Multiple Subcarrier optical communication systems with subcarrier signal-point sequence

1738 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 53, NO. 10, OCTOBER 2005

Multiple-Subcarrier Optical Communication SystemsWith Subcarrier Signal-Point Sequence

Shota Teramoto and Tomoaki Ohtsuki, Senior Member, IEEE

Abstract—We propose a multiple-subcarrier (MS) optical com-munication system with subcarrier signal-point sequence (SSPS).We use the SSPSs having a large minimum value and large Eu-clidean distances, so that the required dc bias is minimized andthe error-rate performance is improved. Note that in the proposedsystem, the signal points having the larger minimum value are se-lected, while the signal points having a lower peak-to-mean-enve-lope-power ratio (PMEPR) are selected in orthogonal frequency-division multiplexing (OFDM) systems. Therefore, the SSPSs goodfor OFDM with phase shifting by rad are not necessarily effectivefor MS optical communication systems. The main contributions ofour paper are: 1) we derive transmit sequences having a large min-imum value and large Euclidean distances by using 8-phase-shiftkeying and (8+1)-amplitude phase-shift keying; and 2) since de-signing optimal sequences would be prohibitively complex, we in-troduce a reasonable procedure for suboptimal sequence design,obtaining good results. We show that the normalized power re-quirements and normalized bandwidth requirements of the MSsystems with SSPS are smaller than those of the conventional MSsystems.

Index Terms—dc bias, (8+1)-amplitude phase-shift keying(APSK), multiple-subcarrier modulation (MSM), subcarriersignal-point sequence (SSPS).

I. INTRODUCTION

OPTICAL wireless communication systems have attractedmuch attention for high-speed indoor wireless communi-

cations. Compared with radio systems, infrared radiation (IR) of-fers many advantages, such as a higher bit rate, an enormous un-regulated bandwidth, and no interference between channels op-erating in the adjacent rooms. In optical wireless communica-tions, optical wireless systems using intensity modulation withdirect detection (IM/DD) are most popular because of their sim-plicity.Multiple-subcarrier(MS)opticalcommunicationsystemsusing IM/DD (IM/DD MS) are also attractive, because the useof several narrow-band subcarriers promises to minimize inter-symbolinterference(ISI)onmultipathchannelsandbecausemul-tiple-subcarrier modulation (MSM) can provide immunity to flu-orescent-light noise near dc. [1]. The main fault of IM/DD MSsystems is their poor average optical power efficiency. An opticalintensity must be nonnegative, and thus a dc bias must be addedto an MS electrical signal to modulate it onto an intensity of anoptical carrier. As the number of subcarriers increases, the min-imum value of the MS electrical signal decreases (becomes more

Paper approved by K. Kitayama, the Editor for Optical Communication ofthe IEEE Communications Society. Manuscript received March 15, 2004. Thispaper was presented in part at the IEEE Global Telecommunications Confer-ence, Taipei, Taiwan, R.O.C., November 2002.

S. Teramoto is with the Department of Electrical Engineering, Tokyo Univer-sity of Science, Chiba, 278-8510 Japan.

T. Ohtsuki is with the Department of Information and Computer Science,Keio University, Yokohama, 223-8522 Japan.

Digital Object Identifier 10.1109/TCOMM.2005.857152

negative), and, thus, the required dc bias increases. The averageoptical power efficiency depends on the bias signal. Therefore, itis important to minimize the bias signal. In IM/DD MS systems,information bits are mapped onto the intensity of an optical car-rier. Some block codes have been proposed to reduce the dc biasand to improve the power efficiency of IM/DD MS systems [1].

