A multiplicity of autonomous terminals simultaneously transmits data streams to a compact array of antennas. The array uses imperfect channel-state information derived from transmitted pilots to extract the individual data streams. The power radiated by the terminals can be made inversely proportional to the square-root of the number of base station antennas with no reduction in performance. In contrast if perfect channel-state information were available the power could be made inversely proportional to the number of antennas. Lower capacity bounds for maximum-ratio combining (MRC), zero-forcing (ZF) and minimum mean-square error (MMSE) detection are derived. An MRC receiver normally performs worse than ZF and MMSE. However as power levels are reduced, the cross-talk introduced by the inferior maximum-ratio receiver eventually falls below the noise level and this simple receiver becomes a viable option. The tradeoff between the energy efficiency (as measured in bits/J) and spectral efficiency (as measured in bits/channel use/terminal) is quantified for a channel model that includes small-scale fading but not large-scale fading. It is shown that the use of moderately large antenna arrays can improve the spectral and energy efficiency with orders of magnitude compared to a single-antenna system.

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Energy and Spectral Efficiency of Very Large Multiuser MIMO Systems

A multiplicity of autonomous terminals simultaneously transmits data streams to a compact array of antennas. The array uses imperfect channel-state information derived from transmitted pilots to extract the individual data streams. The power radiated by the terminals can be made inversely proportional to the square-root of the number of base station antennas with no reduction in performance. In contrast if perfect channel-state information were available the power could be made inversely proportional to the number of antennas. Lower capacity bounds for maximum-ratio combining (MRC), zero-forcing (ZF) and minimum mean-square error (MMSE) detection are derived. A MRC receiver normally performs worse than ZF and MMSE. However as power levels are reduced, the cross-talk introduced by the inferior maximum-ratio receiver eventually falls below the noise level and this simple receiver becomes a viable option. The tradeoff between the energy efficiency (as measured in bits/J) and spectral efficiency (as measured in bits/channel use/terminal) is quantified. It is shown that the use of moderately large antenna arrays can improve the spectral and energy efficiency with orders of magnitude compared to a single-antenna system.

In this paper, we investigate the capacity distribution of spatially correlated, multiple-input-multiple-output (MIMO) channels. In particular, we derive a concise closed-form expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequency-flat Rayleigh-fading environments. Using the exact expression of the c.f., the probability density function (pdf) and the cumulative distribution function (CDF) can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels. Our results are valid for scenarios with the number of transmitting antennas greater than or equal to that of receiving antennas with arbitrary correlation among them. Moreover, the results are valid for an arbitrary number of transmitting and receiving antennas in uncorrelated MIMO channels. It is shown that the capacity loss is negligible even with a correlation coefficient between two adjacent antennas as large as 0.5 for exponential correlation model. Finally, we derive an exact expression for the mean value of the capacity for arbitrary correlation matrices.

/pdf/on-the-capacity-of-spatially-correlated-mimo-rayleigh-fading-3kjr7kz4jb.pdf

On the capacity of spatially correlated MIMO Rayleigh-fading channels

We consider the problem of secure communication with multiantenna transmission in fading channels. The transmitter simultaneously transmits an information-bearing signal to the intended receiver and artificial noise to the eavesdroppers. We obtain an analytical closed-form expression of an achievable secrecy rate and use it as the objective function to optimize the transmit power allocation between the information signal and the artificial noise. Our analytical and numerical results show that equal power allocation is a simple yet near-optimal strategy for the case of noncolluding eavesdroppers. When the number of colluding eavesdroppers increases, more power should be used to generate the artificial noise. We also provide an upper bound on the SNR, above which, the achievable secrecy rate is positive and shows that the bound is tight at low SNR. Furthermore, we consider the impact of imperfect channel state information (CSI) at both the transmitter and the receiver and find that it is wise to create more artificial noise to confuse the eavesdroppers than to increase the signal strength for the intended receiver if the CSI is not accurately obtained.

/pdf/secure-transmission-with-artificial-noise-over-fading-2dg58zvnxk.pdf

Secure Transmission With Artificial Noise Over Fading Channels: Achievable Rate and Optimal Power Allocation

We consider the problem of secure communication with multi-antenna transmission in fading channels. The transmitter simultaneously transmits an information bearing signal to the intended receiver and artificial noise to the eavesdroppers. We obtain an analytical closed-form expression of an achievable secrecy rate, and use it as the objective function to optimize the transmit power allocation between the information signal and the artificial noise. Our analytical and numerical results show that equal power allocation is a simple yet near optimal strategy for the case of non-colluding eavesdroppers. When the number of colluding eavesdroppers increases, more power should be used to generate the artificial noise. We also provide an upper bound on the signal-to-noise ratio (SNR) above which the achievable secrecy rate is positive and show that the bound is tight at low SNR. Furthermore, we consider the impact of imperfect channel state information (CSI) at both the transmitter and the receiver and find that it is wise to create more artificial noise to confuse the eavesdroppers than to increase the signal strength for the intended receiver if the CSI is not accurately obtained.

Secure Transmission with Artificial Noise over Fading Channels: Achievable Rate and Optimal Power Allocation

We derive an exact closed-form solution for the reliability of an ideal M-branch MMSE (minimum mean-squared error) diversity combiner operating in a Rayleigh-fading channel with N interferers, each having some specified average power. The reliability is defined as the probability, taken over fading of the desired and interfering signals, that the combiner's output signal-to-interference ratio (SINR) is greater than some specified threshold. This kind of metric is important in evaluating the potential capacity improvements of using diversity combining and adaptive array processing in interference-limited wireless systems. Our result is remarkably simple, fast, straightforward to compute, and numerically stable. We show a set of special cases, which relate to standard results and reveal valuable insights into how this type of array processing operates in interference-limited environments. We also present a set of numerical examples, which show that our calculated reliabilities agree with estimates from Monte Carlo simulation.

H. Gao

Papers

Theoretical reliability of MMSE linear diversity combining in Rayleigh-fading additive interference channels