Good Code Sets from Complementary Pairs via Discrete Frequency Chips

It is shown that replacing the sinusoidal chip in Golay complementary code pairs by special classes of waveforms that satisfy two conditions, symmetry/anti-symmetry and quazi-orthogonality in the convolution sense, renders the complementary codes immune to frequency selective fading and also allows for concatenating them in time using one frequency band/channel. This results in a zero-sidelobe region around the mainlobe and an adjacent region of small cross-correlation sidelobes. The symmetry/anti-symmetry property results in the zero-sidelobe region on either side of the mainlobe, while quasi-orthogonality of the two chips keeps the adjacent region of cross-correlations small. Such codes are constructed using discrete frequency-coding waveforms (DFCW) based on linear frequency modulation (LFM) and piecewise LFM (PLFM) waveforms as chips for the complementary code pair, as they satisfy both the symmetry/anti-symmetry and quasi-orthogonality conditions. It is also shown that changing the slopes/chirp rates of the DFCW waveforms (based on LFM and PLFM waveforms) used as chips with the same complementary code pair results in good code sets with a zero-sidelobe region. It is also shown that a second good code set with a zero-sidelobe region could be constructed from the mates of the complementary code pair, while using the same DFCW waveforms as their chips. The cross-correlation between the two sets is shown to contain a zero-sidelobe region and an adjacent region of small cross-correlation sidelobes. Thus, the two sets are quasi-orthogonal and could be combined to form a good code set with twice the number of codes without affecting their cross-correlation properties. Or a better good code set with the same number codes could be constructed by choosing the best candidates form the two sets. Such code sets find utility in multiple input-multiple output (MIMO) radar applications

Target localization in passive and active systems : performance bonds

The main goal of this dissertation is to improve the understanding and to develop ways to predict the performance of localization techniques as a function of signal-to-noise ratio (SNR) and of system parameters. To this end, lower bounds on the maximum likelihood estimator (MLE) performance are studied. The Cramer-Rao lower bound (CRLB) for coherent passive localization of a near-field source is derived. It is shown through the Cramer-Rao bound that, the coherent localization systems can provide high accuracies in localization, to the order of carrier frequency of the observed signal. High accuracies come to a price of having a highly multimodal estimation metric which can lead to sidelobes competing with the mainlobe and engendering ambiguity in the selection of the correct peak. The effect of the sidelobes over the estimator performance at different SNR levels is analyzed and predicted with the use of Ziv-Zakai lower bound (ZZB). Through simulations it is shown that ZZB is tight to the MLEs performance over the whole SNR range. Moreover, the ZZB is a convenient tool to assess the coherent localization performance as a function of various system parameters. The ZZB was also used to derive a lower bound on the MSE of estimating the range and the range rate of a target in active systems. From the expression of the derived lower bound it was noted that, the ZZB is determined by SNR and by the ambiguity function (AF). Thus, the ZZB can serve as an alternative to the ambiguity function (AF) as a tool for radar design. Furthermore, the derivation is extended to the problem of estimating target’s location and velocity in a distributed multiple input multiple output (MIMO) radar system. The derived bound is determined by SNR, by the product between the number of transmitting antennas and the number of receiving antennas from the radar system, and by all the ambiguity functions and the cross-ambiguity functions corresponding to all pairs transmitter-target-receiver. Similar to the coherent localization, the ZZB can be applied to study the performance of the estimator as a function of different system parameters. Comparison between the ZZB and the MSE of the MLE obtained through simulations demonstrate that the bound is tight in all SNR regions

Multibeam radar based on linear frequency modulated waveform diversity

Multibeam radar (MBR) systems based on waveform diversity require a set of orthogonal waveforms in order to generate multiple channels in transmission and extract them efficiently at the receiver with digital signal processing. Linear frequency modulated (LFM) signals are extensively used in radar systems due to their pulse compression properties, Doppler tolerance, and ease of generation. Here, the authors investigate the level of isolation between MBR channels based on LFM chirps with rectangular and Gaussian amplitude envelopes. The orthogonal properties and the mathematical expressions of the isolation are derived as a function of the chirp design diversity, and specifically for diverse frequency slopes and frequency offsets. The analytical expressions are validated with a set of simulations as well as with experiments at C-band using a rotating target

