1. Introduction
With the escalating expansion of wireless network infrastructures and exponential growth in traffic rate, a considerable amount of worldwide energy is consumed by information and communication technologies (ICT) of which more than 70% is being used by radio access hardware and radio frequency [
1] which, in turn, increases the overall energy consumption of the system and the production of CO
2 emissions that are threat to global warming. This has given rise to the concept of green communications, the latter is a new research trend which aims to develop innovative methods for the reduction of the total power needed to operate future mobile communication systems and to identify appropriate network architectures and radio technologies which facilitate the required power reduction [
2]. The development of enabling technologies for green communications is currently a priority research area, in which there are several major international projects being carried out such as the European EARTH project [
3], the international Green Touch consortium [
4] and the Mobile VCE Green Radio (GR) [
5]. Multiple-input multiple-output (MIMO) communication systems can allow higher data rates compared to single-antenna-aided systems, this is because they have greater spectral efficiency [
6]. Hence, MIMO systems are expected to be a prominent part of the 5G standard [
7,
8]. However designing reliable and energy efficient MIMO detectors is a challenging task, because of the complexity of the implementation of the signal detection at the receiver due to the interfering sub-streams [
9]. Sphere decoding (SD) is a popular MIMO detection scheme, thanks to its ability to achieve near-maximum likelihood (ML) performance. On the other hand, SD exhibits a variable complexity depending on the channel condition, which makes it not well suited for real-time hardware applications. Meanwhile, K-Best detectors exhibit a fixed complexity irrespective of channel conditions; therefore, they have received significant interest in recent years [
10,
11].
However, the relatively high complexity still required for K-best MIMO detectors imposes great demands on energy consumption and causes drainage of the battery, which may render its use unfeasible in green communication schemes [
8]. A number of energy efficient hardware designs of K-best MIMO detector have been proposed [
12,
13,
14]. Kim and Park in [
13] employed a relaxed sorting operation technique to achieve a significant reduction in the power consumption of the MIMO detector. In [
14], the authors adopted a sort-free approach to path extension in order to minimize energy costs. More recently, an adaptive hardware scheme was proposed in [
12], where favorable channel conditions are exploited to reduce the energy consumption of the MIMO detection hardware, which was achieved through the use of reconfigurable MIMO detection architecture controlled by the signal to noise ratio (SNR).
Although these schemes proved to reduce power consumption of the MIMO detecting hardware, they may still not be suitable candidates for green communication networks, as they do not take into consideration the transmission power requirements. In fact, the transmission power accounts for more than 50% of the overall power consumed in wireless cellular networks [
2], which is expected to rise significantly in 5G wireless networks because of the increase in signal frequencies [
7,
8]. In the context of this work, 5G networks refer to communication systems, which operate at frequencies higher than the conventional microwave frequencies, typically more than 6 GHz. At higher frequencies, the path losses and environment attenuation factors become significantly higher than those experienced in sub-6 GHz frequencies. Therefore, higher transmission power, as well as more sophisticated signal processing, are needed for 5G systems. Additionally, at higher carrier frequencies, 5G networks are expected to have significantly higher bandwidths than the currently operating systems such as 3G and 4G. Therefore, for green wireless communications there is a need for MIMO decoding schemes, which have low-power hardware implementation and minimal transmission power requirements.
Lattice reduction (LR) techniques [
15] have received increasing attention for MIMO detection because of their potential to attain near-ML performance, while having a significantly lower complexity than the maximum likelihood detection (MLD), especially in large-scale MIMO systems [
16]. In comparison with the conventional K-best detectors, the LR-aided K-best algorithm assumes no boundary information about the symbols in the lattice-reduced domain, which means possible children for each layer can be infinite. Therefore, to find the K-best partial candidates from the infinite children set, LR-aided K-best algorithms typically replace the infinite set with a finite subset of the children. The complexity of generating the subset may be reduced by using an on-demand child expansion based on the Schnorr-Euchner (SE) strategy [
17].
