The increased deployment of wireless services has on the one hand, consistently led to greater scarcity of the licensed frequency spectrum [1
] and on the other hand however, has resulted in underutilization of frequency spectrum. This is largely due to the current fixed spectrum access (FSA) policy, which is based on a static allocation of the spectrum resources. This gives licensed users exclusive rights to the spectrum and results in several portions of the licensed spectrum being underutilized [2
]. This justifies demand for a more flexible access policy called dynamic spectrum access (DSA) because it ensures better utilization of the spectrum resources. The spectrum resources are still allocated to the licensed/primary users (PUs) but its usage is not exclusively granted. Unlicensed/secondary users (SUs) with cognition capability [5
] are able to access the spectrum resources opportunistically, as long as the PUs remain idle. These SUs or cognitive radios (CRs) can also concurrently share the spectrum with the PUs, as long as the PUs transmissions are adequately protected. The radio spectrum can therefore be reused in an opportunistic manner or shared all the time, to improve spectral efficiency [6
This cognition capability of CRs can be divided into three main components namely spectrum sensing, spectrum analysis and spectrum access decision. Spectrum sensing is by far the most important component in the establishment of CRs as it provides the awareness of the overall spectrum utilization as well as which bands to sense for gaps in the spectrum (also called spectrum holes), when to sense for those gaps and for how long to sense in real-time [7
]. There are two techniques usually involved in spectrum sensing (SS), namely direct spectrum sensing and indirect spectrum sensing, the former being used to detect the receiver (Rx) of the PU, while the latter is used to detect the transmit (Tx) of the PU. Even though it is more effective for SS to be employed directly, it is the more challenging of the two techniques because the Rx does not usually transmit when it works [7
]. Therefore, most of the existing SS schemes employ indirect SS techniques. Such schemes are generally classified to matched filter detection, energy detection, feature detection, and interference temperature measurement.
The reality however, is that SUs are almost unable to operate concurrently with the PUs without causing harmful interference to the PU system, thus a very crucial task in the design of CR networks is about how best the SUs can avoid interfering with the PUs in their vicinity [9
]. This becomes particularly challenging nowadays due to data communication, where the PU is seldom idle, such that the availability of spectrum holes becomes diminished [12
In attempting to solve to this issue, the emphasis of research has moved in the direction of a innovative interference management strategy called interference alignment (IA) [13
]. It is a radical cooperative interference management strategy that has recently emerged through rigorous analysis of interference channels and networks. This approach exploits the availability of multiple signaling dimensions either from multiple antennas, time slots or frequency blocks as the case may be. The transmitters linearly encode their signals over these multiple signaling dimensions, such that the resulting interference signal observed at each receiver lies in a lower dimensional subspace and is orthogonal to the one spanned by the signal of interest at each receiver while the other subspace is reserved for interference free communication. This helps to achieve the interference channels maximum multiplexing gain, otherwise known as degrees of freedom (DoF) [16
]. DoF is an essential measurement used for capacity approximation. DoF is the amount of signaling dimensions, respective dimension corresponding to an interference-free additive white Gaussian noise (AWGN) channel with signal-to-noise ratio (SNR) that increases proportionally with the overall transmit power [18
The study of DoF initiated in ref. [19
] found surprisingly high DoF, as SNR approached infinity. The results of ref. [19
] in which users are able to transmit at a data rate equal to one-half of their capacity in an ideal interference-free channel motivated the work of refs. [17
], which presented the IA scheme in its linear form for the two user X-channel as a general principle. It was particularly interesting to see that the potential DoF that could be created largely depended on the alignment techniques involved. This implies that the signal space across the entire network nodes could potentially have numerous spatial dimensions as the overall number of transmit and receive antennas. However, achieving ideal signal alignment is a very complex task [19
] of which techniques such as message sharing in the manner of CR, beamforming, zero forcing and successive decoding may be combined in many different ways across users, data streams and antennas to establish inner bounds on the DoF [19
]. This overview will focus on the technique of message sharing.
