Previous works in array processing have proposed two types of snapshot models for the angle of arrival (AoA) estimation problem in multi-antenna systems. The deterministic model assumes that the source waveforms are non-random, while the random sensor noise is white Gaussian with a known covariance matrix. The stochastic model assumes that both the waveforms and the noise are zero-mean Gaussian. Interestingly, the performance of these two models have rarely been compared in integrated sensing and communication (ISAC) systems. Therefore, in this paper, we consider the uplink of a bistatic ISAC system that uses unitary constant envelope signaling and pilot-based channel estimation while transmitting a sensing signal simultaneously with the communication signals. The base station uses both the pilot and data signals to estimate the angle of a passive source and the transmitted data symbol by an active (connected) user equipment device. For this system, we derive the classical Cramér-Rao bound for unbiased estimators of the AoA and the transmitted symbol, along with the Bayesian Cramér-Rao bound, which bounds the error of all estimators. We also derive the ISAC-aware minimum mean squared error receiver for both the deterministic and stochastic models. We study the trade-off between sensing and communication under the deterministic and stochastic waveform assumptions. Specifically, we show that the fundamental trade-off between sensing and communication power allocations is expressed differently in the deterministic and stochastic models and argue that the results serve as basic considerations when designing pilot and sensing signals for ISAC systems.

In the uplink of multiuser multiple input multiple output (MU-MIMO) systems operating over aging channels, pilot spacing is crucial for acquiring channel state information and achieving high signal-to-interference-plus-noise ratio (SINR). Somewhat surprisingly, very few works examine the impact of pilot spacing on the correlation structure of subsequent channel estimates and the resulting quality of channel state information considering channel aging. In this paper, we consider a fast-fading environment characterized by its exponentially decaying autocorrelation function, and model pilot spacing as a sampling problem to capture the inherent trade-off between the quality of channel state information and the number of symbols available for information carrying data symbols. We first establish a quasi-closed form for the achievable deterministic equivalent SINR when the channel estimation algorithm utilizes multiple pilot signals. Next, we establish upper bounds on the achievable SINR and spectral efficiency, as a function of pilot spacing, which helps to find the optimum pilot spacing within a limited search space. Our key insight is that to maximize the achievable SINR and the spectral efficiency of MU-MIMO systems, proper pilot spacing must be applied to control the impact of the aging channel and to tune the trade-off between pilot and data symbols.

Minimizing the symbol error in the uplink of multi-user multiple input multiple output systems is important, because the symbol error affects the achieved signal-to-interference-plus-noise ratio (SINR) and thereby the spectral efficiency of the system. Despite the vast literature available on minimum mean squared error (MMSE) receivers, previously proposed receivers for block fading channels do not minimize the symbol error in time-varying Rayleigh fading channels. Specifically, we show that the true MMSE receiver structure does not only depend on the statistics of the CSI error, but also on the autocorrelation coefficient of the time-variant channel. It turns out that calculating the average SINR when using the proposed receiver is highly non-trivial. In this paper, we employ a random matrix theoretical approach, which allows us to derive a quasi-closed form for the average SINR, which allows to obtain analytical exact results that give valuable insights into how the SINR depends on the number of antennas, employed pilot and data power and the covariance of the time-varying channel. We benchmark the performance of the proposed receiver against recently proposed receivers and find that the proposed MMSE receiver achieves higher SINR than the previously proposed ones, and this benefit increases with increasing autoregressive coefficient.

In the above article[1], the title of the article appears incorrectly. The full title should read “On the Achievable SINR in MU-MIMO Systems Operating in Time-Varying Rayleigh Fading.”

The performance of the uplink of single and multiuser multiple input multiple output (MIMO) systems depends crucially on the receiver architecture and the quality of channel state information at the receiver. Therefore, several previous works have developed minimum mean squared error (MMSE) receivers and proposed balancing the resources spent on acquiring channel state information and transmitting the payload of data packets. Somewhat surprisingly, the most popular MIMO linear MMSE receivers do not exploit the correlation structure that is present in autoregressive Rayleigh fading environments. Therefore, in this article we first develop a new linear receiver that not only takes channel state information errors into account in minimizing the MSE of the received data symbols, but it also utilizes that the subsequent noisy channel coefficients are correlated. For this new linear MMSE receiver, we derive the achieved MSE as a function of the number of receive antennas and the pilot-to-data power ratio. Interestingly, we find that the pilot power that minimizes the MSE of the data symbols does not depend on the number of antennas and that the new linear MMSE receiver outperforms previously proposed MIMO receivers when the autocorrelation coefficient of the channel is high.