# Massive MIMO: Real Hardware Isn't Perfect

Bjornson and colleagues created a model of Massive MIMO that accounts for (some) imperfections in the real world. Components are never perfect, of course, but earlier MM models made that simplifying assumption.

Their conclusion: The ability of the UE/phone is the most important factor. That said, adding more antennas will significantly improve performance.

They warn about cheap antennas. "Large arrays might only be attractive for network deployment if each antenna element consists of inexpensive hardware.

Cheap hardware components are particularly prone to the impairments that exist in any transceiver (e.g., amplifier nonlinearities, I/Q-imbalance, phase noise, and quantization errors. The influence of hardware impairments is usually mitigated by compensation algorithms [14], which can be implemented by analog and digital signal processing. These techniques cannot remove the impairments completely."

The model is run with several different assumptions. Possible errors are explored at length.

I guarantee accurate answers will require results from the field.

Here's the abstract and conclusion.

Massive MIMO Systems with Non-Ideal Hardware: Energy Efficiency, Estimation, and Capacity Limits

Emil Bjornson, ¨ Member, IEEE, Jakob Hoydis, Member, IEEE, Marios Kountouris, Member, IEEE, and Merouane Debbah, ´ Senior Member,

IEEE Abstract—The use of large-scale antenna arrays can bring substantial improvements in energy and/or spectral efficiency to wireless systems due to the greatly improved spatial resolution and array gain. Recent works in the field of massive multiple-input multiple-output (MIMO) show that the user channels decorrelate when the number of antennas at the base stations (BSs) increases, thus strong signal gains are achievable with little inter-user interference. Since these results rely on asymptotics, it is important to investigate whether the conventional system models are reasonable in this asymptotic regime. This paper considers a new system model that incorporates general transceiver hardware impairments at both the BSs (equipped with large antenna arrays) and the single-antenna user equipment (UEs). As opposed to the conventional case of ideal hardware, we show that hardware impairments create finite ceilings on the channel estimation accuracy and on the downlink/uplink capacity of each UE. Surprisingly, the capacity is mainly limited by the hardware at the UE, while the impact of impairments in the large-scale arrays vanishes asymptotically and inter-user interference (in particular, pilot contamination) becomes negligible. Furthermore, we prove that the huge degrees of freedom offered by massive MIMO can be used to reduce the transmit power and/or to tolerate larger hardware impairments, which allows for the use of inexpensive and energy-efficient antenna elements.

CONCLUSION This paper analyzed the capacity and estimation accuracy of massive MIMO systems with non-ideal transceiver hardware. The analysis was based on a new system model that models the hardware impairment at each antenna by an additive distortion noise that is proportional to the signal power at this antenna. This model has several attractive features: it is mathematically tractable, it has been verified experimentally in previous works, and it can be motivated theoretically in systems that apply compensation algorithms to mitigate the hardware impairments. We proved analytically that hardware impairments create non-zero estimation error floors and finite capacity ceilings in the uplink and downlink—irrespective of the SNR and the number of base station antennas N. This stands in contrast to the very optimistic asymptotic results previously reported for ideal hardware. Despite these discouraging results, we showed that massive MIMO systems can still achieve a huge array gain, in the sense that relatively high spectral efficiency and energy efficiency can be obtained. Furthermore, we proved that only the hardware impairments at the UEs limit the capacities as N grows large. This implies that the hardware quality at the BS can be decreased as N grows, which is an important insight and might become a key enabler for future network deployments. In multi-cell scenarios, we proved that the detrimental effect of inter-user interference and pilot contamination drowns in the distortion noise if a simple pilot allocation algorithm is used to avoid the strongest forms of pilot contaminated interference. Many quantitative conclusions can be drawn from the numerical results in Sections III–VI; for example, that there is little gain in having more than 100 antennas for a singleuser link, but additional antennas are useful to suppress interuser interference in multi-cell scenarios. The asymptotic limits under non-ideal hardware are generally reached at much fewer antennas than the asymptotic limits for ideal hardware, which implies that we can expect practical systems to benefit from the asymptotic results. We also gave a brief description of how the system model considered in this paper can be refined to model hardware impairments in even greater detail and how such refinements would affect our results.