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Power Efficiency Evaluation of Mapping Multiplexing Technique and Pulse Amplitude Modulation for Noncoherent Systems Volume 7, Number 4, August 2015 M. A. Elsherif A. Malekmohammadi

DOI: 10.1109/JPHOT.2015.2464083 1943-0655 Ó 2015 IEEE

IEEE Photonics Journal

Power Efficiency Evaluation of MMT and M-PAM

Power Efficiency Evaluation of Mapping Multiplexing Technique and Pulse Amplitude Modulation for Noncoherent Systems M. A. Elsherif and A. Malekmohammadi Applied Electromagnetics and Telecommunications Research Group, George Green Institute for Electromagnetics Research, The University of Nottingham, Nottingham NG7 2RD, U.K. Department of Electrical and Electronic Engineering, The University of Nottingham, Malaysia Campus, 43500 Semenyih, Selangor, Malaysia DOI: 10.1109/JPHOT.2015.2464083 1943-0655 Ó 2015 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Manuscript received June 27, 2015; revised July 26, 2015; accepted July 29, 2015. Date of publication August 3, 2015; date of current version August 17, 2015. Corresponding author: A. Malekmohammadi (e-mail: [email protected]).

Abstract: The two-, three-, and four-channel mapping multiplexing technique (MMT) is demonstrated to increase the data capacity of multilevel intensity-modulated transmission formats to 2, 3, and 4 bits/symbol with a substantial reduction in power penalty. This paper outlines the N-channel MMT design metric consideration influence on the performance enhancement of higher order amplitude modulated systems in terms of power penalty, receiver sensitivity, and spectral efficiency. The signal space model has been developed for N-channel MMT, where the average electrical and optical power expressions are derived. Transmission of 2, 3, and 4 bits/symbol using MMT system shows better performance in terms of the average optical power penalty, in comparison with pulse amplitude modulation (M-PAM) formats, with respect to the information capacity. The proposed scheme can be considered as an alternative to M-PAM systems with enhanced power efficiency. Index Terms: Optical fiber communication systems, optical interconnects, mapping multiplexing technique, electro-optical systems.

1. Introduction The rapid growth in network traffic demand have motivated the continual development in 100 G, 400 G technologies in the context of next-generation Multi-Giga Ethernet and Optical Transport Networks (OTNs) [1]. One way of increasing the bit rate, the employment of one or a plural of different methodologies as increasing the number of levels, channels, modulation order, and baud rate. The IEEE High Speed Study Group (HSSG) is in the process of an extensive investigation of the feasibility of different economic low complex alternatives for next generation 100 G and 400 G optical Ethernet networks [2]. Recently, IEEE 802.3bm Task Force (TF) have investigated the technical performance, feasibility and different design aspects for 4-PAM, 8-PAM, and 16-PAM multilevel formats on Single Mode Fiber (SMF) to be standardized to the existing 100 GBASE-LR4 [3]. The reports demonstrated the deployment practicality of 4-PAM and 8-PAM in the context of being an upper boundary limit for the modulation order due to the exponential increase in impairment penalties with the increment in the number of levels [4], [5].

Vol. 7, No. 4, August 2015

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Fig. 1. (a) MMT transmitter model. (b) MMT symbol format.

