations

require substantial further research.

20 25 30 35 40

−6

−4

−2

10 · log

) (indB) →

bit-error rate →

16-QAM, SISO

(16,0)-QAM, MIMO

(4,4)-QAM, MIMO

Figure 13: BER performance at 1570 nm operating wave-

length (dotted line) and at 1325 nm operating wavelength

(solid line) when using the transmission modes introduced

in Tab. 1 and transmitting 4 bit/s/Hz over frequency selec-

tive optical MIMO channels.

5.2 Channel Encoded MIMO System

The joint optimization of the number of activated

MIMO layers as well as the number of bits per sym-

bol was found to be effective at high SNRs. However,

iterative receivers are able to work in a much lower

SNR region. Therefore it would be interesting to see

how the design criteria change when coding is added

to the transmission system.

Using the half-rate, constraint-length K

= 3

NSNRC code with the generator polynomialsof (7,5)

in octal notation, the BER performance is analyzed

for an effective throughput of 2 bit/s/Hz based on the

best uncoded schemes of Table 1. In addition to the

number of bits per symbol and the number of acti-

vated MIMO layers, the achievable performance of

the iterative decoder is substantially affected by the

speciﬁc mapping of the bits to both the QAM sym-

bols as well as to the MIMO layers. Here, the max-

imum iteration gain can only be guaranteed, if anti-

Gray mapping is used on all activated MIMO layers

(Chindapol, 2001).

Furthermore, observed by comparing the extrinsic

information transfer (EXIT) chart results of Fig. 14

and 15, the overall performance is strongly inﬂuenced

by the allocation of the number of bits to the MIMO

layers.

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

extrinsic demapper output →

extrinsic decoder output →

NSNRC code

(16,0) QAM, MIMO

(4,4) QAM, MIMO

Figure 14: EXIT chart for an effective user-data through-

put of 2 bit/s/Hz and the different QAM constellations at

10log

) = 18 dB (1325 nm operating wavelength

and anti-Gray mapping on all activated MIMO layers).

In order to guarantee an open EXIT tunnel and

therefore an efﬁcient information exchange between

the soft demapper transfer characteristic and the de-

coder transfer characteristic at a given signal-to-noise

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358

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

extrinsic demapper output →

extrinsic decoder output →

NSNRC code

(16,0) QAM, MIMO

(4,4) QAM, MIMO

Figure 15: EXIT chart for an effective user-data through-

put of 2 bit/s/Hz and the different QAM constellations at

10log

) = 18 dB (1570 nm operating wavelength

and anti-Gray mapping on all activated MIMO layers).

ratio, not necessarily all MIMO should be activated.

In the considered example only the strongest MIMO

layer should be used with appropriate modulation

level. Activating all MIMO layers the information

exchange between the soft demapper and the decoder

stops relatively early, resulting in a reduced BER per-

formance.

Furthermore, it turns out that chromatic dispersion

combined with the speciﬁc QAM constellation sizes,

as detailed in Tab. 1, leads to a degradation of the

overall performance as expected.

The BER performance is presented in Fig. 16

based on the different schemes of Table 1 and con-

ﬁrms the EXIT chart results. The information word

length is 3000 bits and a random interleaver is ap-

plied.

Fig. 17 illustrates the wavelength-dependent BER

performance. As already stated by the EXIT charts re-

sults, the chromatic dispersion leads to a degradation

of the overall performance.

The inferior performance is also indicated by the

corresponding BER curves shown in Fig. 17.

6 CONCLUSIONS

Coherent MIMO transmission over measured multi-

mode optical ﬁbers has been investigated targeting at

minimized BER while keeping the transmission bit-

rate constant. The results show that MIMO trans-

mission based on SVD is a promising approach, in

particular when the bit loading is optimized. In that

12 14 16 18 20 22 24

−4

−3

−2

−1

10 · log

) (in dB) →

bit-error rate →

(4,0) QAM, uncoded

(16,0) QAM, 3 Iter.

(16,0) QAM, 10 Iter.

(4,4) QAM, 10 Iter.

Figure 16: BERs assuming anti-Gray mapping scheme

on the activated MIMO layers for an effective user-data

throughput of 2 bit/s/Hz (1325 nm operating wavelength).

14 16 18 20 22 24

−4

−3

−2

−1

10 · log

) (in dB) →

bit-error rate →

(16,0) QAM, 10 Iter.

(4,4) QAM, 10 Iter.

Figure 17: BER comparison at 1325 nm operating wave-

length (solid line) and at 1570 nm operating wavelength

(dotted line) assuming anti-Gray mapping scheme on the

activated MIMO layers for an effective user-data through-

put of 2 bit/s/Hz.

case signiﬁcant BER improvements can be achieved

compared to a conventional SISO system. The pro-

posed MIMO-BICM scheme includes an adaptation

of the transmit parameters. EXIT charts are used for

analysing and optimizing the convergence behaviour

of iterative demapping and decoding. Here, the choice

of the number of bits per symbol and the number of

MIMO layers combined with powerful error correct-

ing codes substantially affects the performance of a

MIMO system, suggesting that not all MIMO layers

have to be activated in order to achieve the best BERs.

ACKNOWLEDGEMENTS

The authors wish to thank their co-worker, Mr. Stef-

fen Schr¨oder, for supporting the measurement cam-

Channel-encodedandSVD-assistedMIMOMultimodeTransmissionSchemeswithIterativeDetection

359

paign.

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