This paper presents an energy-efficient LR-aided K-best detector targeting a 2 × 2 MIMO system with quadrature amplitude modulation (QAM) spatial multiplexing. We developed a new hardware architecture, which was implemented in 32 nm technology for verification and energy cost evaluation. Our results indicate that the proposed decoder reduces the overall power costs by four-fold, on average, compared to existing schemes, thanks to its better bit error rate BER performance. The throughput of the proposed decoder is comparable with existing approaches.
This paper is organised as follows:
Section 2 outlines the main principles of sphere decoding and K-best algorithms;
Section 3 explains how LR techniques can be combined with K-best decoding to enhance performance;
Section 4 describes the proposed hardware architecture of the LR-aided K-best detection;
Section 5 presents a framework to evaluate the overall power costs of a MIMO scheme, which takes into consideration its transmission power requirements;
Section 6 explains the VLSI implementation details and compares the proposed design with recently-published energy efficient MIMO decoders; and, finally, conclusions are drawn in
Section 7.
2. Sphere Decoding and the K-Best Algorithm
In this paper, we consider a MIMO system with
transmit antennas and
receive antennas. The maximum likelihood (ML) detector offers the best achievable BER performance; however, its complexity makes it impractical in terms of hardware implementation. On the other hand, the SD tries to decrease the complexity of ML and to achieve a sub-optimal performance by searching only through those points that fall inside a sphere of radius r, where the SD transforms the ML problem to a tree search [
18]. There are many approaches to perform a tree search, where in this work we focus on Breadth-First Search (BFS) using the K-Best algorithm [
8,
9]. In the following we describe the original SD algorithm [
18] in order to provide some background explanation of the idea of SD, then we describe the LR-aided SD algorithm in the next section, which forms the basis for our implementation.
The MIMO system is normally modeled using the following equation:
y =
Hx +
n, where
y represents the received MIMO signal,
H represents the MIMO channel matrix,
x represents the transmitted MIMO signal and
n represents the additive white gaussian noise (AWGN). The ML algorithm for detecting the transmitted signal given the MIMO received signal model can be expressed as:
Using the K-Best detector, the ML problem shown in Equation (1) is transformed to Equation (2) as:
The operation in Equation (2) is performed after performing QR-decomposition on the channel matrix
H, which results in
H =
QR with
R being an upper triangular matrix and
Q a unitary matrix. In (2),
, and
represents the symbol vector of size
, where the complex vector of size
is transformed to a real vector of size
. Equation (2) refers to a tree search due to the nature of
, where it normally starts from the last row towards the first row in the
matrix. In each layer the K-Best algorithm will select the K candidates having the lowest partial Euclidean distance (PED) from
. The K-Best algorithm can be summarized as follows:
Initialize the first layer ;
Find the PEDs of all expanded nodes at layer and select the K minimum PEDs;
Expand the surviving nodes to their children and set ;
If go to step 2, otherwise continue;
Select the path with the lowest PEDs as the solution.
3. LR-Aided K-Best Decoder
The Lenstra–Lenstra–Lovász (LLL) algorithm is typically used to implement lattice reduction due to its relatively low complexity and good performance [
5,
6]. This section explains how the LR technique based on the LLL algorithm can be combined with the K-Best detector. Given the MIMO model of
y = Hx + n, the received signal of the MIMO system can be transformed in LR form as [
16]:
where
is a unimodular matrix, which has a determinant of
and all the entries of
are integers [
5,
6]. The new channel matrix is represented as
. Multiplying
with
gives a more orthogonal and better-conditioned matrix
than the MIMO channel
H [
16]. By adopting Equation (3), the MIMO system model is transformed from
to
. Therefore, the detector requires to detect
from the reduced-lattice constellation and then recovers the original constellation point by
. Note that
integer set. Both
and
produce the same point in the lattice but
is more orthogonal than
and gives more reliable estimation for the received signal
at the receiver.