M-PAM has M number of levels for the transmission of log2 ðMÞ bits of information. Hence, M-PAM is considered a bandwidth limited signaling format, since the spectral requirement is in the order of 1=log2 ðMÞ of On-Off Keying (OOK), while its power penalty is ðM 1Þ of OOK at fixed bandwidth. On the other hand, Pulse Position modulation (M-PPM) divides the symbol duration Ts in to M number of sub intervals with duration Ts =M for the transmission of log2 ðMÞ bits of information with a two constant distinct levels. Hence, M-PPM is considered a power limited signaling format with a power efficiency advantage, while its spectral requirement is M=log2 ðMÞ. The M-PAM and M-PPM performance have been investigated for intensity modulated direct detection systems (IM/DD) in [6] and [7]. Mapping Multiplexing Technique (MMT) is a recently developed electrical multiplexing technique that enables to increase the dispersion tolerance and the spectral efficiency of wavelength division multiplexing systems [8], [9]. MMT system is a practical interest to expand the capacity of implemented higher order modulation formats in optical interconnects [10]. MMT is a joint multiplexing and modulation format which can be viewed as a hybrid combination between M-PPM and M-PAM modulation formats. N-Channel MMT design nature is an intermediate compromise as a power efficient alternative compared to M-PAM and bandwidth efficient alternative compared with M-PPM for metropolitan fiber network and short range data interconnects. The joint design in MMT causes more degree of freedom in optimizing the performance, which can be viewed as a power efficient alternative and bandwidth efficient alternative compared to M-PAM and M-PPM, respectively. In this paper for the first time, we report a model for 2, 3 and 4-channel MMT transmission system to be considered as practical alternative to M-PAM modulation formats over Additive White Gaussian Noise (AWGN) channel featuring a notable power efficiency advantage.

2. MMT Transceiver Model 2.1. Transmitter Model Fig. 1(a) shows the MMT transmitter. MMT mapper on the transmission side is built with an input array of parallel channels N ¼ ½yn ; ynþ1 ; . . . ; yN1 where n ¼ 0; 1; 2; . . . ; N 1, with an array size of N > 1. Each channel (user) data is represented by yn , where yn 2 f0; 1g. The mapper maps the parallel input channels data to the different unique symbols. The serially converted input data array is split in to two clusters (subsets) YS , where each cluster address is denoted by a subscript index S where S ¼ f1; 2g. The code length ð‘S Þ per cluster YS in principle is dependent upon the number of input channels and is equal to For odd number of channels

zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ N 1 N þ1 bits ‘2 ¼ bits ‘1 ¼ 2 2

For even number of channels

zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{ N bits ‘1 ; ‘2 ¼ 2

:

(1)

A mapper and waveform modulator unit performs bijective-mapping operation to map the input multiplexed cluster YS to a distinct MMT symbol. MMT mapper and waveform generator is


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composed of a subdivided dual slot amplitude modulator. The MMT symbol is composed of a waveform that belongs to a set of signal waveform alphabet XK ¼ fX0 ðt Þ; X1 ðt Þ . . . :; XK 1 ðt Þg where K is the size of the MMT signaling set. Note that the waveform symbol pattern is divided in to two slots S ¼ 1; 2 in which amplitude modulated waveform per slot represented by xk ;1 ðt Þ and xk ;2 ðt Þ where subscript k , S denote the alphabet index and the slot index, respectively. At an instant t , the MMT mapper maps the input data cluster YS to an amplitude modulated waveform following a mapping table which can be expressed in terms of the expression (2) xk ;S ðAm;S ; tÞ ¼ Am;S ¼ MMap ðYS ÞjYS ¼ ½y0 ; y1 ; . . . ; yN1 where xk ;S ðAm;S ; t Þ denotes the amplitude modulated waveform corresponding to slot S. YS is the data cluster mapped to an amplitude level Am;S . The mapper modulator unit generates two consecutive slot waveforms XK ¼ ½xk ;1 ðti Þ; xk ;2 ðtiþ1 Þ. The mapper waveform generator unit can be expressed mathematically as ( ) T S:T t 2sym Am;S WTsym t ðS1Þ ; for ðS 1Þ sym 2 2 xk ;S ðAm;S ; t Þ ¼ (3) 0; otherwise where each k represents an MMT symbol from a total of XK 1 ðt Þ symbols, WTsym is the waveform corresponding to MMT symbol duration Tsym , and S is the slot index where S ¼ f1; 2g. The waveform dependent variables are amplitude and time; the amplitude is based upon the mapping rule in (2), while the time interval depends upon the slot number (S ¼ 1 or S ¼ 2, which corresponds to the slot index). The number of MMT symbol waveform alphabet ðK Þ is equivalent to the number of different possible input channels combinations K ¼ 2N . The MMT method to convey information is not only based on dividing the symbol duration in to two sub interval slots, but also dependent on a varied number of levels per slot. The number of levels per slot ðMS Þ is related to the code length ‘S per cluster YS for the multiplexed channels by MS ¼ 2‘S

