OFDM waveform design parameter for submarine radar

OF THE DISSERTATION Adaptive OFDM Radar for Target Detection and Tracking by Satyabrata Sen Doctor of Philosophy in Electrical Engineering Washington University in St. Louis, December 2010 Research Advisor: Dr. Arye Nehorai We develop algorithms to detect and track targets by employing a wideband orthogonal frequency division multiplexing (OFDM) radar signal. The frequency diversity of the OFDM signal improves the sensing performance since the scattering centers of a target resonate variably at different frequencies. In addition, being a wideband signal, OFDM improves the range resolution and provides spectral efficiency. We first design the spectrum of the OFDM signal to improve the radar’s wideband ambiguity function. Our designed waveform enhances the range resolution and motivates us to use adaptive OFDM waveform in specific problems, such as the detection and tracking of targets. We develop methods for detecting a moving target in the presence of multipath, which exist, for example, in urban environments. We exploit the multipath reflections by utilizing different Doppler shifts. We analytically evaluate the asymptotic performance of the detector and adaptively design the OFDM waveform, by maximizing the noncentrality-parameter expression, to further improve the detection performance. ii Next, we transform the detection problem into the task of a sparse-signal estimation by making use of the sparsity of multiple paths. We propose an efficient sparse-recovery algorithm by employing a collection of multiple small Dantzig selectors, and analytically compute the reconstruction performance in terms of the `1-constrained minimal singular value. We solve a constrained multi-objective optimization algorithm to design the OFDM waveform and infer that the resultant signal-energy distribution is in proportion to the distribution of the target energy across different subcarriers. Then, we develop tracking methods for both a single and multiple targets. We propose a tracking method for a low-grazing angle target by realistically modeling different physical and statistical effects, such as the meteorological conditions in the troposphere, curved surface of the earth, and roughness of the sea-surface. To further enhance the tracking performance, we integrate a maximum mutual information based waveform design technique into the tracker. To track multiple targets, we exploit the inherent sparsity on the delay-Doppler plane to develop an computationally efficient procedure. For computational efficiency, we use more prior information to dynamically partition a small portion of the delay-Doppler plane. We utilize the block-sparsity property to propose a block version of the CoSaMP algorithm in the tracking filter.

In orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced and the system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Unfortunately, the direct ZF method requires the inversion of an NxN ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. As for the direct MMSE method, in addition to an NxN matrix inverse, it requires an extra NxN matrix multiplication, making the required computational complexity higher compared to the direct ZF method. In this dissertation, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and to apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O(N^3) to O(Nlog_2 N) . Also, the required number of the iteration is typically one or two. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-noise-ratio (SINR). For the MMSE method, we first reformulate the MMSE solution in a way that the extra matrix multiplication can be avoided. Similar to the ZF method, we then exploit the structure of the ICI matrix and apply Newton's iteration to reduce the complexity of the matrix inversion. For a multiple-input-multiple-output (MIMO) OFDM system, the required complexity of the ZF and MMSE methods becomes more intractable. We then manage to extend the proposed ZF and MMSE methods for SISO-OFDM systems to MIMO-OFDM systems. It turns out that the computational complexity can be reduced even more significantly. Simulation results show that the performance of the proposed methods is almost as good as that of the direct ZF and MMSE methods, while the required computational complexity is reduced dramatically. Finally, we explore the application of the proposed methods in mobility-induced ICI mitigation for OFDM multiple access (OFDMA) systems, and in carrier frequency offset (CFO) induced ICI mitigation for OFDMA uplink systems. As that in OFDM systems, the proposed methods can reduce the required computational complexity, effectively.

We analyze the performance of a wideband orthogonal frequency division multiplexing (OFDM) signal in estimating the micro-Doppler frequency of a rotating target having multiple scattering centers. The use of a frequency-diverse OFDM signal enables us to independently analyze the micro-Doppler characteristics with respect to a set of orthogonal subcarrier frequencies. We characterize the accuracy of micro-Doppler frequency estimation by computing the Cramer-Rao bound (CRB) on the angular-velocity estimate of the target. Additionally, to improve the accuracy of the estimation procedure, we formulate and solve an optimization problem by minimizing the CRB on the angular-velocity estimate with respect to the OFDM spectral coefficients. We present several numerical examples to demonstrate the CRB variations with respect to the signal-to-noise ratios, number of temporal samples, and number of OFDM subcarriers. The improvement in estimation accuracy due to the adaptive waveform design is also analyzed numerically. A grid-based maximum likelihood estimation technique is applied to evaluate the corresponding mean-squared error performance.

