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Multiple-input multiple-output (MIMO) antenna schemes
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2 Multiple-input multiple-output (MIMO) antenna schemesIn a typical propagation environment in the bands used for mobile systems there are of course many paths for the RF energy to pass along between the transmitter and receiver antenna elements. In a MIMO link there will therefore be many separate paths between the different pairings of antenna elements and Fig. 15 shows a diagram of some of these paths which may exist between the transmit and receive antenna element arrays. Figure 15 I  llustration of multipath transmission between transmit and receive antenna arrays
For adaptive beam forming techniques the signals to and from the antenna elements are adjusted in phase and amplitude to form a beam to select the best single path between the transmit array and the receive array, while minimizing the antenna gain in the direction of the unwanted interfering signals. With multiple antenna elements at both ends of the link it is also possible to transmit different data streams on some, or all, of the transmit elements and separate the different transmissions by several receivers which each maximize one signal while minimizing the others. This process can give significant capacity advantages over the simple beam forming approach for complex scattering environments and the bounds to the capacity achievable with this type of arrangement in typical mobile propagation environment are derived in [1]. The signal handling in these MIMO systems will generally be as shown in Fig. 16. The data streams may be coded independently, which makes for simpler decoding at the receiver [6], or the full potential of the method can be achieved by including all of the data streams in a two dimensional coding scheme [5]. The ultimate capacity is achieved when a feedback from the receiver is used to adjust the power split, coding and modulation at the transmitter. FIGURE 16 Schematic of MIMO transceiver functions
   
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Lower rate parallel data streams 
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Signal encode and split Signal estimation and decode 
 
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hese MIMO techniques are currently the subject of a great deal of research activity and the following sections are included as general guides to the gains that can be achieved, and the type of propagation environments where these techniques have the greatest potential to increase the
capacity of a network. They are not intended as definitive results and more detailed analyses are available in the references given. 3 Spectral efficiency of MIMO systems in isolated linksThe capacity in bits per second per Hertz of an [M,N] MIMO link is given by 
where B is the bandwidth, IN is the N by N identity matrix, r is the average signal-to-noise ratio (SNR), and H is an M by N matrix whose (m,n)th element is the complex amplitude between the m th transmitter and n th receiver. We have assumed perfect channel state information at the receiver (in other words, the entries of the matrix H are known exactly. In a rich scattering environment, the entries in H are independent and identically distributed complex Gaussian random variables. Under this condition and the additional condition that r is much larger than one, as the number of antennas gets large and M = N, the capacity approaches: 
On the other hand, using beam forming the array becomes more directive as M increases, resulting in a linear increase in SNR. Hence the capacity is given by 
where hn is the complex amplitude at the nth receiver. Hence in a sufficiently complex scattering environment the capacity is directly proportional to the number of antennas at each end of the link for the [N,N] MIMO system operating, but only proportional to the log of the number of antennas for phased array beam forming techniques. [See footnote for a grossly simplified explanation of the basis of this effect.]5
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