(4)

i.e., MS ¼ f21 ; 22 ; . . . . . . ; 2‘S g. The MMT signaling symbol set K is equivalent to the product of the number of levels for the two slots K ¼ M1 :M2

(5)

where M1 , M2 denote number of levels for slot 1 and slot 2, respectively. The number of multiplexed bits N is also related to the code length ‘S per cluster by N¼

S X i¼1

log2 ðMi Þ ¼

S X

ð‘i Þ:

(6)

i¼1

Fig. 1(b) depicts the MMT symbol format that employs a varied number of slot amplitude levels ðAm;S Þ (dependent on the cluster code length ‘S ), and two slots ðSÞ, for “N” number of users. The time duration of each slot interval ðTslot Þ is given by Tslot ¼ Tsym =2, where Tsym , is the MMT symbol duration (1/bitrate). The MMT receiver structure is shown in Fig. 2(a). MMT receiver employs a low complexity decision circuit and data recovery algorithm. At the receiver side, the received signal is fed into sampling and decision circuit. The samples are taken at two sampling points SPS (one sampling point per slot S). The outputs of the sampling circuit are fed into a decision and de-mapping unit. In this unit, the sampled values are compared against a number of threshold values i;S ¼ i;S ; iþ1;S ; . . . ; MS 1;S (7)


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Fig. 2. (a) MMT De-Mapping receiver structure. (b) Four-channel MMT eye diagram.

where MS corresponds to the number of levels for a slot S. Fig. 2(b) shows the calculated eye diagram structure for a 4-channel MMT system composed of multiple fragmented eye diagrams. Sampling circuit outputs are driven to decision and regeneration unit for the data recovery. The de-mapping operation is based upon two layer multistage decoding operation to map the received slot waveforms x^ k ;1 ðAm;1 Þ; x^ k ;2 ðAm;2 Þ to a distinct two stage mapping point, which can be expressed as ^ 2 ¼ MDeMap x^ k ;1 ðAm;1 Þ; x^ k ;2 ðAm;2 Þ : ^ 1 Y ½Y (8)

3. Signal Space Model Since MMT signals are dependent upon two orthogonal time slots, the signal calculations can be interpreted from the vector space component by the construction of orthogonal basis functions. Signals can be represented by defining a set of orthonormal basis function j ðt Þ for j ¼ 1; 2; . . . ; R where R is equivalent to the number of signal dimensions or slots ðSÞ as in [11], [12] and [6] which satisfy R K . Therefore each of the signals can be expressed as Xk ðt Þ ¼

S X

xk ;j j ðt Þ

(9)

j¼1

where k ¼ 0; . . . ; K 1, and xk ¼ xk ;1 ; xk ;2 ; . . . ; xk ;R is the vector component representation of xk ðt Þ with respect to the defined basis functions. The basis function per slot is represented by sffiffiffiffiffiffiffiffiffiffi

Tsym S:Tsym 2 S1 t (10) S ðt Þ ¼ rect t for ðS 1Þ Tsym 2 2 2 where rect ðt Þ ¼

1; if 0 t G1 0; otherwise.

Each of the time slots is non-overlapping in the time domain. The MMT symbol can be translated to the weighed sum of two orthogonal basis functions corresponding to two consecutive one-dimensional signal constellations. The signal xk ;S ðt Þ is defined with respect to the basis function as rffiffiffiffiffiffiffiffiffiffi Tsym S ðt Þ (11) xk ;S ðt Þ ¼ Am;S 2 while the whole MMT signal (3) can be represented based on the basis functions as rffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffi S X Tsym Tsym Tsym S ðt Þ ¼ Am;1 1 ðtÞ þ Am;2 2 ðt Þ Xk ðt Þ ¼ Am;S 2 2 2 S¼1


