Complementary Sets, Generalized Reed-Muller Codes, and Power Control for OFDM

The use of error-correcting codes for tight control of the peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency-division multiplexing (OFDM) transmission is considered in this correspondence. By generalizing a result by Paterson, it is shown that each q-phase (q is even) sequence of length 2^m lies in a complementary set of size 2^{k+1}, where k is a nonnegative integer that can be easily determined from the generalized Boolean function associated with the sequence. For small k this result provides a reasonably tight bound for the PMEPR of q-phase sequences of length 2^m. A new 2^h-ary generalization of the classical Reed-Muller code is then used together with the result on complementary sets to derive flexible OFDM coding schemes with low PMEPR. These codes include the codes developed by Davis and Jedwab as a special case. In certain situations the codes in the present correspondence are similar to Paterson's code constructions and often outperform them

Study of modulation techniques for multiple access satellite communications

Multiple access communication utilizing small ground stations for satellite communication modulation - multiplexing technique

A Direct and Generalized Construction of Polyphase Complementary Set with Low PMEPR and High Code-Rate for OFDM System

A major drawback of orthogonal frequency division multiplexing (OFDM) systems is their high peak-to-mean envelope power ratio (PMEPR). The PMEPR problem can be solved by adopting large codebooks consisting of complementary sequences with low PMEPR. In this paper, we present a new construction of polyphase complementary sets (CSs) using generalized Boolean functions (GBFs), which generalizes Schmidt's construction in 2007, Paterson's construction in 2000 and Golay complementary pairs (GCPs) given by Davis and Jedwab in 1999. Compared with Schmidt's approach, our proposed CSs lead to lower PMEPR with higher code-rate for sequences constructed from higher-order ($\geq 3$) GBFs. We obtain polyphase complementary sequences with maximum PMEPR of $2^{k+1}$ and $2^{k+2}-2M$ where $k,M$ are non-negative integers that can be easily derived from the GBF associated with the CS

Bit Loading and Peak Average Power Reduction Techniques for Adaptive Orthogonal Frequency Division Multiplexing Systems

In a frequency-selective channel a large number of resolvable multipaths are present which lead to the fading of the signal. Orthogonal frequency division multiplexing (OFDM) is well-known to be effective against multipath distortion. It is a multicarrier communication scheme, in which the bandwidth of the channel is divided into subcarriers and data symbols are modulated and transmitted on each subcarrier simultaneously. By inserting guard time that is longer than the delay spread of the channel, an OFDM system is able to mitigate intersymbol interference (ISI). Significant improvement in performance is achieved by adaptively loading the bits on the subcarriers based on the channel state information from the receiver. Imperfect channel state information (CSI) arises from noise at the receiver and also due to the time delay in providing the information to the transmitter for the next data transmission. This thesis presents an investigation into the different adaptive techniques for loading the data bits on the subcarriers. The choice of the loading technique is application specific. The spectral efficiency and the bit error rate (BER) performance of adaptive OFDM as well as the implementation complexity of the different loading algorithms is studied by varying any one of the parameters, data rate or BER or total transmit power subject to the constraints on the other two. A novel bit loading algorithm based on comparing the SNR with the threshold in order to minimize the BER is proposed and its performance for different data rates is plotted. Finally, this thesis presents a method for reducing the large peak to average power ratio (PAPR) problem with OFDM which arises when the sinusoidal signals of the subcarriers add constructively. The clipping and the probabilistic approaches were studied. The probabilistic technique shows comparatively better BER performance as well as reduced PAPR ratio but is more complex to implement

Peak-to-Mean Power Control in OFDM, Golay Complementary Sequences, and Reed–Muller Codes

We present a range of coding schemes for OFDM transmission using binary, quaternary, octary, and higher order modulation that give high code rates for moderate numbers of carriers. These schemes have tightly bounded peak-to-mean envelope power ratio (PMEPR) and simultaneously have good error correction capability. The key theoretical result is a previously unrecognized connection between Golay complementary sequences and second-order Reed–Muller codes over alphabets ℤ2h. We obtain additional flexibility in trading off code rate, PMEPR, and error correction capability by partitioning the second-order Reed–Muller code into cosets such that codewords with large values of PMEPR are isolated. For all the proposed schemes we show that encoding is straightforward and give an efficient decoding algorithm involving multiple fast Hadamard transforms. Since the coding schemes are all based on the same formal generator matrix we can deal adaptively with varying channel constraints and evolving system requirements

