Sajid Ahmed

Unconstrained Synthesis of Covariance Matrix for MIMO Radar Transmit Beampattern

Multiple-input multiple-output (MIMO) radars have many advantages over their phased-array counterparts: improved spatial resolution; better parametric identifiably and greater flexibility to design the transmit beampattern. The design of the transmit beampatterns generally requires the waveforms to have arbitrary auto- and cross-correlation properties. The correlation/covariance matrix, R, of the waveforms must be positive semidefinite, therefore synthesis of a desired beampattern is usually a constrained optimization problem. In this paper, to simplify the constrained optimization problem, two algorithms are proposed to synthesize the waveform covariance matrix for the desired beampattern. In the first proposed algorithm the elements of a square-root matrix of the covariance matrix R are parameterized using the coordinates of a hypersphere that implicitly fulfil the constraints. This yields an iterative algorithm, whose convergence speed can be increased significantly by providing good initial values. In the second algorithm the constraints and redundant information in the covariance matrix R are exploited to find a closed-form solution. The drawback of the second algorithm is that it may yield a pseudocovariance matrix (pseudo-CM) that is not guaranteed to be positive semidefinite. However, the pseudo-CM can be easily converted into a covariance matrix using eigenvalue decomposition and/or shrinkage methods. Moreover, a pseudo-CM can also be used to provide good initial values for the first algorithm to enable faster convergence.

Finite Alphabet Constant-Envelope Waveform Design for MIMO Radar

The design of waveforms with specified auto- and cross-correlation properties has a number of applications in multiple-input multiple-output (MIMO) radar beampattern design. In this work, two algorithms are proposed to generate finite alphabet constant-envelope (CE) waveforms with required cross-correlation properties. The first-algorithm proposes a closed-form solution to find the finite alphabet CE waveforms to realize the given covariance matrix. Here, Gaussian random-variables (RVs) are mapped onto binary-phase shift keying (BPSK) and quadrature-phase shift keying (QPSK) symbols using nonlinear functions, and the cross-correlation relationship between the Gaussian RVs and BPSK/QPSK RVs is established. This cross-correlation relationship is exploited to convert the problem of finding the BPSK/QPSK waveforms to realize the covariance matrix, corresponding to the given beampattern, into finding the Gaussian RVs to realize another covariance matrix that can be easily found. In the second-algorithm, by exploiting the results of first-algorithm, a generalized algorithm to generate BPSK waveforms to approximate the given beampattern is proposed. Simulation results show that proposed finite alphabet CE waveforms outperform the existing algorithms to approximate the desired beampattern.

MIMO Radar Transmit Beampattern Design Without Synthesising the Covariance Matrix

Compared to phased-array, multiple-input multiple- output (MIMO) radars provide more degrees-of-freedom (DOF) that can be exploited for improved spatial resolution, better parametric identifiability, lower sidelobe levels at the transmitter/receiver, and design variety of transmit beampatterns. The design of the transmit beampattern generally requires the waveforms to have arbitrary auto- and cross-correlation properties. The generation of such waveforms is a two-step complicated process. In the first step, a waveform covariance matrix is synthesized, which is a constrained optimization problem. In the second step, to realize this covariance matrix actual waveforms are designed, which is also a constrained optimization problem. Our proposed scheme converts this two-step constrained optimization problem into a one-step unconstrained optimization problem. In the proposed scheme, in contrast to synthesizing the covariance matrix for the desired beampattern, nT-independent finite-alphabet constant-envelope waveforms are generated and preprocessed, with weight matrix W, before transmitting from the antennas. In this work, two weight matrices are proposed that can be easily optimized for the desired symmetric and nonsymmetric beampatterns and guarantee equal average power transmission from each antenna. Simulation results validate our claims.

Low-complexity iterative method of equalization for single carrier with cyclic prefix in doubly selective channels

Orthogonal frequency division multiplexing (OFDM) requires an expensive linear amplifier at the transmitter due to its high peak-to-average power ratio (PAPR). Single carrier with cyclic prefix (SC-CP) is a closely related transmission scheme that possesses most of the benefits of OFDM but does not have the PAPR problem. Although in a multipath environment, SC-CP is very robust to frequency-selective fading, it is sensitive to the time-selective fading characteristics of the wireless channel that disturbs the orthogonality of the channel matrix (CM) and increases the computational complexity of the receiver. In this paper, we propose a time-domain low-complexity iterative algorithm to compensate for the effects of time selectivity of the channel that exploits the sparsity present in the channel convolution matrix. Simulation results show the superior performance of the proposed algorithm over the standard linear minimum mean-square error (L-MMSE) equalizer for SC-CP.

Fourier-Based Transmit Beampattern Design Using MIMO Radar

In multiple-input multiple-output (MIMO) radar settings, it is often desirable to transmit power only to a given location or set of locations defined by a beampattern. Transmit waveform design is a topic that has received much attention recently, involving synthesis of both the signal covariance matrix, R, as well as the actual waveforms. Current methods involve a two-step process of designing R via iterative solutions and then using R to generate waveforms that fulfill practical constraints such as having a constant-envelope or drawing from a finite alphabet. In this paper, a closed-form method to design R for a uniform linear array is proposed that utilizes the discrete Fourier transform (DFT) coefficients and Toeplitz matrices. The resulting covariance matrix fulfills the practical constraints such as positive semidefiniteness and the uniform elemental power constraint and provides performance similar to that of iterative methods, which require a much greater computation time. Next, a transmit architecture is presented that exploits the orthogonality of frequencies at discrete DFT values to transmit a sum of orthogonal signals from each antenna. The resulting waveforms provide a lower mean-square error than current methods at a much lower computational cost, and a simulated detection scenario demonstrates the performance advantages achieved.

