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• Goodput: the average number of correctly received information bits per time unit. Goodput is measured in bit/s and, assuming transmission at Nyquist rate and selective repeat ARQ, computed as:

G = BsQMTR(1−BLER). (5.1)

If the communication is error-free (i.e., BLER = 0) it is possible to achieve the ideal information throughput:

Θ_{i= BsQMTR. (5.2)}

Hence:

G = Θ_{i(1−BLER). (5.3)}

In the context of the following analysis, whenever a hardware implementation is involved all the metrics are subject to the processing capabilities of the receiver. As a consequence, definition (5.1) only applies if the receiver can serve the given symbol rate Bs. This condition can be formulated as:

Θ

idd ≥Θi (5.4)

with Θidd being the average hardware information throughput supported by the receiver. For example, for a 4×4 64-QAM configuration with R =5/6 and Bs=20 Msym/s, Θi = 20×6×4×5/6 Mbit/s = 400 Mbit/s; if the average hardware throughput of the receiver Θ_idd is lower than 400 Mbit/s, this setup is considered to be unusable and a less computationally demanding one (e.g., with a lower modulation order) is chosen which complies with condition (5.4). In case condition (5.4) is not verified, the goodput drops to zero since the sys- tem is considered to be in an invalid operating point. Recalling the dual symbol rate constraint introduced in Section 5.1.1 and defining Θi,min = Bs,minQMTR

and Θ_i,max =Bs,maxQMTR, the constrained average information throughput sup- ported by the receiver is defined as:

Θ idd,c=      0 if Θ_idd <Θ_i,min, Θ

idd if Θi,min ≤Θidd ≤Θi,max, Θ_{i,max if Θ}

idd >Θi,max.

(5.5)

For Θi,min < Θidd < Θi,max, the symbol rate is assumed to be adjusted to match Θ_idd. Therefore, when an implementation is considered, the hardware- constrained goodput is computed as:

Gc =Θidd,c(1−BLER). (5.6)

• Spectral efficiency: the number of correctly received information bits per time and bandwidth unit, measured in bit/s/Hz and, assuming transmission at Nyquist rate, computed as:

ηs=QMTR(1−BLER). (5.7) As for the definition of the goodput, if hardware components are involved, spec- tral efficiency is subject to the limitations of the implementation and hence com- puted as:

ηs,c = Θ

idd,c

Bs (1−BLER). (5.8)

Definitions (5.7) and (5.8) obviously coincide if B_s,min ≤Bs ≤Bs,max.

• Area efficiency: the goodput per silicon area unit, measured in bit/s/GE and computed as:

η_a,idd = Gc

A_idd (5.9)

where A_idd is the area of the receiver expressed in GE.

With the present silicon technology, area is typically not the main concern for the designer, especially as compared to throughput, power and energy con- sumption. For this reason, in this thesis area is not constrained to a limit that would be merely arbitrary but rather considered as a result of the implementa- tion. Area efficiency is still one of the key metrics to compare different hardware implementations.

• Energy efficiency: the inverse of the energy consumed to correctly decode one bit, measured in bit/J. For a single hardware component this quantity can be computed simply as the throughput divided by the average power consumption. However, for multiple cascaded components with non-matching throughputs this definition does not apply anymore since only the block with the lowest throughput is always active, while the others are idle for a certain percentage of the time, with a corresponding decrease of the average power consumption. Furthermore, the system goodput is the relevant quantity for computing energy

efficiency rather than the hardware throughput. The goodput is constrained by the symbol rate to a value which is lower than or equal to the hardware throughput, as specified by (5.4), meaning that at times both the detector and the decoder may operate at a lower throughput than they can support. Such a situation corresponds to underutilising the hardware components; the utilisation ratio of a processing element is defined as:

ρpe= Θ

idd,c

Θ_pe (5.10)

where Θpeis the information throughput supported in hardware by the PE. In view of the previous considerations, the energy efficiency of the MIMO IDD receiver is computed as the ratio between the total number of correctly decoded information bits and the energy consumed in the process:

ηe,idd = N_iN_f

E_idd (1−BLER) (5.11)

where Nf is the total number of received frames and Eiddis the energy dissipated to detect and decode those N_f frames.

By separating the individual dynamic and static consumptions of the different components, the previous definition can be written as:

η_e,idd = NiNf

E_d,det+E_d,dec+E_s,idd(1−BLER) (5.12)

= NiNf

P_d,detT_det+P_d,decT_dec+P_s,iddT_idd,c(1−BLER) (5.13) where T_det and T_dec are the total active times of the detector and the decoder respectively; Tidd,c is the total time necessary to receive Nf, also computed as

NiNf

Θ_idd,c. Since both the detector and the decoder are clock gated when not used, their dynamic power consumption is null outside of their active times T_det and T_dec. If Θ_idd >Θ_i,max, T_idd,cincludes some idle time since the receiver processes

the data at a faster rate than it receives them.

By replacing throughputs in the previous equation, the original definition of the energy efficiency as the ratio between throughput and power is recovered for the single contributions:

ηe,idd =  P_d,det Θ det +P_Θd,dec dec +_ΘPs,idd idd,c −1 (1−BLER). (5.14)

Equivalently, by introducing the utilisation ratios of the components, the defini- tion becomes:

η_e,idd = Pd,detρdet

Θ_idd,c + P_d,decρ_dec Θ_idd,c + P_s,idd Θ_idd,c −1 (1−BLER) (5.15) = Θidd,c

Pd,detρdet+Pd,decρdec+Ps,idd

(1−BLER). (5.16)

In the following sections, the energy consumed by the receiver for detection and decoding is computed based on the IteRX chip measurements. Only in Section 5.4 energy is considered on the system level and hence corresponds to an estimate of the complete communication system including the full transmitter and receiver chains; the corresponding definitions are given in Section 5.4. • Latency: the delay between a frame being ready to be processed at the detector

input and the completion of its decoding, denoted by the symbol Lidd and mea- sured in s (see later Figure 5.1 for a visual example of what latency is). As in the case of energy efficiency, in the system-level perspective of Section 5.4 latency includes all communication system components and frame retransmissions; a more precise definition of latency for this specific case is given in Section 5.4.

The common characteristic of all the aforementioned metrics is their dependency on the hardware implementation. Even those typically considered only from an ideal algorithmic point of view, such as spectral efficiency and goodput, are subject to the processing capabilities of the actual implementation. As a consequence, the behaviour of the metrics analysed in the following sections is not always obvious; for instance, in certain scenarios a higher spectral efficiency does not necessarily result in a higher data rate (see Section 5.3.1). This observation stresses the importance of including all hardware constraints in the analysis of a wireless communication system.