(12)

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Fig. 3. Signal space constellation geometry 2, 3, and 4-channel MMT and 4, 8, and 16-PAM for IM/DD.

and each xk ;S ðt Þ is defined to guarantee the non-negativity constraint as min xk ;S ðt Þ 0: t

(13)

By employing vector representation, the Euclidean distance between any pair of signal vectors qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d ¼ kxi xj k2 . This can be translated to compute the Euclidean distance between the two MMT signals slots as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i Tsym h (14) ðxi;1 xj;1 Þ2 þ ðxi;2 xj;2 Þ2 dMMT ¼ kxk ;1 xk ;2 k2 ¼ 2 where i; j ¼ 0; 1; 2; . . . ; MS , and each MMT signal is represented in vectors in terms of each constellation dimension as Xk ¼ ðxk ;1 ; xk ;2 Þ. For IM/DD systems, the constellation diagram for N-channel MMT symbols structure is shown in Fig. 3 compared to its counterpart of M-PAM.

4. Power Performance Metrics In order to assess the performance of MMT power efficiency, the average electrical power and average optical power expressions are developed. These metrics will be the framework for assessing N-channel MMT compared with other IM/DD transmission formats. The average electrical and optical power are derived based upon the basis functions and the constellation geometry in the electrical and optical domain following [11].

4.1. Electrical Domain The first evaluation metric is the average electrical power, which is defined as Pelect

1 ¼ lim T !1 2T

ZT Xk2 ðtÞ dt T

which can be simplified to Pelect ¼

Eavg;e Ts

(15)

where Ts is the total signal duration, and Eavg;e is the average electrical energy per signal constellation in the electrical domain and is equivalent to Eavg;e ¼


K 1X kXk k2 : K k ¼1

(16)

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For MMT, the energy in signal Xk ;S ðt Þ can be expressed by Ee ¼ kXk k2 ¼ kxk2;S k þ kxk2;S k ¼

Tsym 2 Am;1 þ A2m;2 2

(17)

and the average electrical energy for xk ;S per slot S can be expressed by Eavg;eS ¼

MS 1 Tsym X Tsym ðMS 1Þð2MS 1Þ A2i;S ¼ 4MS i¼0 24

(18)

where MS , ðMS ¼ f21 ; 22 ; . . . . . . ; 2‘S gÞ represents the number of levels per slot. While the total average electrical energy per MMT symbol will be Eavg;e ¼ ¼

1 1 MX 2 1 Tsym MX A2i;1 þ A2j;2 2M1 M2 i¼0 j¼0 Tsym ½ðM1 1Þð2M1 1Þ þ ðM2 1Þð2M2 1Þ 12

(19)

for an equivalent number of levels per slot where ðM1 ¼ M2 ¼ M Þ, Eavg;e is Eavg;e ¼

Tsym ðM 1Þð2M 1Þ: 6

(20)

4.2. Optical Domain The second evaluation metric is the average optical power which is defined as Pavg;o ¼ RT T xk ðt Þdt , where v is the electro-optic conversion factor in watts/Ampere, and

lim ðv =2T Þ

T !1

Pavg;o can be simplified to Eavg;o Pavg;o ¼ pffiffiffiffiffi Ts

(21)

where Eavg;o is the average optical energy per signal constellation in the optical domain and v ¼ 1 has been assumed where the average optical energy per signal can be simplified to Eo ¼

K 1X kxk k: K k ¼1

(22)

In a similar manner as the energy electrical domain, the average optical energy per slot S for xk ;S can be expressed by Eavg;oS

pffiffiffiffiffiffiffiffiffiffi MS 1 Tsym X ¼ pffiffiffi Ai;S 2 2MS i¼0

(23)

while the total average optical energy per MMT symbol will be Eavg;o

pffiffiffiffiffiffiffiffiffiffi M1 1 M2 1 pffiffiffiffiffiffiffiffiffiffi X X Tsym Tsym ¼ pffiffiffi ðAi;1 þ Aj;2 Þ ¼ pffiffiffi ½ðM1 1Þ þ ðM2 1Þ: 2M1 M2 i¼0 j¼0 2 2

(24)

This parameter includes the DC bias which satisfies the non-negativity constraint and discussed in [6], [7] and [11]. Note that the peak average power is not considered in the analysis here since this paper considers comparison between N-Channel MMT and M-PAM to be applied for short range fiber optical transmission.