Generalized DFT: extensions in communications

Discrete Fourier Transform (DFT) is a restricted version of Generalized DFT (GDFT) which offers a very limited number of sets to be used in a multicarrier communication system. In contrast, as an extension on Discrete Fourier Transform (DFT) from the linear phase to non-linear phase, the proposed GDFT provides many possible carrier sets of various lengths with comparable or better performance than DFT. The availability of the rich library of orthogonal constant amplitude transforms with good performance allows people to design adaptive systems where user code allocations are made dynamically to exploit the current channel conditions in order to deliver better performance. For MIMO Radar systems, the ideal case to detect a moving target is when all waveforms are orthogonal, which can provide an accurate estimation. But this is not practical in distributed MIMO radars, where sensors are at varying distances from a target. Orthogonal waveforms with low auto- and cross-correlations are of great interest for MIMO radar applications with distributed antennas. Finite length orthogonal codes are required in real-world applications where frequency selectivity and signal correlation features of the optimal subspace are compromised. In the first part of the dissertation, a method is addressed to design optimal waveforms which meets above requirements for various radar systems by designing the phase shaping function (PSF) of GDFT framework with non-linear phase. Multicarrier transmission such as orthogonal frequency-division multiplexing (OFDM) has seen a rise in popularity in wireless communication, as it offers a promising choice for high speed data rate transmission. Meanwhile, high peak-to-average power ratio (PAPR) is one of the well-known drawbacks of the OFDM system due to reduced power efficiency in non-linear modules. Such a situation leads to inefficient amplification and increases the cost of the system, or increases in interference and signal distortion. Therefore, PAPR reduction techniques play an essential role to improve power efficiency in the OFDM systems. There has been a variety of PAPR reduction methods emphasizing different aspects proposed in the literature. The trade-off for PAPR reduction in the existing methods is either increased average power and/or added computational complexity. A new PAPR reduction scheme is proposed that implements a pre-designed symbol alphabet modifier matrix (SAM) to jointly modify the amplitude and phase values of the original data symbol alphabets prior to the IFFT operation of an OFDM system at the transmitter. The method formulated with the GDFT offers a low-complexity framework in four proposed cases devised to be independent of original data symbols. Without degrading the bit error rate (BER) performance, it formulates PAPR reduction problem elegantly and outperforms partial transmit sequences (PTS), selected mapping technique (SLM) and Walsh Hadamard transform (WHT-OFDM) significantly for the communication scenarios considered in the dissertation

Applications of FM Noise Radar Waveforms: Spatial Modulation and Polarization Diversity

Two possible radar application spaces are explored through the exploitation of highdimensional nonrecurrent FM-noise waveforms. The first involving a simultaneous dual-polarized emission scheme that provides good separability with respect to co- and cross-polarized terms and the second mimicking the passive actuation of the human eye with a MIMO emission. A waveform optimization scheme denoted as pseudorandom optimized (PRO) FM has been shown to generate FM-noise radar waveforms that are amenable to high power transmitters. Each pulse is generated and optimized independently and possesses a non-repeating FM-noise modulation structure. Because of this the range sidelobes of each pulse are unique and thus are effectively suppressed given enough coherent integration. The PRO-FM waveform generation scheme is used to create two independent sets of FM-noise waveforms to be incorporated into a simultaneous dual-polarized emission; whereby two independent PRO-FM waveforms will be transmitted simultaneously from orthogonal polarization channels. This effectively creates a polarization diverse emission. The random nature of these waveforms also reduce cross-correlation effects that occur during simultaneous transmission on both channels. This formulation is evaluated using experimental open-air measurements to demonstrate the effectiveness of this high-dimensional emission. This research aims to build upon previous work that has demonstrated the ability to mimic fixational eye movements (FEM) employed by the human eye. To implement FEM on a radar system a MIMO capable digital array must be utilized in conjunction with spatial modulation beamforming. Successful imitation of FEM will require randomized fast-time beamsteering from a two-dimensional array. The inherent randomness associated with FEM will be paired with the PRO-FM waveforms to create an emission possessing randomness in the space and frequency domains, called the FEM radar (FEMR). Unlike traditional MIMO, FEMR emits a coherent and time varying beam. Simulations will show the inherent enhancement to spatial resolution in two-dimensional space (azimuth and elevation) relative to standard beamforming using only the matched filter to process returns

