||Recently, adaptive resource allocation in fading channel attracts a lot of interest because it can improve the system performance. In particular, in systems with parallel channels, it is well known that the availability of CSI at the transmitter allows optimal allocation of bit and power to the component channels and hence increases the capacity significantly. In this thesis, we study the system design and capacity of channels with adaptive resource allocation schemes provided that the transmitter only contains partial CSI of the parallel channels. In the first part of this thesis, we make use of the Space-time Code (STC) and Singular Value Decomposition (SVD) to decompose the MIMO channels into parallel non-interfering channel environment. We assume that the receiver estimates the coarse CSI from the pilots in the forward link and then feedbacks the information to the transmitter. With this coarse CSI at the transmitter, we develop a sub-optimal bit and power allocation algorithm to adaptively allocate the resources amongst the SVD created channels of the MIMO channel to improve the system performance. In the second part of the thesis, we investigate a new adaptive resource allocation scheme to reduce the overhead information to be fed back to the transmitter in the parallel channels environment. We assume that the different power levels are assigned to a selected set of channels whereas the same power level is allocated to the compound channel formed by the rest of the channels. Under this constraint, we take the information theoretic point of view to tackle the problem and obtain the optimal bit and power allocation that achieves the channel capacity. As this algorithm is done at the receiver, only the data rates and the power levels of the set of selected channels, together with the average data rate and the power level of the remaining channels are required to be fed back to the transmitter. Hence, the total overhead is significantly reduced .