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5. Performance Analysis 5.1. Bit Error Rate The development of an explicit BER expression for the N-channel MMT transmission formats in terms of the receiver optical power is essential [12]. The generic SER can be expressed as SER ¼

M 1 X

Pm Py jx

(25)

x ¼0

where Pm is the priori probability of the transmission of symbols, Py jx is the probability of receiving a symbol y given that symbol x is transmitted and can be expressed as Py jx ¼

1 X 1M erfc 2 j¼0

jIth;j Ii j pffiffiffi 2i

(26)

where M denotes number of levels, Ii is the current associated with the optical electric field transmission on the PIN photodiode at symbol i, Ith;j is the threshold current, and i is the root mean square of the noise variance current for a symbol i. The BER formula is dependent upon the type of mapping the binary bit cluster to the symbols, where Gray mapping has an expected slightly improved performance compared with natural mapping. This is because of less number of bit transitions per symbol. The mapping type is influenced by the average hamming distance, which correspond to a BER expression variation. Assuming the thermal noise as the dominant noise source, the BER for N-channel MMT can be expressed as

Iavg dH M1 1 M2 1 1 1 BERMMT ffi þ þ erfc (27) M1 M2 log2 ðM1 :M2 Þ M1 1 M2 1 where dH is the average hamming distance, is the RMS of the current noise, and Iavg is the average photodiode current and dependent upon the received optical power Popt by Iavg ¼ Rr Popt where Rr is the photodiode responsivity. The average hamming distance for N-channel MMT can be estimated for N-channel MMT as dH ¼ 2

log2 ðM1 M2 Þ M1 M2 1

(28)

where for gray mapping, the average hamming distance dH is equal to 1. Assuming directly modulated laser, total current variance noise 2TT can be expressed as 2TT ¼ S þ T þ I ¼ 2qIavg f þ

4kB TFn f 2 þ Iavg NRIN f RL

(29)

where S is the shot noise, T is the thermal noise and I is the relative intensity noise, q is the electron charge, f is the receiver spectral width, kB is the Boltzmann constant, T is the temperature (in Kelvin), RL is the load resistance, Fn is the electrical amplifier noise figure, and NRIN is the relative intensity noise. For simplicity, the dark current has been neglected as its effect is much less than the detected photodiode current. At a fixed bitrate of 40 Gb/s and since each scheme has a different spectral efficiency (shown in Table 1) hence, each scheme needs a varied pre-set receiver spectral width f . The receivers spectral width were set as fOOK ¼ 40 GHz f2ch:MMT ¼ 40 GHz, f3ch:MMT ¼ 26:6 GHz, f4ch:MMT ¼ 20 GHz, f4PAM ¼ 20 GHz, f8PAM ¼ 13:3 GHz, f16PAM ¼ 10 GHz for OOK, 2-channel MMT, 3-channel MMT, 4-channel MMT, 4-PAM, 8-PAM, 16-PAM, respectively. Also, a set of values has been assumed where Fn ¼ 5 dB, T ¼ 298 K, RL ¼ 50 , NRIN ¼ 155 dB/Hz, and Rr ¼ 0:8 A/W.


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Fig. 4. (a) Total noise variance 2 in [A2] versus the received optical power at various spectral width. (b) Theoretical optical receiver sensitivities of N-channel MMT, M-PAM, and OOK transmission formats.