The earliest work to explore the increase in DoF with message sharing in the manner of CR was done in refs. [20
] for both the multiple-input multiple-output (MIMO) interference and X-channels. This is because the CR network can be seen as an interference channel when the SUs coexist with the PUs and the SU transmission is subjected to the PU receiver threshold as well as the cross interference between the SUs themselves. Thus the IA strategy tends to as expected fit in with CR systems mechanisms of managing interference between the PU and SU [10
]. This work explored the impact of distributing a user’s information with other the user’s transmitter or receiver in that manner of singularity. In terms of performance, the DoF for the MIMO interference channel (IC) remained the same as without any form of cognition at either transmitters or receivers. Indeed, even this was a good enough result for further research bearing in mind that with all nodes having equal number of antennas, any increment on the number of antennas would yield higher data rates. However, the IC was shown to achieve higher DoF if both users have some form of cognition at the same time i.e., they either both make use of cognitive receivers, or they both make use cognitive transmitters or one has a cognitive transmitter although the other has a cognitive receiver.
A number of other practical IA algorithms have been developed in the manner of message sharing such as refs. [22
], but these have primarily been developed for the single-tier K-user IC where each transmitter has an intended receiver, and the remaining transmitters are considered as interferers for that receiver. Despite these studies focusing on single-tier systems, they have provided a significant research platform that has been translated into mainstream two-tier CR networks. From all the work done to further exploit this research subject, it has emerged that broadly speaking there are two main system models or paradigms in the design and implementation of IA in two-tier CR networks [24
The first paradigm considers a CR network having a number of SU pairs and a single PU-Tx and PU-Rx pair, where the PU-Tx is assumed far from its Rx and the SU-Rx’s are considered not to be influenced by the interference from the PU-Tx (which is somewhat similar to the direct spectrum sensing scenario [7
]). The main goal of this IA approach is to choose appropriate transmit precoding matrices and receiver interference suppression subspaces for the SUs to ensure that individual SU-Rx can decode their own signals while maintaining an allowable interference level to the PU within the specified threshold by minimizing the interference leaked into the received signal subspace. These matrices impose an upper limit on the interference temperature, short of the constraint on the amount of SUs. This optimization design is solved iteratively until the algorithm converges monotonically, where transmitters and receivers characterise the precoders and receiver subspaces by turns.
The second paradigm considers the same CR network as the first paradigm, but the SUs are in closer proximity to the PU-Tx (in the manner of indirect spectrum sensing [8
]). However, this paradigm proposes that under power-limitation, a PU that maximizes its own rate by using appropriate algorithms (usually water-filling algorithms) on its MIMO channel singular values might leave some of them unused, i.e., no transmission takes place along the corresponding spatial directions. These unused directions may be opportunistically utilized by one of the SU-Tx by designing an IA technique for the SUs, in which a linear pre-coder perfectly aligns the interference generated by the SU-Tx with such unused spatial directions, thereby enabling the SUs to share the licensed spectrum with zero interference to the PU transmission [24
]. An optimization scheme can also be designed to maximize the transmission rates of the SUs.
In this paper, our main objective is to provide a systematic overview on IA in CR communications and networking. We review the key system models/paradigms involved in the implementation of IA in CR networks and explain how these are crossly related. In particular, for each paradigm, we review various strategies for calculating alignment results and wide-ranging interference management techniques. It should be noted that these two paradigms are merely a representation of the direction of research on this subject because majority of the work done fall into either of the two. However, there are quite a number of other equally significant methods of implementing IA in CR that do not fall under the scope of either paradigm. Thus, this overview will include discussions on some of these other research endeavours, some practical implementations of this network model as well as future research challenges that remain in accomplishing IA in practical CR networks.
