**4. MIMO radar systems applied to wireless communications based on GASP**

Multiple-input multiple-output (MIMO) wireless communication systems have received a great attention owing to the following viewpoints: a) MIMO wireless communication systems have been deemed as efficient spatial multiplexers and b) MIMO wireless communication systems have been deemed as a suitable strategy to ensure high-rate communications on wireless channels (Foschini, 1996). Space-time coding has been largely investigated as a viable means to achieve spatial diversity, and thus to contrast the effect of fading (Tarokh, et al., 1998 and Hochwald, et al., 2000). We apply GASP to the design and implementation of MIMO wireless communication systems used space-time coding technique. Theoretical principles of MIMO wireless communication systems were discussed and the potential advantages of MIMO wireless communication systems are thoroughly considered in (Fishler, et al., 2006).

MIMO architecture is able to provide independent diversity paths, thus yielding remarkable performance improvements over conventional wireless communication systems in the medium-high range of detection probability. As was shown in (Fishler, et al., 2006), the MIMO mode can be conceived as a means of bootstrapping to obtain greater coherent gain. Some practical issues concerning implementation (equipment specifications, dynamic range, phase noise, system stability, isolation and spurs) of MIMO wireless communication systems are discussed in (Skolnik, 2008).

MIMO wireless communication systems can be represented by *m* transmit antennas, spaced several wavelengths apart, and *n* receive antennas, not necessarily collocated, and possibly forwarding, through a wired link, the received echoes to a fusion center, whose task is to make the final decision about the signal in the input waveform. If the spacing between the transmit antennas is large enough and so is the spacing between the receive antennas, a rich scattering environment is generated, and each receive antenna processes *l* statistically independent copies of incoming signal. The concept of rich scattering environment is borrowed from communication theory, and models a situation where the MIMO architecture yields interchannel interference, eventually resulting into a number of independent random channels. Unlike a conventional wireless communication array system, which attempts to maximize the coherent processing, MIMO wireless communication system resorts to the fading diversity in order to improve the detection performance. Indeed, it is well known that, in conventional wireless communication array system, multiple access interference (MAI) of the order of 10 dB may arise. This effect leads to severe degradations of the detection performance, due to the high signal correlation at the array elements. This drawback might be partially circumvented under the use of MIMO wireless communication system, which exploits the channel diversity and fading. Otherwise, uncorrelated signals at the array elements are available. Based on mentioned above statements, it was shown in (Fishler, et al., 2006) that in the case of additive white Gaussian noise (AWGN), transmitting orthogonal waveforms result into increasingly constrained fluctuation of interference.

Our approach is based on implementation of GASP and employment of some key results from communication theory, and in particular, the well-known concept that, upon suitably space-time encoding the transmitted waveforms, a maximum diversity order given by *m n* can be achieved. Importing these results in a wireless communication system scenario poses a number of problems, which forms the object of the present study, and in particular: a) the issue of waveform design, which exploits the available knowledge as to space-time codes; b) the issue of designing a suitable detection structure based on GASP, also in the light of the fact that the disturbance can no longer be considered as AWGN, due to the presence of interferences; and c) at the performance assessment level, the issue of evaluating the maximum diversity order that can be achieved and the space-time coding ensuring it under different types of interferences. The first and third tasks are merged in the unified problem of determining the space-time coding achieving maximum diversity order in signal detection, for constrained BER, and for given interference covariance. As to the second task, the decision-making criterion exploiting by GASP is employed.

Unlike (Fishler, et al., 2006), no assumption is made on either the signal model or the disturbance covariance. Thus, a family of detection structures is derived, depending upon the number of transmitting and receiving antennas and the disturbance covariance. A side result, which paves the way to further investigations on the feasibility of fully adaptive MIMO wireless communication systems is that the decision statistic, under the null hypothesis of no signal, is an ancillary statistic, in the sense that it depends on the actual interference covariance matrix, but its probability density function (pdf) is functionally independent of such a matrix. Therefore, threshold setting is feasible with no prior knowledge as to the interference power spectrum. As to the detection performance, a general integral form of the probability of detection *PD* is provided, holding independent of the signal fluctuation model. The formula is not analytically manageable, nor does it appear to admit general approximate expressions, that allow us to give an insightful look in the wireless communication system behavior. We thus restrict our atention to the case of Rayleigh-distributed attenuation, and use discussed in (De Maio & Lops, 2007) an information-theoretic approach to code construction, which, surprisingly enough, leads to the same solution found through the optimization of the Chernoff bound.