Fig. 4(a) shows the effect of varying the spectral width on the total noise variance for N-Channel MMT and M-PAM transmission format. An optimal equidistant MMT and M-PAM signals have been assumed as shown in the constellation diagram Fig. 3 in order to yield an optimized accurate theoretical result. At fixed Bitrate ¼ 40 Gb/s, Fig. 4(b) shows the calculated theoretical BER for OOK, N-Channel MMT and M-PAM formats. The M-PAM modulation formats have been analyzed following the M-PAM BER expression in [13]. At BER of 109 , OOK format has an optical sensitivity of 13.15 dBm, while the received optical powers are 11.6 dBm, 9.85 dBm, 9.3 dBm, 7.1 dBm, 8.3 dBm, and 4.3 dBm for 2-channel MMT, 4-PAM, 3-channel MMT, 8-PAM, 4-channel MMT and 16-PAM, respectively. Therefore the optical power penalty relative to OOK are, 1.55 dB, 3.3 dB, 3.85 dB, 6.05 dB, 4.85 dB, and 8.85 dB for 2-channel MMT, 4-PAM, 3-channel MMT, 8-PAM, 4-channel MMT and 16-PAM, respectively.

5.2. Power Efficiency For Intensity Modulated (IM) non-coherent transmission formats, the basic element for power penalty is directly related to the number of amplitude levels. Assuming stationary noise only with AWGN spectral density, at fixed bit rate, the M-PAM power penalty is equivalent to ðM 1Þ= pffiffiffiffiffiffiffiffiffiffiffiffiffi log2 M [14]. At fixed baud rate, the N-Channel MMT optical power penalty with respect to OOK can be represented by

Pavg;oMMT ðM1 1Þ þ ðM2 1Þ pffiffiffi Pp;MMT ¼ 10log ½dB (30) ¼ 10log Pavg;oOOK 2 where Pavg;oOOK is the average optical power for OOK signaling, while Pavg;oMMT is the average optical power for MMT symbol substituted from (24) in (21). By taking in consideration of the relative spectral width requirement of N-Channel MMT proportional to OOK as SWMMT ¼

number of slots ðSÞ SWOOK 2 ¼ SWOOK ½Hz number of MMT channels ðNÞ log2 ðM1 :M2 Þ

(31)

where SWOOK is the spectral width of OOK for IM/DD system.


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Fig. 5. (a) Average optical power penalty for M-PAM and N-channel MMT relative to OOK at a fixed bandwidth. (b) Average optical power penalty for M-PAM and N-channel MMT relative to OOK at a fixed bitrate.

At fixed bitrate, the N-Channel MMT optical power penalty with respect to OOK can be represented by

Ppb;MMT

"sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

# 2 ðM1 1Þ þ ðM2 1Þ pffiffiffi ¼ 10log ½dB log2 ðM1 :M2 Þ 2

(32)

with taking in consideration the relative proportionality of the noise power to the noise voltage. To measure the differences in power efficiency with respect to the information capacity, the asymptotic power penalty relative to OOK, is provided. At fixed bandwidth, Fig. 5(a) shows the asymptotic power penalty of N-Channel MMT and M-PAM modulation format relative to OOK to achieve an equivalent BER performance at asymptotically high SNR. For information capacity ¼ 2 bits/symbol, 2-channel MMT has a power gain of 3.27 dB over 4-PAM compared to OOK at a fixed baud rate. For information capacity ¼ 3 bits/symbol, 8-PAM need 3.94 dB more required optical power compared to 3-channel MMT, both with respect to OOK. For information capacity ¼ 4 bits/symbol, 16-PAM has an optical power penalty of 5.5 dB worse than 4-channel MMT at the same BER performance. In order to have a meaningful assessment figure, the N-Channel MMT is compared with M-PAM at a constant bit rate constraint. At fixed Bit rate, Fig. 5(b) depicts the asymptotic power penalty of N-Channel MMT and M-PAM modulation format proportional to OOK as in (32) to achieve a proportional BER performance at asymptotically high SNR. For information capacity ¼ 2 bits/symbol, 2-channel MMT has an incremental gain of 1.76 dB over 4-PAM relative to OOK at fixed aggregated data rate. For information capacity ¼ 3 bits/symbol, 3-channel MMT require 2.2 dB reduced optical power against 8-PAM at a BER figure 106 . For information capacity ¼ 4 bits/symbol, 4-channel MMT has an optical power gain of 4 dB more than 16-PAM, relative to OOK. It's worth noting that the asymptotic optical power penalty of the calculated data formats has an agreement with the theoretical results obtained in Fig. 4(b) at BER ¼ 109 since the results are compared in both cases relative to OOK. Also, the M-PAM penalties matches the verified experimentally results discussed in [15]. Table 1 summarizes the performance of MMT and PAM formats in terms of spectral efficiency, number of levels and receiver sensitivity for transmission of 2, 3 and 4 bits/symbol. Although the transmission of 4 bits/symbol using 16-PAM system has a spectral efficiency advantage over 4-channel MMT system, but it suffers from a significant power penalty due to the division of its eye diagram to 15 narrow eyes, which has not proven practical for implementation [4].


