Mario Kiessling

Short-term and long-term diagonalization of correlated MIMO channels with adaptive modulation

Theoretical results on MIMO capacity maximization suggest the decoupling of the MIMO channel into independent subchannels with optimum water-filling on these subchannels. Those results inspire the development of real systems that diagonalize the MIMO channel and adaptively control the modulation on each of the resulting subchannels. We study the design of a fully adaptive transmitter, where transmit filtering and adaptive modulation is controlled by short-term as well as long-term channel state information (channel correlation), where the focus is on channels with correlated fading at transmitter and receiver array. To this end, we are motivating the use of long-term channel eigenmodes by capacity-independent considerations. Simulation results confirm the potential of fully adaptive transmit processing.

Mutual information of MIMO channels in correlated Rayleigh fading environments - a general solution

We present a novel approach on the calculation of the moment generating function of mutual information, of MIMO channels with correlated Rayleigh fading. For the first time, a concise mathematical formulation of the moment generating function is given in terms of a hypergeometric function of matrix arguments. In contrast to existing literature, our approach is not based on eigenvalue probability density functions but uses a direct integration technique. In principle, via the moment generating function it is possible to calculate exact, i.e. non-asymptotic moments, including e.g. ergodic capacity, for arbitrary array sizes and arbitrary correlation properties at receiver as well as transmitter, thus unifying and completing existing partial solutions for special propagation scenarios. Monte-Carlo simulations of ergodic capacity verify the accuracy of the analysis.

Analytical performance of MIMO zero-forcing receivers in correlated Rayleigh fading environments

Simulation results show that fading correlation between the antenna elements of a wireless system can seriously affect the symbol error rate of MIMO receivers, especially in case of linear processing. In order to gain a better understanding of the fading effects, we present an analytical framework to assess the performance of a system with zero-forcing receiver in a correlated Rayleigh fading scenario. Closed-form expressions are derived for the symbol error rate with arbitrary array sizes in case of transmit correlation only. In the presence of a fully correlated channel, we study the 2/spl times/2 case. High SNR asymptotics allow an insightful comparison of systems with transmit and receive correlation, respectively. Monte-Carlo simulations evidence the accuracy of the analysis.

A closed-form bound on correlated MIMO channel capacity

The exact calculation of the ergodic MIMO channel capacity with channel correlation is mathematically at least very challenging. Having no closed-form analytical expression available for the capacity is making it difficult to derive optimum stochastic water-filling schemes that are based on long-term channel state information (channel correlation) only. We therefore derive a closed-form tight upper bound on the ergodic capacity of correlated MIMO channels. The bound takes into account both the effects of correlation at the transmitter as well as the receiver. Furthermore, we give a recursive algorithm for its efficient calculation. Simulations demonstrate the tightness of the bound and show that a long-term water-filling scheme based on the new bound yields almost the same performance as a scheme with full short-term (instantaneous) channel state information.

Exact ergodic capacity of MIMO channels in correlated Rayleigh fading environments

Using recent results on the moment generating function of mutual information, we derive exact formulas for the calculation of ergodic capacity of a fully correlated MIMO channel with transmit as well as receive correlation in a flat Rayleigh fading environment. The analysis is non-asymptotic, i.e. it is applicable without constraints to systems with a small number of elements. It turns out that the ergodic capacity can be expressed in terms of a sum of determinants with elements that are a combination of polynomials, exponentials, and the exponential integral E/sub 1/ solely. Various Monte-Carlo simulations confirm the validity and accuracy of the analysis.

Performance analysis of MIMO maximum likelihood receivers with channel correlation, colored Gaussian noise, and linear prefiltering

We present an analytical performance evaluation of a Rayleigh fading MIMO link with matrix transmit prefiltering, channel correlation at transmitter and receiver, and spatially colored Gaussian noise for arbitrary two-dimensional signal constellations based on a tight union bound of the pairwise error probabilities. Asymptotic results for the high SNR region allow a simple characterization of the correlation effects and a quantification of the SNR penalty. It is shown that the diversity level of ML detection is unaffected by fading correlation and demonstrated that the effects of transmit and receive correlation may be assessed independently with the standard simplified channel model. Prefiltering algorithms based on long-term stable channel correlation characteristics are derived using the framework at hand. Simulations results illustrate the effectiveness of transmit prefilter designs based on the performance bound.

