The topic of detection, tracking and classification of weak targets in interferencedominated environment using radars is studied in this thesis. The problem is approached from the perspective of both resource-friendly radar systems and resourcelimited radar systems. In the case of resource-friendly radar systems, cognitive architectures that can progressively sense the environment and adjust its operating waveform-receiver filters are analyzed. The study of joint optimal transmit waveform and receive filters such that they operate optimally in the presence of weak targets and interference has been of huge interest in both academia and industry. Recent advances in adaptive waveform synthesis have focused on joint design and implementation of knowledge-aided receiver signal processing techniques and adaptive transmit signals. This closed loop radar framework that mimics mammals’ neurological capability to tune system parameters in response to cognition of the environment is commonly referred to as "cognitive radar" or "fully adaptive radar". In this thesis, the output signal to interference noise ratio maximizing jointly optimal transmit waveform and receive filter for a single-input, single-output radar design in the presence of extended target and colored interference is presented. The ambiguity function, processing gain and Cramer-Rao bound for such waveformfilters are derived. Apart from the optimal waveform dictated by the joint optimization strategy, it is desired that the radar transmit waveforms possess constant time envelope to drive the power amplifiers at saturation. This constraint requires reconstruction of constant envelope signals, which is addressed using proposed relaxed iterative error reduction algorithm. In general, iterative algorithms are sensitive to the initial seed, which is solved by deriving a closed-form solution making stationary phase assumption. In the case of multiple-input multiple-output (MIMO) radars, the interference between signals can significantly limit the radar’s ability for observation of weak targets in presence of stronger targets and background clutter. For the multi-channel radars, in this thesis orthogonally coded Linear Frequency Modulated (LFM) waveforms is proposed, wherein consecutive complex LFM signals in a frame are coded by orthogonal codes, namely Golay complementary, Zadoff Chu, direct spread spectrum, space-time block coded, discrete Fourier transform and Costasbased sequences. The orthogonal codes to modulate the LFM across symbol form fixed library waveforms leading to partial adaptation instead of arbitrary waveform dictated by "fully adaptive radar". The ambiguity function for such orthogonallycoded MIMO radar is derived, and the waveforms are analyzed in terms of their ambiguity function and imaging performance. With the advancement in silicon and packaging technology, radars have evolved from high-end aerospace technology into relatively low-cost Human-Machine Interface (HMI) sensors. However, the sensor in such industrial and consumer setting should have a small form-factor and low-cost, thus they cannot sustain cognitive architectures to detect and classify weak human targets. To improve detection and classification performance for HMI applications, novel processing and learning algorithms are proposed. In practice, there are several challenges to learningbased solutions using low-cost radars particularly with respect to open set classification. In open set classification, the system needs to handle variations of the input data, alien operating environment and unknown classes. Conventional deep learning approaches use a simple softmax layer and evaluate the accuracy on known classes, thus on closed set classification. The softmax layer provides separability of classes but does not provide discriminative class boundaries. Hence, many unknown classes are erroneously predicted as one of the known classes with a high confidence, resulting in poor performance in real world environments. Other challenges arise due to the inconspicuous interclass difference between features from one class and other closely-related class and large intra-class variations in the radar data from the same classes. To address these challenges, novel representation learning algorithms along with novel loss functions are proposed in this thesis. Unlike conventional deep learning approaches using softmax that learns to classify, deep representation learning learns the process to classify by projecting the input feature images to an embedded space where similar classes are grouped together while dissimilar classes are far apart. Thus, deep representation learning approaches simultaneously learn separable inter-class difference and compact discriminative intraclass, essential for open set classification. Specifically, the proposed representation learning algorithms are evaluated in the context of gesture sensing, material classification, air-writing and kick sensing HMI applications.