Sistemas de acabados

2.1.1 Wireless Channels

The performance of wireless communication systems depends on the propagation environ-ments of wireless channels, which are characterized by fading, i.e., the variation of the signal amplitude over time and frequency. The fading phenomenon consists of small-scale fading and large-scale fading factors [24]. The large-scale fading is caused by path loss which depends on the distance and propagation conditions, as well as shadowing which is characterized by variation of median path loss between the transmitter and receiver, due to large objects such as mountains, vegetation and buildings. The small-scale fading refers to rapid variation of signal levels because of the destructive and constructive multipath fading effect of transmitted

Chapter 2: Background and Literature Review

signals. Moreover, the small-scale fading can be classified according to different criteria. Based on multipath delay spread, the small-scale fading is characterized by frequency-selective fading or frequency flat fading. On the other hand, based on time variation in the channel due to the Doppler spread, the small-scale fading are classified as either time variant fading or time invariant fading. These two propagation mechanisms are independent of one another. The classification of fading channel is presented in Fig. 2.1.

Fading channel

Large-scale fading

Shadowing

Path loss

Small-scale fading

Flat fading

Frequency-selective fading

Time variant fading Time invariant

fading

Figure 2.1: Classification of fading channels.

Mathematically, in a downlink MU-MIMO system, where the base station is equipped with N transmit antennas to serve its K single-antenna users, a channel vector of the kth user can be modelled as¹

gk =p

βkhk, (2.1)

where h_k ∈ C^{N ×1} is the small-scale fading vector whose elements are independent and identi-cally distributed (i.i.d.) zero-mean complex Gaussian random variables with unit variance, i.e., h_k ∼ CN (0, I). Parameter β_k is the large-scale fading coefficient accounting for shadowing and path loss. In [25], the role of βk has been investigated in the uplink transmission. Moreover,

1Note that all the notations are only applicable to this chapter.

Chapter 2: Background and Literature Review

by using the fact that the channel vectors of different users are independent and applying the law of large numbers, it is well known that [6, 7]

N →∞lim g^H_i gk

N

−→ 0a.s. and lim

N →∞

g_k^Hg_k N

−→ βa.s. _k, (2.2)

where−→ denotes almost convergence. In the literature, these convergence properties of channel^a.s.

vectors have been widely applied for evaluating the performance of massive MIMO systems.

2.1.2 Key Performance Indicators

In wireless communication systems, capacity (or throughput) indicates how much informa-tion can be transmitted for given limited spectral resources. It is defined as

Capacity (bits/s) = Bandwidth (Hz) × Spectral efficiency (bits/s/Hz). (2.3)

The spectral efficiency is a conventional metric to evaluate the efficiency of a wireless system.

It presents how efficient a limited frequency spectrum is utilized, but it does not show any insight on how efficient the energy is consumed. The achievable rate can be used instead for some communication systems, where the capacity are unknown. Another metric to evaluate the performance of the next-generation cellular networks is the energy efficiency. It is obtained as the ratio between the achievable capacity and the total power consumption (measured in Watt=Joule/s), which is expressed as [26]

Energy efficiency (bits/Joule) = Capacity (bits/s)

Total power consumption (Watt). (2.4)

Without loss of generality, the system is assumed to have unit bandwidth in order to simplify the notation in this thesis.

Chapter 2: Background and Literature Review 2.1.3 Power Consumption Model

In order to investigate the EE performance of a cellular network, the power consumption of the BS needs to be captured as well. This is because the BSs take the main power consump-tion of the network operaconsump-tion. In the literature, several works have assumed that the power consumption model (PCM) only consists of the emitted power consumption [13, 27]. However, since the number of antennas is large in massive MIMO systems, the effects of circuit and digi-tal signal processing (DSP) power consumptions can contribute significantly to the todigi-tal power consumption [28]. Therefore, to evaluate the practical aspects of the PCM, we study the power consumptions of all the implemented components at the BS. Note that we only consider the downlink scenarios in the thesis. Based on approaches in [28] and [29], a block diagram of the BS, which can be generalized to all BS types including macro, micro, pico and femto BSs, is shown in Fig. 2.2.

DC-DC

Cooling

Main supply

N antennas Filter PA

Filter DAC

Mixer

Filter PA Filter

DAC

Mixer LO

Feeder

Baseband

RF

Figure 2.2: Block diagram of a base station.

Specifically, a BS consists of multiple transmitters, each of which serves one transmit antenna element. Each transmitter comprises a power amplifier (PA), a radio frequency (RF) module, a baseband engine transmitter downlink section, a direct current-direct current (DC-DC) power

Chapter 2: Background and Literature Review

supply, an active cooling system, and an alternating current-direct current (AC-DC) unit (main supply) for connection to an electrical power grid [28]. For the RF module, the circuit blocks along the signal path consist of digital-to-analog converter (DAC), filter, mixer, and frequency synthesizer [29, 30]. We assume that all the antenna paths share a frequency synthesizer, i.e., a local oscillator (LO) [30]. The baseband unit performs DSP at the BS, including modula-tion/demodulation, signal detection (synchronization, channel estimation, equalization), as well as channel coding/decoding [28].

Let us denote Pant and σam as the output power at each antenna element and the power efficiency of the PA, respectively. Due to influences of the antenna type on the power efficiency, the power consumption of the PA is defined as

P_{P A} = Pant

σ_am(1 − σ_{f eed}), (2.5)

where σ_{f eed} is the factor loss of feeder. The feeder loss for a macrocell BS is about 3 dB, while the feeder loss for a small BS type can be typically negligible. Moreover, other factor losses, which are incurred by DC-DC power supply, mains supply, and active cooling, are also considered in this PCM. We assume that the BS power consumption is linearly proportional to the number of transmitter chains. When the BS is equipped with N antenna elements, the total power consumption can be defined as

P_total= N

Pant

σam(1−σf eed)+ p_dac+ p_mix+ p_{f ilt}

+ p_syn+ P_bb

(1 − σ_DC)(1 − σ_{M S})(1 − σ_cool) , (2.6)

where p_dac, p_mix, p_{f ilt}, p_syn, P_bb denote the power consumptions from the DAC, the mixer, the filter, the frequency synthesizer, and the baseband unit, respectively [28,31,32]. The parameters σ_cool, σ_{M S}, σ_DC are the loss factors of active cooling system, main power supply and DC-DC

Chapter 2: Background and Literature Review power supply, respectively. We denote

ω = (1 − σ_DC)(1 − σ_{M S})(1 − σ_cool) (2.7)

and

Pc= N (p_dac+ pmix+ p_{f ilt}) + psyn. (2.8)

Due to P_ant= ^P_N, where P is the transmit power consumption of the base station, (2.6) can be rewritten as

P_total= 1 ω

 P

σ_am(1 − σ_{f eed})+ Pc+ P_bb



. (2.9)

Note that the loss factor of active cooling is only applicable to macrocell BSs, and it can be omitted in the small BS types.