1.1.Wireless Channels 5 sults in Section 2 to the fundamental limits of wireless communication channels described by random matrices.Section 3.1 deals with direct- sequence code-division multiple-access(DS-CDMA),with and without fading (both frequency-flat and frequency-selective)and with single and multiple receive antennas.Section 3.2 deals with multi-carrier code- division multiple access(MC-CDMA),which is the time-frequency dual of the model considered in Section 3.1.Channels with multiple receive and transmit antennas are reviewed in Section 3.3 using models that incorporate nonideal effects such as antenna correlation,polarization, and line-of-sight components. 1.1 Wireless Channels The last decade has witnessed a renaissance in the information theory of wireless communication channels.Two prime reasons for the strong level of activity in this field can be identified.The first is the grow- ing importance of the efficient use of bandwidth and power in view of the ever-increasing demand for wireless services.The second is the fact that some of the main challenges in the study of the capacity of wireless channels have only been successfully tackled recently.Fading, wideband,multiuser and multi-antenna are some of the key features that characterize wireless channels of contemporary interest.Most of the information theoretic literature that studies the effect of those fea- tures on channel capacity deals with linear vector memoryless channels of the form y=Hx+n (1.1) where x is the K-dimensional input vector,y is the N-dimensional output vector,and the N-dimensional vector n models the additive circularly symmetric Gaussian noise.All these quantities are,in gen- eral,complex-valued.In addition to input constraints,and the degree of knowledge of the channel at receiver and transmitter,(1.1)is char- acterized by the distribution of the N x K random channel matrix H whose entries are also complex-valued. The nature of the K and N dimensions depends on the actual ap- plication.For example,in the single-user narrowband channel with nr1.1. Wireless Channels 5 sults in Section 2 to the fundamental limits of wireless communication channels described by random matrices. Section 3.1 deals with direct￾sequence code-division multiple-access (DS-CDMA), with and without fading (both frequency-flat and frequency-selective) and with single and multiple receive antennas. Section 3.2 deals with multi-carrier code￾division multiple access (MC-CDMA), which is the time-frequency dual of the model considered in Section 3.1. Channels with multiple receive and transmit antennas are reviewed in Section 3.3 using models that incorporate nonideal effects such as antenna correlation, polarization, and line-of-sight components. 1.1 Wireless Channels The last decade has witnessed a renaissance in the information theory of wireless communication channels. Two prime reasons for the strong level of activity in this field can be identified. The first is the grow￾ing importance of the efficient use of bandwidth and power in view of the ever-increasing demand for wireless services. The second is the fact that some of the main challenges in the study of the capacity of wireless channels have only been successfully tackled recently. Fading, wideband, multiuser and multi-antenna are some of the key features that characterize wireless channels of contemporary interest. Most of the information theoretic literature that studies the effect of those fea￾tures on channel capacity deals with linear vector memoryless channels of the form y = Hx + n (1.1) where x is the K-dimensional input vector, y is the N-dimensional output vector, and the N-dimensional vector n models the additive circularly symmetric Gaussian noise. All these quantities are, in gen￾eral, complex-valued. In addition to input constraints, and the degree of knowledge of the channel at receiver and transmitter, (1.1) is char￾acterized by the distribution of the N × K random channel matrix H whose entries are also complex-valued. The nature of the K and N dimensions depends on the actual ap￾plication. For example, in the single-user narrowband channel with nT