In this paper, we propose an IM/DD MS optical communi-cation system with subcarrier signal-point sequence (SSPS)to improve the power efficiency of IM/DD MS systems. TheSSPS is a set of sequences that consists of a signal point ofeach subcarrier. An SSPS consisting of signal points isselected according to input data. The proposed system usesthe SSPSs having a large minimum value and large Euclideandistance, so that the required dc bias is minimized and theerror-rate performance is improved. Note that in the pro-posed systems, the signal points having the larger minimumvalue are selected, while the signal points having a lowerpeak-to-mean-envelope-power ratio (PMEPR) are selectedin orthogonal frequency-division multiplexing (OFDM) sys-tems. Therefore, the SSPSs good for OFDM in [2] with phaseshifting by rad are not necessarily effective for MS opticalcommunication systems. We derive the SSPS that is suitablefor MS optical communication systems. We analyze the powerand bandwidth requirements of the proposed system. Themain contributions of our paper are as follows: 1) we derivetransmit sequences having a large minimum value and largeEuclidean distances by using 8-ary phase-shift keying (8-PSK)and (8+1)-ary amplitude phase-shift keying [(8+1)-APSK] and2) since designing optimal sequences would be prohibitivelycomplex, we introduce a reasonable procedure for suboptimalsequence design, obtaining good results. We show that thenormalized power requirements and the normalized bandwidthrequirements of the MS systems with SSPS (MS-SSPS) aresmaller than those of the MS systems with the minimum-powerblock coding (MS-Min-Power), respectively. We also show thatthe MS-SSPS with (8+1)-APSK MS-SSPS whose constellationconsists of 8-PSK signal points plus zero-signal point [3], [4]can achieve better normalized power requirement and normal-ized bandwidth requirement than the MS-SSPS with 8-PSK[MS-SSPS (8-PSK)].

II. MULTIPLE-SUBCARRIER OPTICAL

COMMUNICATION SYSTEMS

A. IM/DD Optical Channel Model

In the IM/DD optical channel with the impulse response ,the received photocurrent is given by [5]

(1)

0090-6778/$20.00 © 2005 IEEE

TERAMOTO AND OHTSUKI: MULTIPLE-SUBCARRIER OPTICAL COMMUNICATION SYSTEMS WITH SSPS 1739

where represents the photodetector responsivity, repre-sents the transmitted optical intensity, and is the receiverthermal noise and the intense ambient shot light noise. Thechannel is modeled by a linear system having the impulseresponse and the frequency response . The noise

can be modeled as Gaussian, independent of , andwhite with two-sided power spectral density (PSD) . Weassume that the multipath distortion is negligible, as in [1] and[6]. Wireless infrared links are subject to intense ambient lightthat gives rise to a high-rate, signal-independent shot noise,which can be modeled as white and Gaussian [5]. Note thatthe electrical input must be nonnegative. Note also thatthe average amplitude of is limited because of powerconsumption and eye safety considerations. Scaling the currentof the photodiode at the receiver by for convenience,has the same unit as . The average optical power is givenby the mean value of ; . Note that in electricalchannels, the average power is the mean value of .

B. MS Optical Communication Systems

An MS system is a system that multiplexes subcarriers withdifferent frequencies in the electrical domain and modulatesan optical subcarrier by the multiplexed signal. The transmitteruses a set of subcarrier frequencies. During each symbol in-terval of duration , it transmits a vector of information bits.A block coder maps a vector of information bits to a corre-sponding vector of symbol amplitudes, and it is modulated ontosubcarriers. The MS electrical signal is formed by summingthe modulated subcarriers. We assume the rectangular transmitpulse of width and unit amplitude. We also assume that eachsubcarrier is mutually orthogonal. The average optical power isgiven by [1] , where is a nonnegative scalefactor and is a bias signal.

C. Block Code

In the MS systems, the block coder maps the vector ofinformation bits to the corresponding vector of symbol ampli-tudes. The vector of symbol amplitudes is modulated onto thesubcarriers. Some block codes have been proposed for MS sys-tems to reduce the bias signal and improve the average powerefficiency [1].

The normal block code is generally used in the MS system,whose subcarriers are used for transmission of informationbits. Information bits can be mapped independently to the cor-responding vector of symbol amplitudes. At the receiver, eachvector of the detected symbol amplitudes can be demapped in-dependently to information bits. Therefore, the number of trans-mitted bits is for binary phase-shift keying (BPSK).

In the reserved-subcarrier block code [1], subcarriers areused to enlarge the minimum value of the MS electrical signal,thereby reducing the average optical power, where the ampli-tudes of the reserved subcarriers are 1 and the phases of the re-served subcarriers are 0 or . The number of transmitted bits inthe reserved-subcarrier block code is for BPSK.For each choice of and , there exists an optimal set of re-served subcarriers, though this set is often not unique.

In the minimum-power block code [1], information bits aremapped to the set of all of the subcarriers. Thus, the information

bits are not mapped onto each subcarrier independently. It wasshown in [1] that the average optical power of the minimum-power block code is smaller than that of the reserved-subcarrierblock code.