Advanced data communication techniques for sub-sea applications

This thesis details research carried out in the through-water data communication field. An overview of the phenomena that prohibit acoustic communication in long-range shallow-water channels is constructed. Background research found that robust communications has not been achieved using single receiver reception in this environment. This work investigates the modulation technique itself and aims to improve on existing schemes (that have been applied to this environment). This is achieved with innovative techniques, based on multiple-frequency-shift-keying (MFSK) and space-frequency-shift-keying (SFSK). A number of industrial specified restrictions are placed on this work, including bandwidth restriction. Novel ways of intrinsically transmitting synchronisation information are therefore implemented. The development of appropriate systems is covered with general and platform specific implementation strategies being covered. A single modulation scheme (the three-chip four-frequency-shift-keying, 3C4FSK, scheme) has been put forward for consideration in any future research. Practical lab-based tests and the mathematical analysis is detailed. Conclusions recommend further funding of long-range shallow sea-water trails of the 3C4FSK scheme and for the industrial scope of this work to allow investigation into multiple receiver systems that allow spatial processing of the signal as these schemes have been shown lately to have potential in long-range channels

Collaborative modulation multiple access for single hop and multihop networks

While the bandwidth available for wireless networks is limited, the world has seen an unprecedented growth in the number of mobile subscribers and an ever increasing demand for high data rates. Therefore efficient utilisation of bandwidth to maximise link spectral efficiency and number of users that can be served simultaneously are primary goals in the design of wireless systems. To achieve these goals, in this thesis, a new non-orthogonal uplink multiple access scheme which combines the functionalities of adaptive modulation and multiple access called collaborative modulation multiple access (CMMA) is proposed. CMMA enables multiple users to access the network simultaneously and share the same bandwidth even when only a single receive antenna is available and in the presence of high channel correlation. Instead of competing for resources, users in CMMA share resources collaboratively by employing unique modulation sets (UMS) that differ in phase, power, and/or mapping structure. These UMS are designed to insure that the received signal formed from the superposition of all users’ signals belongs to a composite QAM constellation (CC) with a rate equal to the sum rate of all users. The CC and its constituent UMSs are designed centrally at the BS to remove ambiguity, maximize the minimum Euclidian distance (dmin) of the CC and insure a minimum BER performance is maintained. Users collaboratively precode their transmitted signal by performing truncated channel inversion and phase rotation using channel state information (CSI ) obtained from a periodic common pilot to insure that their combined signal at the BS belongs to the CC known at the BS which in turn performs a simple joint maximum likelihood detection without the need for CSI. The coherent addition of users’ power enables CMMA to achieve high link spectral efficiency at any time without extra power or bandwidth but on the expense of graceful degradation in BER performance. To improve the BER performance of CMMA while preserving its precoding and detection structure and without the need for pilot-aided channel estimation, a new selective diversity combining scheme called SC-CMMA is proposed. SC-CMMA optimises the overall group performance providing fairness and diversity gain for various users with different transmit powers and channel conditions by selecting a single antenna out of a group of L available antennas that minimises the total transmit power required for precoding at any one time. A detailed study of capacity and BER performance of CMMA and SC-CMMA is carried out under different level of channel correlations which shows that both offer high capacity gain and resilience to channel correlation. SC-CMMA capacity even increase with high channel correlation between users’ channels. CMMA provides a practical solution for implementing the multiple access adder channel (MAAC) in fading environments hence a hybrid approach combining both collaborative coding and modulation referred to as H-CMMA is investigated. H-CMMA divides users into a number of subgroups where users within a subgroup are assigned the same modulation set and different multiple access codes. H-CMMA adjusts the dmin of the received CC by varying the number of subgroups which in turn varies the number of unique constellation points for the same number of users and average total power. Therefore H-CMMA can accommodate many users with different rates while flexibly managing the complexity, rate and BER performance depending on the SNR. Next a new scheme combining CMMA with opportunistic scheduling using only partial CSI at the receiver called CMMA-OS is proposed to combine both the power gain of CMMA and the multiuser diversity gain that arises from users’ channel independence. To avoid the complexity and excessive feedback associated with the dynamic update of the CC, the BS takes into account the independence of users’ channels in the design of the CC and its constituent UMSs but both remain unchanged thereafter. However UMS are no longer associated with users, instead channel gain’s probability density function is divided into regions with identical probability and each UMS is associated with a specific region. This will simplify scheduling as users can initially chose their UMS based on their CSI and the BS will only need to resolve any collision when the channels of two or more users are located at the same region. Finally a high rate cooperative communication scheme, called cooperative modulation (CM) is proposed for cooperative multiuser systems. CM combines the reliability of the cooperative diversity with the high spectral efficiency and multiple access capabilities of CMMA. CM maintains low feedback and high spectral efficiency by restricting relaying to a single route with the best overall channel. Two possible variations of CM are proposed depending on whether CSI available only at the users or just at the BS and the selected relay. The first is referred to Precode, Amplify, and Forward (PAF) while the second one is called Decode, Remap, and Forward (DMF). A new route selection algorithm for DMF based on maximising dmin of random CC is also proposed using a novel fast low-complexity multi-stage sphere based algorithm to calculate the dmin at the relay of random CC that is used for both relay selection and detection