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Power Efficiency Evaluation of MMT and M-PAM TABLE 1

Overall Comparison Between N-Channel MMT and M-PAM

As illustrated in Table 1, 4-channel MMT with the spectral efficiency of 2 b/s/Hz can be considered as an effective and desirable practical compromise between power efficiency advantage and an appropriate spectral efficiency for 4 bits/symbol transmission systems.

5.3. Other Aspects Chromatic dispersion is the dominant source of dispersion in SMF. Since chromatic dispersion tolerance of a transmission format is dependent upon the signal spectral width, hence a higher dispersion tolerance can be expected for M-PAM over N-channel MMT. However, by an insightful analysis, 8-PAM and 16-PAM have a higher sensitivity toward ISI due to their increased power penalty as discussed before which affects their optical-signal-to-noise ratio (OSNR) requirement and not proven practical for implementation [4]. Hence, 4-PAM and 4-channel MMT can be comparable transmission formats where both have the same spectral width. At BER ¼ 109 and aggregated bitrate of 40 Gb/s a positive chromatic dispersion tolerance was reported þ137 ps/nm and þ96 ps/nm for 4-channel MMT and 4-PAM, respectively, [8], [9]. Also, nowadays there is a fast progression in the employment of integrated silicon photonics combining low cost optics and high-speed complementary metal-oxide-semiconductor (CMOS) processing modules. This has enabled the compensation of Inter Symbol Interference (ISI) impairments as a result of chromatic dispersion and polarization mode dispersion, achievable [16]. Referring to the MMT data recovery concept, one may argue that the complexity of MMT receiver is higher than M-PAM system. However, the complexity is due to additional sampling circuit, the solution of which is available in term of technology and experts [17], [18]. Work on technologies aspect for 40 Gb/s integrated circuit (IC) has now reached the stage where cost-effective commercial products are being developed. High speed digital processing modules are available with sampling rate reaching 65 GSamples/s employing 40 nm CMOS technology [19]. On the other hand, higher order M-PAM formats with an increased number of levels (e.g., 8-PAM and 16-PAM) are more susceptible to non-linearity due to the fragmentation consequences of main eyes to smaller eyes. Hence, this will result in the generation of a non-equally spaced intensity levels where a high resolution DAC is needed to produce linear signals with an acceptable extinction ratio [20].

6. Conclusion Higher order amplitude modulated formats such as 4, 8-PAM are of practical interest to expand the capacity for optical communication systems. In this paper, we proposed and discussed 2, 3, and 4-Channel MMT transmission system as power efficient alternatives to M-PAM systems, with possible future application in metro and short haul networks. MMT is a method of mapping parallel data channels for an increased data rate while maintain a lower baud rate system. The results show a clear advantage of the proposed MMT technique over PAM in terms of receiver sensitivities and power efficiency. The N-channel MMT data capacity advantage enhances the eligibility for scaling the baud rate with the limitations that exists in electronic and optical components operating at a fraction of the aggregated data rate.


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