III. MULTIPLE-SUBCARRIER OPTICAL COMMUNICATION

SYSTEMS WITH SUBCARRIER SIGNAL-POINT SEQUENCE (MS-SSPS)

We propose the MS optical communication system withSSPS to reduce the optical power requirement. The block dia-gram of the proposed MS system with quaternary phase-shiftkeying (QPSK) is illustrated in Fig. 1. The transmitter uses a setof subcarriers. During each symbol interval of duration ,it transmits a vector of information bits .The SSPS coder first determines the phases of SSPS withreference to the look-up table (LUT), where the suboptimumphases of SSPSs selected beforehand are written in the LUT.Then, the SSPS block coder maps a set of information bits

to a set of corresponding vectors of symbol amplitudesas follows:

(2)

where is a mapping function of the proposed system. Ex-amples of the proposed mapping function are shown in Tables Iand II. Note that, in the conventional MS systems (except forthe system with the minimum-power block code), the blockcoder independently maps information bits to the cor-responding vectors of symbol amplitudes as follows:

(3)

where is a mapping function of the conventional system.In this paper, we assume the rectangular transmit pulse

of width and unit amplitude. We also assume that each sub-carrier is mutually orthogonal. The bias signal is chosen sothat , where is a nonnegative scalefactor. We set the subcarrier frequencies to ,where . We refer to as the position of the subcar-rier with . With choosing , , andas shown above, , and the average optical power isgiven by [1]. In evaluating the average transmit power require-ment, we thus consider the minimum value of the MS electricalsignal described with the amplitude over the symbol interval

(4)

At the receiver, the MS optical signal is converted to theMS electrical signal by photodetector (PD), and each subcarriercomponent isobtainedusingamatchedfilter.Thereceiverdetectsthe transmittedsymbolsbasedonthemaximum-likelihooddetec-tion (MLD). According to the Euclidean distance between the re-ceived SSPS and the locally generated SSPS, the detector selectsthe SSPSs having the minimum value ofEuclidean distance as thetransmitted symbol. The Euclidean distance is given by

(5)


Fig. 1. Block diagram of the proposed system.

TABLE ISSPS (N = 4,K = 4, 8-PSK, TIME-VARYING BIAS)

where is the total number of subcarriers, is the th preparedSSPS for the th subcarrier, is the th received SSPS for the

th subcarrier, and is mapped onto with reference to theLUT. The receiver detects the transmitted symbols based on theMLD, and the vector of the detected symbol amplitudes is ob-tained. The SSPS decoder maps the vector of the detected symbolamplitudes to a vector of the detected information bits .

TABLE IISSPS (N = 4,K = 4, (8+1)-APSK, TIME-VARYING BIAS)

The SSPS is a set of sequences that consists of a signal pointof each subcarrier. The SSPS consisting of signal points isselected according to input data. As we explained above, theproposed MS system uses the SSPSs having the large min-imum value of the MS electrical signal and the large minimumEuclidean distance between each pair of SSPSs. Thus, therequired dc bias is minimized, and the error-rate performance is


Fig. 2. (8+1)-APSK signal constellations.

improved. The SSPSs used in the proposed system are selectedas follows. The bias signal corresponding to each sequenceis calculated for all of the possible sequences: sequencesfor -PSK and sequences for -APSK. Fig. 2shows (8+1)-APSK signal constellations. The (8+1)-APSKsignal constellation consists of 8-PSK signal points plus azero-signal point. As shown in [3] and [4], the modulation thathas the signal constellation in Fig. 2 is generally referred to as(8+1)-APSK. Note that the available SSPSs are limited by theacceptable bias value and the minimum Euclidean distance.

The computation for selecting the optimum SSPSs is pro-hibitive because of a large number of candidate sets. Therefore,we use the suboptimal selection method shown below. First, wechoose the set of the SSPSs having the large minimum value ofthe MS electrical signal

(6)

where represents the set of the SSPSs, represents the se-lected set of the SSPSs, represents the specific threshold ofminimum value of MS electrical signal, and is definedas

(7)

Second, we choose the set of the SSPSs having the large min-imum Euclidean distance between each pair of SSPSs among

(8)

where represents the selected set of the SSPSs, representsthe specific threshold of minimum Euclidean distance betweeneach pair of SSPSs, and is defined as

(9)

Tables I and II show sets of SSPSs and the bias values forfour subcarriers ( ) with time-varying bias when fourbits per sequence can be transmitted ( ), where eachsignal point of the sequences in Tables I and II corresponds to asignal point of 8-PSK and (8+1)-APSK signal constellations,respectively. In these tables, the bias value of the MS-SSPSwith (8+1)-APSK is smaller than that of the MS-SSPS with8-PSK in most sequences. This is because, in the MS-SSPS with(8+1)-APSK, some subcarriers corresponding to the zero-signalpoint in (8+1)-APSK are not transmitted. In addition, the errorprobability can be improved, because we can choose sequencesfrom more candidates in the MS-SSPS with (8+1)-APSK.

