Analysis of Massive MIMO With Low-Resolution ADC in Nakagami- m Fading

Analysis of Massive MIMO with Low-Resolution ADC in Nakagami- m Fading

Abstract: The uplink of multi-user massive multi-input-multi output systems, in which the base station is equipped with low resolution analog-to-digital converter architecture, is considered in this paper. All the channels are assumed to ender go independent and non-identically distributed Nakagami-m fading. By means of moment matching, the signal-to-interference-plus quantization noise-ratio at the output of maximum ratio combiner is approximated by a gamma random variable.

Using this approximate pdf, tight approximations for metrics like outage probability and rate are derived. The gap between the simulation and the approximate result is negligible. Also, for large number of antennas, a decrease in the number of antennas should be accompanied by a proportionate decrease in the threshold to maintain the same outage probability.

Existing system: The derived OP and rate approximate expressions, respectively, are verified using Monte-Carlo simulations. For simulations, we generate the Nakagami-m RVs from the complex pdf given. We then use these variables to determine the SIQNR n. It

can be observed from that the simulation results for Nakagami-m fading channel matches our approximation for various values of and M. Recall that, as decreases, resolution of ADC decreases, which is our regime of interest. Note from that, our approximation is tighter as the resolution decreases. This is because, as decreases, the quantization term Zn dominates the interference term in the denominator. In such scenarios, the ratio becomes much closer to a gamma distribution and moment-matching with gamma distribution is tighter. Moreover, increase in the ADC resolution (given by a decrease in) or an increase in M decreases the OP. Proposed system: Though the well-cited works like derive the expressions for uplink rate, in all these works, the average rate is obtained by approximating the expectation of logarithm of signal-to-interference plus quantization noise ratio (SIQNR). This was initially proposed then used. The limitation of this approximation is that it is very specific to obtaining rate expressions and cannot be adopted to obtaining approximate probability density function (pdf)/ cumulative distribution function (CDF) of SIQNR. Very recently, the authors of have derived an approximate outage probability (OP) expression using the fact that if the squared coefficient of variation (SCV) of a random variable (RV) tends to zero, the RV approaches a deterministic value equal to its mean. However, the approximate expressions in are shown to be tight only for a very large number of antennas at the base station (BS) and for Rayleigh fading channels. Hence, this approach for deriving the approximation for OP cannot be used if we assume any other type of channel fading, for example, Nakagami-m fading.

Advantages: Though the well-cited works like derive the expressions for uplink rate, in all these works, the average rate is obtained by approximating the expectation of logarithm of signal-to-interference plus quantization noise ratio (SIQNR). This was initially proposed in then used. The limitation of this approximation is that it is very specific to obtaining rate expressions and cannot be adopted to obtaining approximate probability density function (pdf)/ cumulative distribution function (CDF) of SIQNR.

Very recently, the authors of have derived an approximate outage probability (OP) expression using the fact that if the squared coefficient of variation (SCV) of a random variable (RV) tends to zero, the RV approaches a deterministic value equal to its mean.

Disadvantages: However, one drawback with massive MIMO systems is that, since a large number of antennas are required, there is a substantial increase in the hardware cost and power consumption.

Using high-speed high-resolution analog-to-digital converter (ADC) for all the antennas increases the power consumption of massive MIMO systems severely and this is considered as the bottleneck to realize massive MIMO in practice. To solve the power consumption problem, typically low-resolution ADCs (e.g., 1-3 bits) are employed at the RF chains.

Modules: Analog –to-digital converter: Massive multi-input-multi-output (MIMO) system has been widely accepted as a key technology to meet the increasing demand for wireless throughput in both mobile and fixed scenarios and has been widely investigated. However, one drawback with massive MIMO systems is that, since a large number of antennas are required, there is a substantial increase in the hardware cost and power consumption. Using high-speed high-resolution analog-to-digital converter (ADC) for all the antennas increases the power consumption of massive MIMO systems severely and this is considered as the bottleneck to realize massive MIMO in practice. To solve the power consumption problem, typically low-resolution ADCs (e.g., 1-3 bits) are employed at the RF chains. Hence, it is imperative to study the performance of MIMO systems in conjunction with a quantizer. Works like have analyzed such quantized MIMO systems. In, the exact non-linear nature of quantizer is studied. Due to the complicated nature of the exact quantization error, in the quantization is modeled as additive and independent noise.

Cumulative distribution function:

Though the well-cited works like derive the expressions for uplink rate, in all these works, the average rate is obtained by approximating the expectation of logarithm of signal-to-interference plus quantization noise ratio (SIQNR). This was initially proposed in and then used. The limitation of this approximation is that it is very specific to obtaining rate expressions and cannot be adopted to obtaining approximate probability density function (pdf)/ cumulative distribution function (CDF) of SIQNR. Very recently, the authors of have derived an approximate outage probability (OP) expression using the fact that if the squared coefficient of variation (SCV) of a random variable (RV) tends to zero, the RV approaches a deterministic value equal to its mean. However, the approximate expressions in are shown to be tight only for a very large number of antennas at the base station (BS) and for Rayleigh fading channels. Hence, this approach for deriving the approximation for OP cannot be used if we assume any other type of channel fading, for example, Nakagami-m fading.

Non – identically distributed: Though there are a few works like, which does performance analysis of massive MIMO systems with Nakagamim fading channels, the impact of low resolution ADCs is not studied in these works. If low resolution ADCs are present, the quantization noise effect should also be taken into account. The quantization noise will have a covariance which depends on the fading channels, which makes the analysis completely different from those of conventional systems. In this work, we consider the channels to be independent and non-identically distributed (i.n.i.d.)

Nakagami-m fading and derive a simple approximate pdf for the SIQNR, using moment matching. This pdf can be further used to obtain metrics like OP, rate, etc., for MIMO systems, where the quantization is modeled using AQNM. The derived approximations are simpler and tighter even for smaller values of number of antennas when compared to the expressions for Rayleigh fading users. Moreover, our approach can be used for deriving OP expressions for other types of fading channels also.