In order to perform K-Best detection, the decoder finds the
matrix from
by performing LLL algorithm [
15]. Then, the orthogonal
matrix is obtained by
. Then, similarly to the conventional K-Best detector, QR decomposition is performed for
so that
, where
is an upper triangular matrix and
is a unitary matrix. The size of both
and
is
, which is due to taking the real model into consideration. After QR decomposition, we can rewrite
as
. Then, the ML process in Equation (1) is reshaped to represent the detected
as:
where z is computed as:
.
is a shifted and scaled version of
y and it is computed as follows:
Afterwards, from Equation (4) the detector requires performing a tree search to detect
and then recovers the original symbols by multiplying with
T after rescaling and re-shifting
as
, which can be expressed as [
17]:
where
is a matrix of size
with all entries one.
To implement Equation (7) the breadth-first K-Best algorithm is used, where in the shift and scale of
y transforms the points searched for into continuous numbers (−1, 0, 1, 2…) in each dimension. The detection of candidates in each layer exploits the on-demand child expansion the Schnorr-Euchner (SE) enumeration, hence there will be no fixed format of the candidates. The value of the candidates in the current layer is only based on the initial child (
) and steps obtained. The order of the detection in each layer can be presented in
Figure 1.
The crosses in
Figure 1 represent the points in the lattice, while the black point is rounded to −1, which is the initial child in this example. The other candidates in the current layer will be based on the order as the
Figure 1 shows. The constant k will determine the times of the jumping across the candidates. For the complex model used in this work, the order in two dimensions can be presented as
Figure 2.
The removal of the fixed format of the candidates, combined with the on-demand child expansion method, significantly reduces the correlation among the candidates, which can improve the performance of the MIMO detection process and reduces its complexity.
6. VLSI Design and Comparative Analysis
A chip which implements an LR-aided K-Best detector targeting a 2 × 2 MIMO system was synthesized using 32 nm standard CMOS technology. The frequency of operation was set to 253 MHz at a supply voltage of 1 V. To estimate the power consumption of the MIMO decoder hardware () under normal operation conditions, first we computed the channel matrix (H) based on free space medium. The latter was then applied to the MIMO decoder along with large number of typically received inputs (Y), the average power consumption has then been estimated for all test cases.
The minimum transmission power requirement is estimated using Equation (9) based on free space communication medium, where we have considered the minimum acceptable BER of 10
−3, this is because received signals with BER higher than this figure may not be reliably detected [
20]. We have considered two study cases: 4G and 5G wireless communication networks. The operation parameters of 4G systems are obtained from the third-generation partnership project which provide detailed information on the operating conditions of such networks [
21], where we consider a 4G network transmission frequency of 1.8 GHz. The operation parameters of 5G networks are still in the development stage; initial estimates of the transmission frequencies indicate they are within the range 10–100 GHz [
22]. For the purpose of this work we have considered the first successful implementation of a 5G wireless communication network recently announced by Ericsson [
22], where in the transmission frequency was set to 15 GHz. In both of the above cases we consider the average distance between a mobile device and a base station around 200 m [
20].
Figure 5 and
Figure 6 illustrate the power costs of the proposed design in comparison with conventional K-best decoder and recently published energy efficient MIMO detection schemes. The two components of the power overheads: MIMO decoder power consumption and transmission power are illustrated separately. For completeness we have also included a comparison of the VLSI implementation in
Table 1.
For the first case study, i.e., the 4G wireless mobile network,
Figure 5 shows that the proposed MIMO can significantly reduce the transmission power requirements at the expense of increased power consumption of the MIMO decoder; therefore, its overall power costs is comparable to existing approaches. However for the second case study, i.e., the 5G wireless network, our decoder exhibits remarkably higher power efficiency, because it reduces the overall power cost: by two- and seven-fold, compared with conventional K-best implementations in [
13,
14], respectively. These large power saving are expected to be higher as the carrier frequency increases.
Figure 7 show the relationship between the transmission carrier frequency and the overall power consumption costs for the four schemes.
Finally, it is worth noting that the throughput of the proposed design is comparable to existing approaches as outlined in
Table 1.