Orthogonal waveform separation is an important process to realize high resolution radar imaging for multi-input and multi-output synthetic aperture radar (MIMOSAR). In this paper, orthogonal frequency division multiplexing (OFDM) waveforms are used to realize the received echoes separation in one snapshot. Then, we reconstruct MIMO-SAR signal for each carrier frequency in multiple snapshots, and high range resolution is achieved by synthesizing the linear frequency modulation signals of different carrier frequencies at the same phase center of virtual element. Furthermore, cross correlation of OFDM waveforms and the integrated sidelobe rate influenced by the interval factor of center carrier frequency are analyzed in the range profile. Simulations demonstrate the validity of bandwidth synthesis method.

In this paper, we present a novel 3B/4B coding scheme for the reduction of peak-to-average power ratio (PAPR) in the orthogonal frequency division multiplexing (OFDM) communication system. In the proposed technique, we apply the encoding in the time domain of the OFDM transmitter to redistribute the power distribution of each transmitting signal samples. PAPR of the OFDM signal at the CCDF (Complementary Cumulative Distribution Function) of 10-5 can be reduced to about 11, 15 and 17 dB for N = 16, 64, and 256 respectively by applying the proposed scheme. Our analysis also shows that the proposed method would have bounded PAPR as the number of OFDM subcarriers N approaches infinity. Moreover, the method has very low complexity and the complexity does not increase as the number of OFDM sub-carriers increases. The proposed scheme also has error correction capability to reduce bit error rate (BER) at the same time.

Orthogonal frequency division multiplexing (OFDM) systems work well if the subcarriers are orthogonal to each other. However, the orthogonality among subcarriers may not exist and result in inter-carrier interference (ICI) at the receiver. This may cause by residual carrier frequency offset, time variations due to Doppler shift or phase noise. Further developing the parallel cancellation (PC) scheme to mitigate the ICI of OFDM systems, we expand this OFDM symbol-based PC scheme into a space-frequency (SF) coded system. This new simple space- frequency parallel cancellation (SFPC) scheme is a technique that combines the SF and PC schemes together. Computer simulations indicate that OFDM systems using the SFPC scheme outperform the regular PC and SF systems in slow and fast frequency selective fading channels, specifically at a high signal-noise-ratio (SNR). Furthermore, the error floor of the SFPC-OFDM system is significantly lower than that of the PC and SF systems without increasing computational load. Additionally, the SFPC scheme is a simple multiple input and multiple output (MIMO) system.

We have proposed a physical wireless parameter conversion sensor network (PHY-C SN). In PHY-C SN, each sensor node converts its sensing information into subcarrier number of orthogonal frequency division multiplexing (OFDM) signals. Although information gathering in a short time can be realized by PHY-C SN, the accuracy of frequency mapping depends on the available number of subcarriers. In this paper, we propose an adaptive parameter setting method for PHY-C SN to realize efficient utilization of spectrum resource with high accurate information gathering. Simulation results show that the proposed method can gather sensing information effectively with utilizing the limited number of OFDM subcarriers.

Since decades, orthogonal frequency division multiplexing (OFDM) has been drawing its attention in the area of wireless and satellite communication systems such as IEEE 802.11 a/g/n, ADSL, WiMAX and DVB-T/SH. In these applications, OFDM has drawbacks of high Peak-to-Average Power Ratio (PAPR) and Inter carrier symbol interference (ISI). Recently, Carrier Interferometry OFDM (CI-OFDM) as an alternative to OFDM is being studied to minimize the aforesaid drawbacks. To the knowledge of authors, there is no Field Programmable Gate Array (FPGA) prototyping of CI-OFDM is addressed for real time wireless and satellite communication system. In this context, authors in this paper have proposed a new hardware efficient and flexible CO-ordinate Rotational Digital Computer (CORDIC) based CI-OFDM architecture. The novelty of this proposed architecture is its capability to change the number of orthogonal subcarriers and data symbols upto the maximum 32K, that shall be suitable for most of the standards of wireless and satellite communication system and prototyped using commercially available FPGA device XC3S500E-5FG320. The implementation and experimental results of this proposed scheme are highlighted and validated with the result from MATLAB simulation.

The problem of adaptive orthogonal frequency division multiplexing (OFDM) waveform design in the case of stochastic extended targets in the presence of strong and nonstationary interferences is an essential part of a cognitive radar system. In this article, a new approach is developed based on maximizing the mutual information between the random target impulse response and the received echoes with respect to the transmitted waveform. We use the advantage of OFDM signals and present an adaptive structure to match the complex weights of OFDM signal with the radar scene for making complete use of the transmission power. The interference reflections are utilized rather than eliminating them to design the weights of the transmitted OFDM signal. The optimization algorithm for designing transmitted signals is based on adaptive learning whose essential information is obtained by a feedback between receiver and transmitter. This feedback includes essential target and interference characteristics which extracted from the reflected echoes. Based on changes in interference features, the weights of the transmitted OFDM signal on each subcarrier are designed and transmitted in the next coherent processing interval. Experimental results reveal that the proposed approach achieves a higher rate of performance compared to nonadaptive waveform design approaches.