Statistical prefilter design for MIMO ZF and MMSE receivers based on majorization theory

Recently, the authors proposed statistical prefilters for MMSE and ZF receivers that minimize SER (Kiessling, M. et al., IEEE WCNC, 2003; IEEE VTC, 2003). We now give a general derivation of their structure based on majorization theory. For both receiver types, it is shown that the optimal prefilter essentially transmits on the strongest long-term eigenmodes of the channel with proper power allocation. Moreover, simple closed-form power allocation schemes are presented for Rayleigh and Ricean fading environments. Interestingly, while the statistical prefilters exhibit the same basic mathematical structure as their short-term counterparts, they require only statistical information of the correlation properties and the Ricean component of the channel. Monte-Carlo simulations show that the proposed filters can achieve a considerable performance gain. Specifically, it is demonstrated that they can completely counteract the SER degradation due to a Ricean channel component.

Analytical performance of MIMO MMSE receivers in correlated Rayleigh fading environments

Closed-form analytical symbol error rate expressions are derived for a MIMO link with linear matrix transmits prefilter and minimum mean squared error receiver in a Rayleigh fading environment. Specifically, using a well-known simplified MIMO channel model, where correlation between the transmit and receive antenna elements is modeled independently, we present exact expressions for vanishing fading correlation as well as the case of correlation between the transmit antenna elements with long-term eigenmode transmission for arbitrary array sizes. Furthermore, exact results are given for a 2/spl times/2 system with fading correlation at both transmitter and receiver. High SNR approximations allow a simple quantification of the influence of fading correlation. The accuracy of the analysis is demonstrated via Monte-Carlo simulations.

Multi-user MIMO-OFDM cell throughput under real-world propagation conditions

An innumerable number of papers has been published on MIMO (multiple input multiple output) systems. The original and most of the current work deals with a single link between a multi-element antenna (MEA) transmitter and a MEA receiver. However, link-level capacity gain does not necessarily translate into a similar system-level gain. Therefore, several researchers have investigated the performance of MIMO systems on cell or even system level, including intracell and/or intercell interference. While these multi-user MIMO investigations are very helpful, presented (simulation) results have been mostly limited to simple propagation scenarios (e.g., flat fading and/or i.i.d. Rayleigh fading). Here we present results for the uplink sum capacity of multiple MIMO users in a single cell (i.e., intercell interference is not explicitly accounted for) based on a channel model which accounts for partial MIMO correlations, large-scale fading effects, variable delay spread, non-vanishing Rician factor, and random user orientation. We concentrate on the cell capacity. However, estimation of the maximum uplink cell throughput for real-world AMC (adaptive modulation and coding) is similarly possible via the SNR gap approximation and power/bit loading. According to the simulation results, beamforming is the capacity-achieving strategy for a large number of users within the cell. This is consistent with theoretical results derived by other researchers. However, the simulated results here cover the entire range from optimum single-user performance (i.e., transmission on spatial eigenmodes plus water filling) to the capacity when the number of users greatly exceeds the number of base station antennas (i.e., with beamforming being the best strategy).

Statistical prefiltering for MMSE and ML receivers with correlated MIMO channels

The performance of wireless MIMO systems is known to suffer significantly from fading correlation between the antenna elements in a poor scattering environment if the transmitter is non-adaptive. However, acquiring accurate short-term channel state information to control TX adaptivity can be serious problem, in particular in FDD systems. Thus, we are proposing statistical linear transmit prefiltering schemes for MMSE and ML detection in the receiver that are solely based on long-term channel state information. It is demonstrated that long-term channel state information. It is demonstrated that long-term adaptive prefiltering can achieve a significant gain over non-adaptive (blind) transmission. Prefiltering for ML detection in a strongly correlated channel is shown to yield almost the same performance as the blind scheme in an uncorrelated channel. Moreover, exploiting long-term properties of the channel is especially appealing in terms of computational complexity and channel estimation, as the long-term channel estimation process can be carried out in a wide time window.