This work deals with the design of MT transmit, MR receive antenna MIMO (Multiple Input Multiple Output) communication system where the transmitter performs a linear operation on data. This linear precoding model includes systems which involve signal shaping for achieving higher data rates, uncoded MIMO Multicarrier and Single-Carrier systems and, the more recent, MIMO-OFDM (Orthogonal Frequency Division Multiplexing) systems employing full diversity Space-Frequency codes. The objective of this work is to design diversity centric and rate centric linear precoded MIMO systems whose performance is better than the existing designs. In particular, we consider MIMO-OFDM systems, Zero Padded MIMO systems and MIMO systems with limited rate feedback. Design of full diversity MIMO-OFDM systems of rate symbol per channel use (1 s/ pcu) : In literature, MIMO-OFDM systems exploiting full diversity at a rate of 1 s/ pcu are based on a few specific Space-Frequency (SF)/ Space-Time-Frequency (STF) codes. In this work, we devise a general parameterized framework for the design of MIMO-OFDM systems employing full diversity STF codes of rate 1 s/ pcu. This framework unifies all existing designs and provides tools for the design of new systems with interesting properties and superior performance. Apart from rate and diversity, the parameters of the framework are designed for a low complexity receiver. The parameters of the framework usually depend on the channel characteristics (number of multipath, Delay Profile (DP)). When channel characteristics are available at the transmitter, a procedure to optimize the performance of STF codes is provided. The resulting codes are termed as DP optimized codes. Designs obtained using the optimization are illustrated and their performance is shown to be better than the existing ones. To cater to the scenarios where channel characteristics are not available at the transmitter, a complete characterization of a class of full diversity DP Independent (DPI) STF codes is provided. These codes exploit full diversity on channels with a given number of multipath irrespective of their characteristics. Design of DP optimized STF codes and DPI codes from the same framework highlights the flexibility of the framework. Design of Zero Padded (ZP) MIMO systems : While the MIMO-OFDM transmitter needs to precode data for exploiting channel induced multipath diversity, ZP MIMO systems with ML receivers are shown to exploit multipath diversity without any precoding. However, the receiver complexity of such systems is enormous and hence a study ZP MIMO system with linear receivers is undertaken. Central to this study involves devising low complexity receivers and deriving the diversity gain of linear receivers. Reduced complexity receiver implementations are presented for two classes of precoding schemes. An upper bound on the diversity gain of linear receivers is evaluated for certain precoding schemes. For uncoded systems operating on a channel of length L, this bound is shown to be MRL_MT +1 for uncoded transmissions, i.e, such systems tend to exploit receiver and multipath diversities. On the other hand, MIMO-OFDM systems designed earlier have to trade diversity with receiver complexity. These observations motivate us to use ZP MIMO systems with linear receivers for channels with large delay spread when receiver complexity is at a premium. Design examples highlighting the attractiveness of ZP systems when employed on channels with large delay spread are also presented. Efficient design of MIMO systems with limited feedback : Literature presents a number of works that consider the design of MIMO systems with partial feedback. The works that consider feedback of complete CSI, however, do not provide for an efficient system design. In this work, we consider two schemes, Correlation matrix feedback and Channel information feedback that convey complete CSI to the transmitter. This CSI is perturbed due to various impairments. A perturbation analysis is carried out to study the variations in mutual information for each of the proposed schemes. For ergodic channels, this analysis is used to design a MIMO system with a limited rate feedback. Using a codebook based approach, vector quantizers are designed to minimize the loss in ergodic capacity for each of the proposed schemes. The efficiency of the design stems from the ability to obtain closed-form expression for centroids during the iterative vector quantizer design. The performance of designed vector quantizers compare favorably with the existing designs. The vector quantizer design for channel information feedback is robust in the sense that the same codebook can be used across all operating SNR. Use of vector quantizers for improving the outage performance is also presented.