IV. PERFORMANCE ANALYSIS

In the proposed system, the receiver detects the transmittedSSPSs while comparing the received sequence with all of thepossible sequences, and selects the sequence having the smallestEuclidean distance from the received sequence. The receivedSSPS has a noise component. The probability that the MLDdetects the incorrect sequence when , , is transmittedis derived as

(10)

where , is the transmitted signalenergy per symbol, and the noise is white Gaussian noise withtwo-sided PSD . Assuming that all symbols are equallylikely, we get a union bound of symbol-error probability byaveraging (10) over all the possible sequences, that is

(11)

V. NUMERICAL RESULTS

In this section, we evaluate the bandwidth and power require-ments of the proposed systems (MS-SSPS (8-PSK), MS-SSPS[(8+1)-APSK], and the MS system with the minimum-powerblock coding (MS-Min-Power), comparing them with those ofon–off keying (OOK). For each scheme, represents the in-formation bit rate, represents the total electrical bandwidthrequired at the receiver, and represents the probability of in-formation bit error. We set the required bit-error probability to

. We get the power requirement by using theamplitude scale factor of subcarrier . For comparison, the re-quired power is normalized with that of OOK at the same bitrate . We first consider a reference system using OOK withrectangular pulses of duration and the symbol rate of .We have , , and

(12)

For the MS-SSPS, we use (11), and for the MS-Min-Power, weuse [1]. In each scheme, the informa-tion bit rate is given by , where is the numberof information bits transmitted by an MS symbol. The electricalbandwidth requirement is given by . We assume

in all of the systems. We also assume in theMS-Min-Power, where is the number of reserved subcarriers.We use two bias signals for all of the systems: the fixed bias andthe time-varying bias [1]. The fixed bias always adds the fixedbias to all the symbols, while the time-varying bias adds the cor-responding bias to each symbol, that is, the symbol-dependentbias.


Fig. 3. Normalized power requirement versus the number of subcarriers forthe systems with BPSK. (a) Fixed bias. (b) Time-varying bias.

A. Normalized Power Requirement Versus the Total Numberof Bits

Fig. 3(a) and (b) shows the normalized power requirementversus the total number of bits for the systems with BPSK,with fixed bias and time-varying bias. In Fig. 3(a), the nor-malized power requirements of the MS-SSPS are smaller thanthose of the MS-Normal and the MS-Min-Power with

. For instance, at 8 b, the normalized power require-ment of the MS-SSPS (8-PSK) is 4.5 dB smaller than that of theMS-Normal, and 1.9 dB smaller than that of the MS-Min-Power,respectively. Similar trends can be seen in Fig. 3(b); the normal-ized power requirements of the MS-SSPS are smaller than thoseof the MS-Normal and the MS-Min-Power for . Thisis because the required dc bias of the proposed system is smallerthan those of the conventional MS systems. In Fig. 3(a), thenormalized power requirement of the MS-SSPS [(8+1)-APSK]is smaller than that of the MS-SSPS (8-PSK) for

. For instance, at 8 b, the normalized power requirement ofthe MS-SSPS [(8+1)-APSK] is 1.6 dB smaller than that of theMS-SSPS (8-PSK). Similar trends can be seen in Fig. 3(b); thenormalized power requirement of the MS-SSPS [(8+1)-APSK]is smaller than that of the MS-SSPS (8-PSK) for .

Fig. 4. Normalized power requirement versus normalized bandwidthrequirement for the systems with BPSK. (a) Fixed bias. (b) Time-varying bias.

This is because in the MS-SSPS with (8+1)-APSK, some sub-carriers are not transmitted, and thus, the negative peak valueis large. Comparing the performances of the MS-SSPS withboth biases, the performance improvement of the MS-SSPS overthe other systems is large for the fixed bias. Note that the nor-malized power requirements of all of the MS systems with thetime-varying bias are smaller than those of the systems with thefixed bias, respectively.