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This paper investigates space-frequency (SF) coding for non-coherent (NC) Multiple Input Multiple Output (MIMO)-Orthogonal Frequency Division Multiplexing (OFDM) fading links, where neither the transmitter nor the receiver knows the channel. Our strategy consists in distributing the convolutional encoded and interleaved bits over the different transmit antennas, OFDM tones and OFDM symbols. The combination of the convolutional coding and bit interleaving with the SF coding can exploit the maximum spatial/frequency diversity over frequency-selective channels. In order to reduce the decoding complexity, we divide the OFDM symbol into several groups and apply differential encoding and decoding between adjacent groups. The proposed NC SF matrix is designed as a combination of a differential Cayley code and a systematic NC SF code, which leads to a simple decoding rule over the multipath channel. We show through asymptotic Pairwise Error Probability (PEP) analysis and simulation results that our encoding strategy can provide full diversity gain and achieves better performance in terms of spectrum efficiency and symbol error rate than all three the systematic NC-SF coding, the Cayley differential SF coding and our proposed SF coding without convolutional encoding and bit interleaving.

Multi-Carrier Waveform (MCW) modeling and design are envisioned as one of the most important and challenging for the 6th generation (6G) communication networks. In oppose to Orthogonal Frequency Division Multiplexing (OFDM) waveforms, new and innovative design techniques for MCWs have been designed and proposed in recent literature because of their performance superiority. The typical OFDM waveforms have dominated the previous generation of communication systems and proven their potential in many real-time communication environments, but it may not be sufficient to meet the ambitious target of 6G communication systems. Hence, need for new solutions like flexible MCWs and relevant technological advancements in waveform design are needed. This paper proposes designing and evaluating a new MCW design to meet the 6G requirements for spectral efficiency, throughput, and overall system capacity. On the transmitter side, the MCW design proposed in this article employs power domain multiplexing, such as Non-Orthogonal Multiple Access (NOMA), and phase-rotations of the input signal to the Universal Filtered Multi-Carriers (UFMC) modulations, where the Base-Station (BS) assigns different power levels to each user while using the same frequency resources. MATLAB® simulations were performed to assess the proposed MCW performance. Detailed simulation data are employed for comparative performance analysis of the proposed MCW. The results have shown the superior performance of the proposed MCW approach compared to the conventional 5th generation (5G) NOMA-UFMC waveform.

Next generation wireless communication systems are considering orthogonal time frequency space (OTFS) waveform as an alternative to the existing orthogonal frequency division multiplexing (OFDM) waveform. It is more robust to high Doppler and high carrier frequencies. Multiple recent papers have evaluated OTFS at higher Doppler with long term evolution (LTE) system, to show its performance benefits over OFDM. In this paper, we provide the performance evaluation of OTFS waveform at mmWave frequencies using the third generation partnership project (3GPP) 5G new radio (NR) transmit-receive chain for different quadrature amplitude modulation (QAM) schemes. We compare the OTFS performance with that of OFDM, for 3GPP defined tapped delay line (TDL) and cluster delay line (CDL) channel models at multiple mobility conditions. We analyze the performance difference between OTFS and OFDM using both minimum mean-squared error (MMSE) and decision feedback equalizers (DFE) at the receiver, and show the need for DFE at higher modulation order, to compensate the inter symbol interference. We show that the OTFS has 10 dB gain in signal to noise ratio (SNR) over OFDM, for TDL-C channel with delay spread of 300 ns, at high speed train mobility of 500 kmph for 64-QAM, when evaluated with DFE. We further present the computational complexity of OTFS system, in comparison to OFDM.

Orthogonal frequency division multiplexing (OFDM) is widely used and works efficiently for the communication, but emerging applications requires OFDM to be flexible to meet sensing requirements. The time-frequency waveform design of OFDM for dual-functional radar-communications (DFRC) is critical to achieve the future communication and sensing requirements. Therefore, we propose a novel method to minimize Cramér-Rao bounds (CRBs) of the delay and Doppler estimation to improve radar performance of an OFDM DFRC system. Although some methods are proposed in the literature to improve the CRBs, these methods either require feedforward signaling or subcarrier reservation. However, it is possible to exploit the constellation extension of quadrature amplitude modulation (QAM) to achieve lower CRBs without these requirements. Therefore, the proposed method provides a transparent communication along with the CRB minimization for conventional OFDM systems. For the evaluation of the proposed method, CRB and symbol error rate (SER) are considered in the simulation results. Furthermore, the theoretical SER analysis of the proposed method is derived to understand the effects of CRB minimization on the communication performance.

Simulation and Comparison of Channel Estimation Based on Block-type Pilot Frequency in OFDM System