Patrik Bohlin

Training-Based MIMO Systems—Part I: Performance Comparison

In this paper, we make a performance comparison between two different training-based schemes for multiple-input multiple-output (MIMO) channel estimation. The two schemes are the conventional time-multiplexed pilot (CP) scheme and the more recently suggested superimposed pilot (SIP) scheme. Unlike previous comparisons found in the literature, which are mostly based on estimation error performances, the performance comparison in this paper is made by deriving and comparing the maximum data rate (or rather a tight lower bound on the maximum mutual information) achieved by each scheme. By using the maximum mutual information criterion, for each training scheme, we can optimally allocate the time and power spent on transmission of training and data sequences. Once the system parameters (time and power) are tuned to give optimal performance, we can compare their respective maximum data rate. The theory is applied to a blockwise flat-fading MIMO channel, and it is found that in certain scenarios (such as many receive antennas and/or short channel coherence times), it is beneficial to use the SIP. In other scenarios, the SIP scheme suffers from a higher estimation error, and its gain over the CP scheme is often lost.

Training-Based MIMO Systems: Part II— Improvements Using Detected Symbol Information

In this paper, the maximum achievable data rate performance is addressed for MIMO systems that employ transmission of known training sequences for channel estimation. In Part I of this paper, it was found that systems based on superimposed pilots (SIP) offer an increased performance over conventional time-multiplexed pilots for fast fading channels. In other cases, the performance gain is lost due the poor channel estimates that are attained when there is interfering data power present during the channel estimation process. By allowing channel reestimation using a decision-directed approach, this interfering data power can instead be utilized as additional training power, which significantly improves the quality of the channel estimates. As the channel estimates improve within the coherence interval, a higher coding rate can successfully be applied. These multiple coding rate schemes can also be applied to conventional time-multiplexed pilot schemes. However, our numerical examples show that a larger performance increase in maximum achievable data rate is attained if the decision-directed approach is applied to a SIP scheme.

Performance evaluation of MIMO communication systems based on superimposed pilots

In the recent past, a number of publications have suggested superimposed pilots (SIP) for channel estimation in MIMO systems. However, the performance gain achieved by SIP compared to conventional (time-multiplexed) training is still questionable. In this paper we introduce a framework for modeling a general SIP scheme, of which the conventional scheme is a special case. Utilizing this framework, we derive a lower bound on the channel capacity to compare the performance between the two systems. It is found that in certain scenarios (high SNR, many receive antennas and short coherence times), it is beneficial to also transmit data during the training mode (i.e., use SIP). The main conclusion though, is that for most cases where these kind of schemes would be realistic, i.e. for systems with coherence lengths of more than a few symbols, the general SIP-scheme reduces to the conventional scheme. Hence, rendering the same capacity.

Multipath characterization of antennas for MIMO systems in reverberation chamber including effects of coupling and efficiency

We describe how to measure the radiation efficiency, correlation, diversity gain and capacity of a six-monopole antenna array in a reverberation chamber in order to characterize it by these parameters for a MIMO system. We show how these measurements can be used to find the channel capacity when a particular antenna array is used in a MIMO system. We also explain how numerical modeling of the MIMO array in a commercial code can be used to find the channel capacity.

Optimized data aided training in MIMO systems

We evaluate the achievable capacity of training-based MIMO systems, when the channel is allowed to be re-estimated, e.g., a decision-directed system. A lower bound on the capacity is derived for the single user block fading MIMO model for systems based on superimposed pilots, which include conventional time-multiplexed pilot based systems as special cases. The system is optimized with respect to the proportion of time and power spent on training and data, respectively, and how the power should be allocated over the block. It is found that the capacity can be very close to the fundamental capacity of the non-coherent channel, especially when the channel coherence time is short, and that a significant gain compared to conventional receivers is achieved at the expense of a linear increase in complexity.

A capacity comparison between time-multiplexed and superimposed pilots

In pilot-based communication systems, a known pilot (training) sequence is transmitted and used for estimation of the unknown channel. Without any strong motivation, recent publications suggest superimposing the pilot to the data instead of time-multiplexing it. In this paper an information theoretic approach is used to compare the communication performances of systems that employ time-multiplexed or superimposed pilots (SIP) for estimation of a frequency-selective blockwise-fading channel. By maximizing a parameterized expression on the mutual information of a SIP-based scheme, we investigate whether SIP-based systems have any gain in performance compared to conventional time-multiplexed systems.

A blind and robust space-time receiver for a turbo coded system

We propose an adaptive joint space-time algorithm for decoding turbo coded signals arriving at an antenna array. This is done in a (semi)blind manner using a finite alphabet property of the coded signal and iteratively estimating the channel jointly with the turbo decoding. An advantage of the proposed method is that the symbols can be detected in a robust way, as no assumptions on the array geometry or propagation environment are made. Further, simulations show that in a single user scenario the performance-loss is negligible compared to a system utilizing perfect channel knowledge. The method is also shown to give significantly enhanced performance compared to a system where the channel estimation and decoding are done sequentially in both static as well as fading multiuser scenarios.

Time delay estimation for multipath CDMA-systems based on a fast minimization technique for subspace fitting

A low complexity algorithm for parameter estimation in a block fading multipath DS-CDMA system is presented. The main contribution is a novel technique for minimizing a subspace fitting criterion which is obtained as a large sample approximation of the maximum likelihood (ML) estimator. The minimization procedure is based on an approximation of the exact criterion function, allowing a direct analytic solution. For the acquisition phase, an initialization procedure similar to alternating projections is employed which exhibits remarkable global convergence properties. The efficacy of the proposed method is demonstrated by means of numerical simulations.

A comment on the bandwidth expansion of Data Dependent Superimposed Training

This paper clarifies the issue of bandwidth expansion of Data Dependent Superimposed Training (DDST) schemes. It has previously been claimed that DDST schemes have the benefits of both Time Division Multiplexed (TDM) training and Superimposed Training (ST) based schemes without any of their respective drawbacks. That is, that channel estimation can be done without interference from the super imposed data as in a TDM scheme, while at the same time transmit data in all timeslots and hence not have the bandwidth increase associated with TDM, where a number of time-slots are dedicated strictly to training. While the estimation accuracy claim is valid we show that the bandwidth expansion claim is not. It is instead shown that the bandwidth expansion of a DDST system is identical to that of a TDM based system.

CDMA-synchronization: multi-user performance at single-user complexity

In this paper we present a large sample decoupled maximum likelihood time-delay estimator for multi-user CDMA systems in the presence of unknown and arbitrarily colored noise. The high-dimensional optimization problem is decoupled into the corresponding single-user problems, with lower dimensionality, where the dimensions correspond to the number of paths for the user of interest. This means that multi-user performance is achieved at the cost of a single-user estimator. The asymptotic statistical performance of the estimator is derived and compared with the Cramer-Rao bound and the estimator is shown to be asymptotically statistically efficient. Numerical simulations are also included to corroborate the analysis.