The family of Low Density Parity Check (LDPC) codes is a strong candidate to be used as Forward Error Correction (FEC) in future communication systems due to its strong error correction capability. Most LDPC decoders use the Message Passing algorithm for decoding, which is an iterative algorithm that passes messages between its variable nodes and check nodes. It is not until recently that computation power has become strong enough to make Message Passing on LDPC codes feasible. Although locally simple, the LDPC codes are usually large, which increases the required computation power. Earlier work on LDPC codes has been concentrated on the binary Galois Field, GF(2), but it has been shown that codes from higher order fields have better error correction capability. However, the most efficient LDPC decoder, the Belief Propagation Decoder, has a squared complexity increase when moving to higher order Galois Fields. Transmission over a channel with M-PSK signalling is a common technique to increase spectral efficiency. The information is transmitted as the phase angle of the signal. The focus in this Master’s Thesis is on simplifying the Message Passing decoding when having inputs from M-PSK signals transmitted over an AWGN channel. Symbols from higher order Galois Fields were mapped to M-PSK signals, since M-PSK is very bandwidth efficient and the information can be found in the angle of the signal. Several simplifications of the Belief Propagation has been developed and tested. The most promising is the Table Vector Decoder, which is a Message Passing Decoder that uses a table lookup technique for check node operations and vector summation as variable node operations. The table lookup is used to approximate the check node operation in a Belief Propagation decoder. Vector summation is used as an equivalent operation to the variable node operation. Monte Carlo simulations have shown that the Table Vector Decoder can achieve a performance close to the Belief Propagation. The capability of the Table Vector Decoder depends on the number of reconstruction points and the placement of them. The main advantage of the Table Vector Decoder is that its complexity is unaffected by the Galois Field used. Instead, there will be a memory space requirement which depends on the desired number of reconstruction points.

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: This thesis investigates orthogonal frequency division multiplexing (OFDM) as a viable modulation technique for an ultrasonic acoustic underwater modem. The underwater environment provides a challenging setting for acoustic communications. Long delay spreads due to multipath propagation, severe Doppler frequency shifts, frequency dependent absorption and very limited bandwidth are but some of the challenges to overcome. OFDM essentially provides the parallel transmission of symbols in the frequency domain by simultaneously modulating many closely spaced orthogonal subcarriers. The resulting long parallel symbol rate together with the cyclic extension of symbols render the signal robust against intersymbol interference (ISI) caused by multipath propagation. Intercarrier interference (ICI) between the overlapping frequency responses of subcarriers is mitigated by their property of orthogonality. Doppler spread contributes to the loss of orthogonality and can result in severe ICI. A method of measuring the Doppler shift by means of including a preamble and postamble symbol with each data frame is proposed. The detected frequency offset is corrected by resampling the frame at the desired sample rate. Not only do the ambles serve as a mechanism for timing and frequency synchronisation, but they are also applied in the channel estimation process. The equalisation of channel response is required for the coherent demodulation of the received symbols. An investigation into different phase shift keying (PSK) and quadrature amplitude modulation (QAM) constellations reveal optimal arrangements for minimal symbol errors. The optimised QAM constellations do not lend themselves to Gray-coding, so that an efficient interleaving scheme is needed to mitigate the non-uniform distribution of bit errors among symbol errors. Forward error correction is provided via a Bose Chaudhuri Hocquenghem (BCH) block code. Variable code rates, together with the ability to switch between different constellations, enable the modem to perform so-called variable modulation in an attempt to maximise the throughput under specific channel conditions. The modulation/demodulation scheme is wholly defined in software as to provide flexibility and facilitate experimentation with different signal processing methods. The accompanying hardware platform allows for the transmission of a pre-generated signal and the recording of a received signal for off-line processing. The prototype design serves as a proof of concept and thus provides only simplex communication. Field tests over limited distances demonstrate the successful operation of the prototype modem. We conclude that OFDM is indeed a suitable modulation technique for acoustic underwater communication. / AFRIKAANSE OPSOMMING: Hierdie tesis ondersoek die toepassing van ortogonale frekwensiedeling multipleksering (OFDM) as modulasie tegniek op ʼn onderwater kommunikasie modem. Die onderwater omgewing bied vele uitdagings vir akoestiese kommunikasie. Lang vertraging-verstrooiings as gevolg van multipad voortplanting, Doppler frekwensieskuif, frekwensieafhanklike absorpsie, en beperkte bandwydte is van die uitdagings wat oorkom moet word. In essensie bied OFDM die parallelle versending van ʼn aantal simbole deur die gelyktydige modulasie van verskeie nou-gespasieerde subdraers in die frekwensiegebied. Die gevolglike lang parallelle simboolperiodes, tesame met die sikliese uitbreiding van simbole, verleen immuniteit teen intersimbool steurnisse (ISI) wat ontstaan as gevolg van multipad voortplanting. Die ortogonaliteit van naburige draers in die frekwensiegebied beperk interdraer steuring (ICI) tussen hul oorvleuelende frekwensie weergawes. Doppler frekwensieskuif kan egter lei tot die verlies aan ortogonaliteit en bydra tot ernstige interdraer steurings. ʼn Metode wat gebruik maak van aanhef en slot simbole, ingesluit by elke raam, word voorgestel om die Dopplerskuif te meet. Die bepaalde frekwensieafset word gekorrigeer deur die monstertempo van die raam aan te pas na die verlangde tempo. Buiten die tyd- en frekwensie-sinkronisasie funksies van die aanhef en slot simbole, speel dit ook ʼn belangrike rol in die ontrekking van die frekwensie weergawe van die kanaal. Die effening van die kanaal se frekwensieweergawe is noodsaaklik vir die koherente demodulasie van die ontvangde simbole. ʼn Ondersoek na verskillende fase verskuif sleuteling (PSK) en kwadratuur amplitude modulasie (QAM) konstellasies het optimale rangskikkings opgelewer vir minimale simboolfoute. Hierdie optimale QAM konstellasies verleen hulself egter nie na Gray-kodering nie. ʼn Effektiewe invlegtegniek is nodig om die nie-uniforme verspreiding van bisfoute tussen simboolfoute te beperk. Fout korrigering funksionaliteit word gebied deur ʼn Bose Chaudhuri Hocquenghem (BCH) blokkode. Verstelbare koderingstempo’s en die vermoë om tussen verskillende konstellasies te skakel, stel die modem in staat om sogenaamde verstelbare modulasie te gebruik in ʼn poging om die data deurset te optimeer onder spesifieke kanaal kondisies. Die modulasie en demodulasie skema is volledig in sagteware gedefinieer. Dit verleen buigbaarheid en vergemaklik eksperimentering met verskeie seinverwerkingstegnieke. Die meegaande hardeware platvorm stel die modem in staat om vooraf opgewekte seine uit te saai en rou ontvangde siene op te neem vir na-tydse verwerking. Die prototipe ontwerp dien as ʼn konseptuele bewys en bied dus slegs simplekse kommunikasie. Die suksesvolle werking van die modem is gedemonstreer deur toetsing oor beperkte afstande. Hieruit word afgelei dat OFDM inderdaad geskik is vir akoestiese onderwater kommunikasie.

