This dissertation addresses physical layer security concerns, resiliency of the Orthogonal Frequency Division Multiplexing (OFDM) and the Multiple Input Multiple Output (MIMO) systems; the `de-facto' air-interface of most wireless broadband standards including LTE and WiMAX. The major contributions of this dissertation are: 1) developing jamming taxonomy, 2) proposing OFDM and MIMO equalization jamming attacks and countermeasures, 3) developing antijam (AJ) MIMO systems, and 4) designing null space projected overlapped-MIMO radar waveform for spectrum sharing between radar and communications system. First, we consider OFDM systems under various jamming attacks. Previous research is focused on jamming OFDM data transmissions. We focus on energy efficient attacks that can disrupt communication severely by exploiting the knowledge of target waveform. Specifically, these attacks seek to manipulate information used by the equalization algorithm to cause errors to a significant number of symbols, i.e., pilot tones jamming and nulling. Potential countermeasures are presented in an attempt to make OFDM waveform robust and resilient. The threats were mitigated by randomizing the location and value of pilot tones, causing the optimal attack to devolve into barrage jamming. We also address the security aspects of MIMO systems in this dissertation. All MIMO systems need a method to estimate and equalize channel, whether through channel reciprocity or sounding. Most OFDM-based MIMO systems use sounding via pilot tones. Like OFDM attacks, this research introduces MIMO channel sounding attack, which attempts to manipulate pilot tones to skew the channel state information (CSI) at the receiver. We describe methods of designing AJ MIMO system. The key insight is that many of the theoretical concepts learned from transmit beamforming and interference alignment (IA) in MIMO systems can be applied to the field of AJ and robust communications in the presence of jammers. We consider a realistic jamming scenario and provide a `receiver-only' and a transmitter `precoding' technique that allow a pair of two-antenna transceivers to communicate while being jammed by a malicious non-cooperative single-antenna adversary. Finally, we consider designing a collocated MIMO radar waveform, which employs a new MIMO architecture where antenna arrays are allowed to overlap. This overlapped-MIMO radar poses many advantages including superior beampattern and improvement in SNR gain. We combine this radar architecture with a projection-based algorithm that allows the radar waveform to project onto the null space of the interference channel of MIMO communications system, thus enabling the coexistence of radar and communications system. / Ph. D.