B. Normalized Power Requirement Versus NormalizedBandwidth Requirement

Fig. 4(a) and (b) shows the normalized power requirementversus the normalized bandwidth requirement for the systemswith BPSK, with fixed bias and time-varying bias. In Fig. 4(a),the MS-SSPS can reduce the normalized power requirement atthe same normalized bandwidth requirement as the other sys-tems. For instance, at the normalized bandwidth requirementof 1.25, the normalized power requirement of the MS-SSPS(8-PSK) is 4.0 dB smaller than that of the MS-Normal, and3.0 dB smaller than that of the MS-Min-Power, respectively.This is because the required dc bias of the proposed systemis smaller than those of the conventional MS systems. Whenthe normalized bandwidth requirement is smaller than 1.25, the


normalized power requirement of the MS-SSPS [(8+1)-APSK]is smaller than that of the MS-SSPS (8-PSK). For instance, atthe normalized bandwidth requirement of 1.2, the normalizedpower requirement of the MS-SSPS [(8+1)-APSK] is 0.6 dBsmaller than that of the MS-SSPS (8-PSK). Similar trends canbe seen in Fig. 4(b). The normalized power requirement of theMS-SSPS is smaller than that of the other systems. When thenormalized bandwidth requirement is smaller than 1.25, the nor-malized power requirement of the MS-SSPS [(8+1)-APSK] issmaller than that of the MS-SSPS (8-PSK). Comparing the per-formances of the MS-SSPS with both biases, the normalizedpower requirement is small for the time-varying bias.

In Figs. 3 and 4, the proposed system needs more power thanthe OOK system in many cases. However, note that at high band-width efficiency (when the number of subcarriers is ), theproposed system needs less optical power. In addition, similarto the MSM in [1], the proposed system has the following ad-vantages: 1) the use of several narrowband subcarriers promisesto minimize ISI on multipath channels; and 2) MSM can pro-vide immunity to fluorescent-light noise near dc. Therefore, theproposed system is attractive.

VI. CONCLUSION

We have proposed an MS optical communication system withSSPS to reduce the power requirement. In the proposed MSsystem, an SSPS is a set of sequences that consists of a signalpoint of each subcarrier, and the received signal is detected withMLD. In the proposed system, the signal-point sequence havingthe large minimum value and the large Euclidean distances areused, so that the required dc bias is minimized and the error-rate performance is improved. We showed that the normalizedpower requirements of the MS systems with SSPS (MS-SSPS)are smaller than that of the MS system with the normal blockcoding (MS-Normal), and that of the MS system with the min-imum-power block coding (MS-Min-Power), respectively. Wealso showed that the MS-SSPS can reduce the normalized powerrequirement at the same normalized bandwidth requirement asthe other systems. Moreover, we showed that the normalizedpower requirement and the normalized bandwidth requirementof the MS-SSPS with (8+1)-APSK are smaller than those ofthe MS-SSPS with 8-PSK, respectively. Comparing the perfor-mances of the MS-SSPS with the fixed bias and the time-varyingbias, the normalized power requirement is small for the time-varying bias.

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Shota Teramoto received the B.E. and M.E. degrees in electrical engineeringfrom Tokyo University of Science, Chiba, Japan, in 2002 and 2004, respectively.

His research interests were in optical communication systems.

Tomoaki Ohtsuki (M’90–SM’01) received the B.E.,M.E., and Ph.D. degrees in electrical engineeringfrom Keio University, Yokohama, Japan, in 1990,1992, and 1994, respectively.

From 1994 to 1995, he was a Post Doctoral Fellowand a Visiting Researcher in electrical engineeringwith Keio University. From 1993 to 1995, he wasa Special Researcher of Fellowships with the JapanSociety for the Promotion of Science for JapaneseJunior Scientists. From 1995 to 2005, he was withTokyo University of Science, Chiba, Japan. From

1998 to 1999, he was with the Department of Electrical Engineering andComputer Sciences, University of California, Berkeley. He is now an AssociateProfessor with Keio University, where he is engaged in research on wirelesscommunications, optical communications, signal processing, and informationtheory.

Dr. Ohtsuki is a member of the IEICE and the Symposium on InformationTheory and Its Applications (SITA). He was a recipient of the 1997 Inoue Re-search Award for Young Scientist, the 1997 Hiroshi Ando Memorial Young En-gineering Award, the Ericsson Young Scientist Award in 2000, the 2002 FunaiInformation and Science Award for Young Scientists, and the IEEE First Asia-Pacific Young Researcher Award in 2001.

Technology

Multiple Subcarrier optical communication systems with subcarrier signal-point sequence