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The purpose of this semestral project is to explain the basic issues of simple digital modulations through the creation of simple digital modulations using direct digital synthesis. It begins with a short review of digital modulation theory and the theory about direct digital synthesis. All the technical documentation is attached, including schematics and boards of functional modulator.

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This thesis deals with optical synthesis of unmodulated and modulated microwave signals. Generation of microwave signals based on optical heterodyning is discussed in detail. The effect of phase noise of laser on heterodyned output has been studied for different phase noise profiles. Towards this, we propose a generic algorithm to numerically model the linewidth broadening of a laser due to phase noise. Generation of microwave signals is demonstrated practically by conducting an optical heterodyning experiment. Signals ranging in frequency from 12.5 MHz to 27 GHz have been generated. Limitations of optical heterodyning based approach in terms of phase noise performance and frequency stability are discussed and practically demonstrated. A hardware-efficient Optical Phase Locked Loop (OPLL) is proposed to overcome these issues. Phase noise tracking performance of the proposed OPLL has been experimentally demonstrated. Phase noise values as low as -105 dBc/Hz at 10 KHz offset have been achieved. Optical modulators, owing to their extremely low electro-optic response time, can support high frequency modulating signals. This makes them highly attractive in comparison to their microwave counterparts. In this thesis, we propose techniques to generate microwave signals modulated at very high bit rates by down-converting the corresponding modulated optical signals to microwave domain. Down-conversion required for this process is achieved by optical heterodyning. The proposed concept has been theoretically analyzed, simulated and experimentally validated. Amplitude Modulated and ASK modulated microwave signals have been generated as Proof-of-Concept. Limitations posed by OPLL in generation of angle modulated microwave signals by optical heterodyning have been brought out. Schemes overcoming these limitations have been proposed towards generation of BPSK and QPSK modulated microwave signals. Integrated Optics (IO) technology has been studied as a means of implementation of the proposed concepts. IO components like Sinusoidal bends, Y-branch splitters and Electro-Optic-Modulators (EOMs) have been designed towards optical synthesis of modulated microwave signals. Propagation of modulated optical signal through these IO components has also been studied. An all-optic scheme based on Optical Beam Forming is proposed for transmission of QPSK modulated signal. Limitation of phase-shifting based approach, in terms of beam-squint, has been brought out. True-Time-Delay based approach has been proposed for applications demanding wide instantaneous bandwidth to avoid beam-squint. Algorithms / numerical methods required for analyses and simulations associated with the above-mentioned tasks have been evolved. This study is envisaged to provide useful insight into the realization of high-speed, compact, light-weight data transmitting systems based on Integrated Optics for future onboard spacecraft applications. This work, we believe, is a step towards realization of an Integrated Optic System-on-Chip solution for specific microwave data transmission applications.