Binary-Phase vs. Frequency Modulated Radar Measured Performances for Automotive Applications

Radars have been widely deployed in cars in recent years, for advanced driving assistance systems. The most popular and studied modulated waveform for automotive radar is the frequencymodulated continuous wave (FMCW), due to FMCW radar technology’s ease of implementation and low power consumption. However, FMCW radars have several limitations, such as low interference resilience, range-Doppler coupling, limited maximum velocity with time-division multiplexing (TDM), and high-range sidelobes that reduce high-contrast resolution (HCR). These issues can be tackled by adopting other modulated waveforms. The most interesting modulated waveform for automotive radar, which has been the focus of research in recent years, is the phase-modulated continuous wave (PMCW): this modulated waveform has a better HCR, allows large maximum velocity, permits interference mitigation, thanks to codes orthogonality, and eases integration of communication and sensing. Despite the growing interest in PMCW technology, and while simulations have been extensively performed to analyze and compare its performance to FMCW, there are still only limited real-world measured data available for automotive applications. In this paper, the realization of a 1 Tx/1 Rx binary PMCW radar, assembled with connectorized modules and an FPGA, is presented. Its captured data were compared to the captured data of an off-the-shelf system-on-chip (SoC) FMCW radar. The radar processing firmware of both radars were fully developed and optimized for the tests. The measured performances in real-world conditions showed that PMCW radars manifest better behavior than FMCW radars, regarding the above-mentioned issues. Our analysis demonstrates that PMCW radars can be successfully adopted by future automotive radars

Multibeam radar system based on waveform diversity for RF seeker applications

Existing radiofrequency (RF) seekers use mechanically steerable antennas. In order to improve the robustness and performance of the missile seeker, current research is investigating the replacement of mechanical 2D antennas with active electronically controlled 3D antenna arrays capable of steering much faster and more accurately than existing solutions. 3D antenna arrays provide increased radar coverage, as a result of the conformal shape and flexible beam steering in all directions. Therefore, additional degrees of freedom can be exploited to develop a multifunctional seeker, a very sophisticated sensor that can perform multiple simultaneous tasks and meet spectral allocation requirements. This thesis presents a novel radar configuration, named multibeam radar (MBR), to generate multiple beams in transmission by means of waveform diversity. MBR systems based on waveform diversity require a set of orthogonal waveforms in order to generate multiple channels in transmission and extract them efficiently at the receiver with digital signal processing. The advantage is that MBR transmit differently designed waveforms in arbitrary directions so that waveforms can be selected to provide multiple radar functions and better manage the available resources. An analytical model of an MBR is derived to analyse the relationship between individual channels and their performance in terms of isolation and phase steering effects. Combinations of linear frequency modulated (LFM) waveforms are investigated and the analytical expressions of the isolation between adjacent channels are presented for rectangular and Gaussian amplitude modulated LFM signals with different bandwidths, slopes and frequency offsets. The theoretical results have been tested experimentally to corroborate the isolation properties of the proposed waveforms. In addition, the practical feasibility of the MBR concept has been proved with a radar test bed with two orthogonal channels simultaneously detecting a moving target