An Artificial Neural Network Based Learning Method for Mobile Robot Localization
Matthew Conforth, Yan Meng · InTech eBooks · 2008
tradeoff, an adaptive control of the number of transmit antennas and symbol constellations is proposed to improve the performance of spatial multiplexing in correlated fading channels.Moreover, theoretical analysis that shows a fundamental tradeoff between multiplexing gain and/or diversity gain including Vertical-Bell Laboratories Layered Space-Time (V-BLAST) and Space-Time Codes (STC) have been reported (Tse and Viswanath, 2005;Zheng and Tse, 2003).Capacity or ergodic capacity, which is the capacity averaged over fading channels, are often utilized to evaluate capacity gain.On the other hand, BER or average BER, which is the BER averaged over fading channels, relate to diversity gain.These gains have been analyzed by approximate expressions for these measures at the SNR extremes, or by directly evaluating them for a particular channel probability density function (pdf), e.g., i.i.d.complex-normal distribution (Chiani et al., 2003;Marzetta and Hochwald, 1999;Smith et al., 2003).However, since the full diversity order appears only at high SNR, having higher diversity order does not necessarily mean having better performance at a particular value of SNR.Moreover, diversity gain of Rayleigh channels does not necessarily imply the existence of diversity gain for other distributed channels.In this chapter, we study universal properties of the performance of MIMO system as in (Ohno and Teo, 2007), which is independent of channel probability density functions and hold at any SNR.We only consider the case where the performance measure is a convex or concave function of SNR.However, it is shown that important performance measures, including channel capacity and BER, are convex or concave.Thus, our results are significant.To get more insights into MIMO systems, we study capacity gain from a different point of view.A similar approach is adopted in (Ohno and Teo, 2007) to analyze the impact of antenna size of MIMO systems on BER performance with zero-forcing (ZF) equalization.Take channel capacity for example.Let us suppose that you can install an additional receive antenna in the N r × N t system to construct an (N r + 1) × N t system.Assume that the underlying channel environment is not time-varying (i.e., static).Then, can any other gain (besides power gain) be obtained by increasing the number of receive antennas?Without the values of channel coefficients or the associated channel pdf, no one can answer this question or evaluate the possible gain correctly.Now, we look at the problem from another perspective.For simplicity, we put N r = 2a n dN t = 2. From a 3 × 2 system, we can remove one receive antenna in three different ways to obtain three possible 2 × 2 systems.Then, we compare the performance of the original 3 × 2 system with the average performance of the three 2 × 2 systems.We show in this chapter that without the knowledge of channel coefficients and at any value of SNR, the capacity of the original 3 × 2 system is greater than the average capacity of the three 2 × 2 systems.More generally, our analysis reveals that increasing the number of receive antennas generates capacity gain even in static channels.From this, we can prove that the mean capacity with respect to channel pdf, which is mathematically equivalent to the so-called ergodic capacity for fading channels, increases as the number of receive antennas increases at any value of SNR.Our proof relies not on the channel pdf but on the concavity of the capacity function.This implies that the concavity is indispensable to obtain receive antenna diversity.Next, we consider removing a transmit antenna from an N r × N t system and compare the capacity of the N r × N t system with the average capacity of N r × (N t -1) systems.Clearly, removing one transmit antenna reduces the multiplexing gain.For comparison, we adopt the capacity per transmit antenna as a parameter.Then, we prove that reducing the number 116 MIMO Systems, Theory and Applications www.intechopen.