Massive-MIMO

High-dynamic-range and low-power M-MIMO Communications. The massive multiple-input multiple-output architecture (M-MIMO) is a communication system that utilizes a large number of antennas and the base station, serving a large number of users. While M-MIMO offers substantial potential for spectral efficiency gains, it faces considerable practical challenges. Among the limitations are the power consumption and receiver saturation, which are particularly critical in M-MIMO since each antenna has a corresponding radio frequency (RF) chain.

\(\lambda\)-MIMO is a new approach for holistically addressing the high power consumption and receiver saturation problems in M-MIMO architectures. Compared to de-coupled approaches, the overall performance can be optimized, as balancing trade-offs can be avoided. The uplink system architecture is constructed by replacing the ADC in each RG chain by the M-ADC.

M-MIMO uplink architecture.

Fig. 37 M-MIMO uplink architecture.

Theoretical analysis and hardware experiments indicate that the proposed \(\lambda\)-MIMO architecture achieves better energy efficiency compared to the conventional M-MIMO architecture. The reconstruction, detection and sum-rate performance are also improved.

System Model. At the transmitter side, the Narrowband Single-Carrier Signal Model (NBSC) and the wideband MIMO–OFDM were studied. At the receiver side, the received signal at the \(n^{\mathsf{th}}\) antenna, denoted by \(z_{n}(t)\) is amplified and de-modulated to the baseband. The quadrature and in-phase signal are then lowpass filtered, and sampled by the M-ADC.

Performance Analysis

The M-ADC achieves lower quantization noise (more information: Sampling Resolution), and the impact on the performance of communication is shown by analyzing the analysis of the SQNR and achievable sum-rate for a maximum ratio combining (MRC), and zero forcing (ZF) combiners.

SQNR

The baseband sampled single-carrier signal is subject to uniform distribution \(r[k] \sim U(0,1)\). The SQNR for a conventional ADC is: \(\text{SQNR}_{\text{unif}} = 10 \log_{10} \frac{\sigma^2_{r,\text{unif}}}{\sigma^2_{q,\text{unif}}} = 6.02 b \, (\text{dB})\).

The modulo folded samples follow a uniform distribution \(\mathscr{M}_{\lambda}(r(t))\vert_{t=kT} \sim U(0, \zeta^{2})\). Consequentially, the quantization error is lowered by: \(\sigma^2_{q,\lambda} = \zeta^2 \sigma^2_{q,\text{unif}}\), and the SQNR becomes:

\[\text{SQNR}_{\text{unif}, \lambda} = 10 \log_{10} \frac{\sigma^2_{r,\text{unif}}}{\sigma^2_{q,\lambda}} = 6.02 b + 20 \log_{10}(1 / \zeta) \, (\text{dB}).\]

Notably, the M-ADC gives an \(20 \log_{10}(1/\zeta)\) enhancement on the SQNR.

The OFDM signal is commonly assumed to be a centered, wide-sense stationary, ergodic Gaussian process \(r[k] \sim \mathcal{N}(0,1)\). The SQNR for a conventional ADC is: \(\text{SQNR}_{\text{Gau}} = 10 \log_{10} \frac{\sigma^2_{r,\text{Gau}}}{\sigma^2_{q,\text{Gau},(m)}}\approx 6.02 b - 4.35\). The modulo folded samples follow a wrapped distribution, which was empirically found to be uniform \(\mathscr{M}_{\lambda}(r(t))\vert_{t=kT} \sim U(0, \zeta^{2})\) for \(\lambda\) being a fraction of \(\sigma^{2}\). The SQNR is,

\[\text{SQNR}_{\text{Gau}, \lambda} = 10 \log_{10} \frac{\sigma^2_{r,\text{Gau}}}{\sigma^2_{q,\lambda}} \approx 6.02 b + 20 \log_{10}(1 / \zeta).\]
M-MIMO SQNR.

Fig. 38 M-MIMO SQNR.

Sum-Rate Analysis

Analytical approximations for the achievable sum-rate are derived for two combiners.

MRC Analytical Approximation of Achievable Sum-Rate:

The uplink rate of the \(m\)th user with MRC is given by:

\[\widetilde{R}{m, (\text{MRC})} = \log_2 \left( 1 + \frac{p_u \gamma_{\lambda} \eta_{m} (N + 1)}{I_{\text{MRC}}} \right),\]

where \(I_{\text{MRC}}\) is the expectation of the noise-plus-interference term, with:

\[I_{\text{MRC}} = p_u \gamma_{\lambda} \sum_{i=1, i \neq n}^{M} \eta_i + p_u (1 - \gamma_{\lambda}) \left( \sum_{i=1}^{M} \eta_i + \eta_m \right) + 1.\]

The sum-rate for the system is: \(R = \sum_{m=1}^{M} \widetilde{R}_{m}\).

ZF Analytical Approximation of Achievable Sum-Rate:

The uplink rate of the \(m\)th user with ZF is given by:

\[\widetilde{R}_{m,(\text{ZF})} = \log_2 \left( 1 + \frac{\gamma_{\lambda} p_u}{\frac{\gamma_{\lambda}}{(N - M) \eta_m} + (1 - \gamma_{\lambda}) I_{\text{ZF}}} \right),\]

where \(I_{\text{ZF}}\) is the expectation of the noise-plus-interference term. Here, \(\delta < 1\) is the attenuation coefficient. The following figure present the comparison of the sum-rate for conventional and M-ADC on simulated data. As observed, by setting \(b\) as low as \(1\) or \(2\) with M-ADC the up-link sum-rate approaches that of \(b=\infty\) for conventional ADC.

M-MIMO Sum-Rate.

Fig. 39 M-MIMO Sum-Rate.

The advantages of the M-ADC are also present via comparison of the energy efficiency, especially for low bit resolutions.