<p>The task of the project was to evaluate a differential phase shift keying demodulation technique by replacing a Mach-Zehnder interferometer receiver with an optical filter (Fiber Bragg Grating). Computer simulations were made with single optical transmission, multi channel systems and transmission with combined angle/intensity modulated optical signals. The simulations showed good results at both 10 and 40 Gbit/s. Laboratory experiments were made at 10 Gbit/s to verify the simulation results. It was found that the demodulation technique worked, but not with satisfactory experimental results. The work was performed at Eindhoven University of Technology, Holland, within the framework of the STOLAS project at the department of Electro-optical communication.</p>

The task of the project was to evaluate a differential phase shift keying demodulation technique by replacing a Mach-Zehnder interferometer receiver with an optical filter (Fiber Bragg Grating). Computer simulations were made with single optical transmission, multi channel systems and transmission with combined angle/intensity modulated optical signals. The simulations showed good results at both 10 and 40 Gbit/s. Laboratory experiments were made at 10 Gbit/s to verify the simulation results. It was found that the demodulation technique worked, but not with satisfactory experimental results. The work was performed at Eindhoven University of Technology, Holland, within the framework of the STOLAS project at the department of Electro-optical communication.

Direct-Sequence Code Division Multiple Access (DS-CDMA), over the last few years, has become a popular technique and finds a place in many modern communication systems. The performance of this technique is closely linked to the signature (or spreading) sequences employed in the system. In the past, there have been many successful attempts by research groups to construct families of signature sequences that offer the potential gains promised by theoretical bounds. In this thesis, we present constructions of families of signature sequences over the AM-PSK and QAM alphabet with low correlation. In this thesis, we construct a family of sequences over the 8-ary AM-PSK constella- tion, Family AOpt(16) that is asymptotically optimal with respect to the Welch bound on maximum magnitude of correlation for complex sequences. The maximum magnitude of correlation for this family, θmax, is upper bounded by √N , where N is the period of the sequences. The 8-ary AM-PSK constellation is a subset of the 16-QAM constellation. We also construct two families of sequences over 16-QAM, Family A16A, and Family A16,B , with the maximum magnitude of correlation upper bounded by √2√N . We construct a family, A(M 2), of sequences over the 2m+1-ary AM-PSK constellation of period N = 2r- 1 and family size (N + 1)/2m-1 . The 2m+1-ary AM-PSK constellation is a subset of the M 2-QAM constellation with M =2m . The maximum nontrivial normalized correlation parameter is bounded above by θmax < a √N where a ranges from 1.34 in the case of M 2 = 16 to √5 for large m. Apart from low correlation values, the family possesses several interesting and useful features. In Family A(M 2), users have the ability to transmit 2m bits of data per period of the spreading sequence. The sequences in Family A(M 2) are balanced; all points from the 2m+1-ary AM-PSK constellation occur approximately equally often in sequences of long period. The Euclidean distance between the signals assigned to a particular user in A(M 2), corresponding to different data symbols, is larger than the corresponding value for the case when 2m+1-PSK modulation and spreading is used. Perhaps most interestingly, Family A(M 2) permits users on the reverse link of a CDMA system to communicate asynchronously at varying data rates by switching between different QAM constellations. Family A(M 2) is compatible with QPSK sequence families S(p) in the sense that the maximum correlation magnitude is increased only slightly if one adds sequences from (p) S(p)\ S(0) to Family A(M 2). We also construct families of sequences over AM-PSK that tradeoff data rate per sequence period and θmax for a given family size. We have extended the construction of sequences over AM-PSK constellation to construct sequences over the M 2-QAM constellation for M =2m . The QAM sequence families, Families (AM 2), have size, data rate and minimum squared Euclidean distance same as the corresponding AM-PSK construction but have higher values of θmax. Also included in the thesis are constructions for large families of sequences over the M 2-QAM alphabet.

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