MIMO-Radar Waveform Covariance Matrix for High SINR and Low Side-Lobe Levels

Multiple-input multiple-output (MIMO) radar has better parametric identifiability but compared to phased-array radar, it shows loss in signal-to-noise ratio due to noncoherent processing. To exploit the benefits of both MIMO radar and phased array, a waveform covariance matrix is proposed. To generate the proposed covariance matrix, the values of the cosine function between 0 and π with a step size of π/nT are used to form a positive semi-definite Toeplitz matrix, where nT is the number of transmit antennas. The proposed covariance matrix yields gain in the signal-to-interference-plus-noise ratio (SINR) compared to MIMO radar and have lower sidelobe levels (SLLs) compared to phased-array, MIMO-radar, and the recently proposed phased-MIMO scheme. Moreover, in contrast to the phased-MIMO scheme, where each antenna transmits a different power, our proposed scheme allows same power transmission from each antenna. Simulation results validate our analytical results.

Parameter estimation and equalization techniques for communication channels with multipath and multiple frequency offsets

We consider estimation of frequency offset (FO) and equalization of a wireless communication channel, within a general framework which allows for different frequency offsets for various multipaths. Such a scenario may arise due to different Doppler shifts associated with various multipaths, or in situations where multiple basestations are used to transmit identical information. For this general framework, we propose an approximative maximum-likelihood estimator exploiting the correlation property of the transmitted pilot signal. We further show that the conventional minimum mean-square error equalizer is computationally cumbersome, as the effective channel-convolution matrix changes deterministically between symbols, due to the multiple FOs. Exploiting the structural property of these variations, we propose a computationally efficient recursive algorithm for the equalizer design. Simulation results show that the proposed estimator is statistically efficient, as the mean-square estimation error attains the Crame/spl acute/r-Rao lower bound. Further, we show via extensive simulations that our proposed scheme significantly outperforms equalizers not employing FO estimation.

Iterative Receivers for MIMO-OFDM and Their Convergence Behavior

In this paper, we investigate two reduced-complexity iterative soft interference cancellation minimum mean square error (SIC-MMSE) receivers for frequency-selective multiple-input-multiple-output (MIMO) channels. In the first receiver, the extrinsic information is exchanged between the SIC-MMSE equalizer and the channel decoding stages at each iteration. In the second receiver, the extrinsic information obtained from the SIC-MMSE equalizer is fed back to itself only up to a certain number of iterations and then passed to the channel decoder at the end of the last iteration only to reduce the computational complexity. Moreover, to better understand the convergence behavior of the proposed iterative receivers, we study the notion of extrinsic information transfer (EXIT) characteristics. Using simulations, we derive the extrinsic information trajectory on the EXIT chart at various bit-energy-to-noise-spectral-density ratio (Eb/No) ranges to predict the number of iterations required to converge and the turbo cliff region. The predicted behavior of the proposed receivers is then confirmed by the bit-error-rate (BER) performance curves.

Generation of Correlated Finite Alphabet Waveforms Using Gaussian Random Variables

Correlated waveforms have a number of applications in different fields, such as radar and communication. It is very easy to generate correlated waveforms using infinite alphabets, but for some of the applications, it is very challenging to use them in practice. Moreover, to generate infinite alphabet constant envelope correlated waveforms, the available research uses iterative algorithms, which are computationally very expensive. In this work, we propose simple novel methods to generate correlated waveforms using finite alphabet constant and non-constant-envelope symbols. To generate finite alphabet waveforms, the proposed method map the Gaussian random variables onto the phase-shift-keying, pulse-amplitude, and quadrature-amplitude modulation schemes. For such mapping, the probability-density-function of Gaussian random variables is divided into M regions, where M is the number of alphabets in the corresponding modulation scheme. By exploiting the mapping function, the relationship between the cross-correlation of Gaussian and finite alphabet symbols is derived. To generate equiprobable symbols, the area of each region is kept same. If the requirement is to have each symbol with its own unique probability, the proposed scheme allows us that as well. Although, the proposed scheme is general, the main focus of this paper is to generate finite alphabet waveforms for multiple-input multiple-output radar, where correlated waveforms are used to achieve desired beam patterns.

Low complexity iterative detection for OFDMA uplink with frequency offsets

In this work, we propose an iterative algorithm for the detection of transmitted symbols at the uplink of an orthogonal frequency-division multiple access (OFDMA) system. The algorithm allows distinct frequency-offsets (FO)s from each user that cause multiple-access and self interference. The proposed algorithm squeezes the interference of subcarrier k into 2D + 1 nearby subcarriers by preprocessing the received signal and yields a banded structure interference matrix. Here, the value of D depends on the FO and determines the squeezing depth. The proposed algorithm exploits this banded structure and realizes a low complexity iterative soft-interference-cancellation minimum mean-squared error (SIC-MMSE) equalizer that can be used in Turbo equalization. Simulation results show that the bit-error-rate (BER) performance of the proposed algorithm outperforms existing detection algorithms and is very much close to the zero-FO frequency-domain-equalization (zero-FO-FDE).