The remainder of this paper is organized as follows: Section 2
gives a brief introduction of IA principles, techniques and applications. Section 3
focuses on a CR network having a number of SU pairs and a single PU-Tx and PU-Rx pair, where the PU-Tx is assumed far from its Rx and the SU-Rx’s are considered not to be influenced by the interference from the PU-Tx. Section 4
considers the same CR network as the first paradigm in Section 3
, but the SUs are in closer proximity to the PU-Tx in the manner of indirect spectrum sensing. Comparison of research literature and analysis, computational complexity of different methods, observations and recommendations are presented in Section 5
. Section 6
presents open research challenges and lastly, Section 7
The definitions of the acronyms that will be frequently used in this paper are summarized in Table 1
for ease of reference.
5. Comparison of Research Literature and Analysis
This section present some of the results obtained from the research literature, and their analysis was based on achievable sum rates (bits/s/Hertz) of the SU systems and SNR (dB).
The first sets of results shown in Table 4
are for the achievable sum rates of the first paradigm. The sum rates for the leakage LIF algorithms are actually average values obtained from refs. [80
]. These results are strikingly similar despite the fact that the work in refs. [80
] assume perfect CSI while refs. [82
] take CSI estimation errors into consideration. This is an indication that LIF, is still very much a mitigating factor to achievable sum rates in the first paradigm, and as will be shown later, in the second paradigm as well. Even though not reflected in Table 4
, the values for sum rates when symbol extensions [93
] are used are much higher than the other techniques.
It should be noted that for ease of simplicity and analysis, this work only considered results with the minimal number of antennas at the PU and SU as well as the minimum DoF. Obviously, the higher the number of antennas, the higher the DoF and therefore the higher the achievable sum rates. Thus from the comparison of results in Table 4
and Figure 6
, the enhanced algorithms associated with the LIF technique perform better than the others enhancements, despite its effects on achievable sum rates.
considers the IA sum rate values for the second paradigm with SWF for the single SU scenario. Even though the sum rate results from the work in ref. [24
] are quite low, they do provide the basis for this paradigm and shows just how critical it is to not only identify TOs, but useable TOs for the system model to work. Thus, a lot depends on the methods adopted for optimizing the SU transmission rates. Of all the results obtained, the work in ref. [115
] that makes use of an intermediate relay was shown in Figure 7
, to achieve maximum sum rates, thus corroborating the benefit of incorporating relays in wireless systems [74
The work done on symbol extensions was a stark contrast to the first paradigm because of the sum rates achieved. The use of symbol extensions did not produce greater performance as it did with the first paradigm even though it had slightly marginal performance than ref. [24
]. This could be attributed to the fact that the power allocation method used for optimizing the SUs transmission is similar to ref. [24
], which has been established to be sub-optimal. Whilst the LIF technique was shown to have greater performance to other IA techniques in the first paradigm, it did not have quite the same effect in the second paradigm as seen in Figure 8
. This is due to the fact that the PU transmission is completely orthogonal to that of the SU, making the effects of LIF very minimal. It could be argued that the results comparison for LIF was similar across both paradigms, implying that however minimal, interference plays a significant role in wireless communications.
considers sum rate values for the second paradigm with SWF, for the multiple SU MIMO link. As was expected, the results from the feasibility condition technique of linear IA over constant MIMO channels were the most optimal sum rate values because of the feasibility condition defined in ref. [121
], which states that by counting the number of equations and the number of variables in the IA condition, the DoF can be analysed. This flexible approach to determine the feasibility of a network makes it easy to define a system as proper or improper, and does so with an improved iterative algorithm that has a faster convergence rate [123
shows the sum rate values for the second paradigm with ST-WF and MEB. It can be seen from both Table 7
and Figure 9
that the scheme used in ref. [127
] performs better than the other techniques despite the single SU scenario. The OIA schemes in refs. [69
] had similar performance in terms of sum rates largely because they both employed TBF to optimize the SU transmission, which is effective for saving the transmit energy in poor channel conditions and thus improving the spectrum efficiency of the SUs.
The proposed OFDM-VFDM scheme seems to increase the sum rate performance especially within the intermediate SNR range. On a wider scope, this scheme can simultaneously transmit more symbols for each SU than TDMA, and with the potential of extending the SU system to more than two cells, the spectral efficiency can only be improved.