In this series:

- Massive MIMO – Part 1. Introduction: From theory to implementation
- Massive MIMO – Part 3: Capacity, coherence time and hardware capability
- Massive MIMO – Part 4: Massive MIMO and small cells, the next generation network
- Massive MIMO – Part 5: The need for practical prototyping and implementation
- Massive MIMO – Part 6: Estimation and capacity limits due to transceiver impairments

The promising multiplexing gain achieved in point-to-point MIMO requires a favorable radio propagation link and a good signal-to-noise ratio (SNR). Disappointing performance can be observed in line of sight (LOS) radio propagation environments or when the user terminal is located at the edge of the cell (a low SNR case). Additional receive antennas can compensate for a low SNR at the expense of increased detection computational burden at the terminal.

Multi-user MIMO differs from point-to-point MIMO in two fundamental aspects: first, the user terminals are basically separated by several wavelengths and second, they cannot collaborate among themselves. A comprehensive overview of the opportunities and challenges with very large arrays can be found in

For educational purposes, lets look at the massive MIMO performance analysis case from [3]. The ergodic achievable rate has been derived for a non-cooperative multi-cell TDD system with a realistic uplink and downlink. This accounts for (i) imperfect channel estimation, (ii) pilot contamination, (iii) antenna correlation, and (iv) path loss. Asymptotic approximations of the achievable rates using several low complexity linear detectors and precoders are derived (namely matched filter (MF) and minimum mean square error detector (MMSE) in the uplink, and eigen-beamforming (BF) and regularized zero forcing precoders in the downlink). For the sake of brevity, we will concern ourselves with only the MF detector and BF precoder. Following the simplified channel model in section IV [3] on massive MIMO effects, the asymptotic signal to interference and noise ratio (SINR) is given by:

where . The other parameters are defined in the table below.

The above equation is readily broken down into the following contributions:

The lessons learned from these terms are:

- The asymptotic SINR depends on the transmit power SNR
*ρ*which shows that the effective SNR*ρN*increases linearly with the number of antennas. Therefore the transmit power can be reduced accordingly. Or, as shown in [4], if the training power is equal to the transmit signal power then the transmit power can be made inversely proportional to*√N*. - The interference depends on the degree of freedom (DoF) per UT P/K and not on
*N*. Additional antennas can reduce interference if the DoF increases. - The noise, channel estimation imperfection, and interference will diminish as the number of antennas and DoF increases.
- The pilot contamination remains the performance bottleneck, however.

_{2 .}

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