**2.** *K***-user (***K***>2) interference networks**

Consider a *K*-user (*K*>2) interference network. Several techniques have been devised for interference management in multi-user interference networks. Three major approaches to deal with interference are illustrated in Fig. 1. In Fig. 1 (a) all sources simultaneously transmit their signals in the same frequency band. Each source applies the conventional single-user coding technique. At each destination, the desired signal is superimposed by interference signals. The destination performs decoding by treating the interference signals as noise. This strategy is reasonable for cases that the receiver only knows the transmitted codebooks of the intended source. In the low signal-to-noise ratio (SNR) region, the level of interference can be controlled by proper power control techniques. However, in the high-SNR regime, inter-user interference is dominant. Therefore, the power control alone is not sufficient to manage the interference and this transmission strategy may not lead to a desirable performance.

allocating orthogonal resources in time and frequency to different users, respectively. Inter‐ ference is consequently avoided at the cost of low spectral efficiency. Thus, it was believed that the performance of wireless networks is limited by interference in general. However, the elegant *interference alignment* concept [3], [4] reveals that with proper transmission signalling design, different interference signals can in fact be aligned together, such that more radio resources can be assigned to the desired transmission. For instance, in the case of a multi-user interference network with more than two source–destination pairs, the interference signals at each destination can be aligned such that maximally half of the signal space can be left to its desired signal [4]. Therefore, each user may achieve half of the interference-free transmission rate no matter how many interferers exist [4]. Although interference alignment can achieve a larger data rate compared to orthogonal transmission strategies, several challenges should be addressed to enable the deployment of this technique in future wireless networks [1], [5]. For instance, to perform interference alignment, normally, global channel state information (CSI) is required to be perfectly known at all terminals. Clearly, acquiring such channel knowledge is a challenging problem in practice and proper channel training and channel state feedback techniques need to be deployed. In addition, since the channels are time-varying proper

To investigate whether the outstanding performance of signal processing algorithms inspired by interference alignment can be preserved in real environment, practical verifications is needed. Wireless test-beds (e.g. the ones based on USRP or WARP) can be used as a platform

This chapter review recent advances in practical aspects of interference alignment. It also presents recent test-bed implementations of signal processing algorithms for the realization of interference alignment. In Section 2 we give a brief overview on the interference alignment concept. Section 3 presents the structure of a canonical transmitter and receiver to realize interference alignment, and discuss channel training and channel state feedback for these systems. A brief review on test-bed implementations of interference alignment solutions is presented in Section 4. Section 5, introduces hardware and software setup of the test-bed used in this chapter for implementation of interference alignment. The test-bed implementation of iterative transceiver design and power control algorithm is presented in Section 6. We discuss the test-bed implementation of compressed feedback scheme for interference alignment

Consider a *K*-user (*K*>2) interference network. Several techniques have been devised for interference management in multi-user interference networks. Three major approaches to deal with interference are illustrated in Fig. 1. In Fig. 1 (a) all sources simultaneously transmit their signals in the same frequency band. Each source applies the conventional single-user coding technique. At each destination, the desired signal is superimposed by interference signals. The destination performs decoding by treating the interference signals as noise. This strategy is

for the experimental verification of the novel interference management algorithms.

scheme in Section 7. Finally, Section 8 concludes the chapter.

**2.** *K***-user (***K***>2) interference networks**

adaptive transmission is needed.

52 Contemporary Issues in Wireless Communications

**Figure 1.** Transmission schemes in three-user interference networks: (a) non-orthogonal transmission and decdoing by treating interference as noise, (b) orthogonal transmission, and (c) interference alignment.

The conventional approach to avoid interference at destinations is to orthogonalize the transmissions of different users. Each source–destination pair has access to only a portion of the available channel, as shown in Fig. 1 (b). Although signal reception at each destination does not directly suffer from inter-user interference, this scheme is not spectrally efficient due to the fact the resource; i.e. time or bandwidth, are divided among the source–destination pairs. From Fig. 1 (b), we see that the interference signals span a large dimension of the received signal space at each destination to ensure orthogonal reception. However, if at each destination the dimension of the subspace occupied by only the interference signals can be reduced, a larger interference-free subspace would be left for desired transmission. This can be realized using a new technique called *interference alignment* [3].

Specifically, interference alignment for interference networks refers to "*a construction of signals in such a manner that they cast overlapping shadows at the receivers where they constitute interference while they remain distinguishable at the intended receivers where they are desired*" [4]. In general, two conditions should be satisfied to perform interference alignment technique. First, interference signals should be aligned at the same subspace, termed *interference subspace*. Next, we need to check whether the subspace left for the desired signal, called *desired subspace*, is independent from the interference subspace. The conditions are essentially required for the realization of the interference alignment techniques. An illustrative representation of this concept is shown in Fig. 1 (c).

Interference alignment can be realized in different domains such as space (across multiple antennas [3], [4]), time (exploiting propagation delays [6], [7] or coding across time-varying channels [4], [8]), frequency (coding across different carriers in frequency-selective channels [9]), and code (aligning interference in signal levels [10]). Combinations of domains can also be used e.g. space and frequency, [11]. In the following, we briefly introduce *Degrees of Freedom (DoF)* which is a performance measure for wireless networks at high-SNR regime.

#### **2.1. Degrees of freedom region**

Consider the *K*-user interference network in Fig. 1. Source S*k* (*k* ∈ {1, 2,..., *K*}) intends to send an independent message w*<sup>k</sup>* ∈ W*k* to its destination, where W*<sup>k</sup>* denotes the corresponding message set. The message |wk | is encoded to a codeword of length N. Thus, the corresponding code rate is Rk<sup>=</sup> log <sup>|</sup> wk | n where |wk | denotes the cardinality of |wk |. The rate tuple (*R*1, *R*2,..., *RK*) is said to be achievable if a sequence of codebooks exists, such that the probability that each destination decodes its message in error can be arbitrarily small, by choosing long enough codewords. The capacity region of the network is the closure of the set of all achievable rates. In Gaussian interference networks where the noise is additive white Gaussian, the capacity region depends on the transmission powers of sources, the noise powers and channel gains. Since the exact capacity region is difficult to find, as a starting point one can use the DoF region to characterize/approximate the capacity/achievable rate region in the high-SNR region (where interference is the dominant phenomenon that degrades system performance). The DoF region is defined as follows

$$\mathbf{D} = \left\{ (d\_1, \dots, d\_K) \in \mathbb{R}^+ \mid \exists (\mathcal{R}\_1, \dots, \mathcal{R}\_K) \in \mathbb{Q}(P), d\_k = \lim\_{P \to \infty} \frac{\mathcal{R}\_k}{\log P}, 1 \le k \le K \right\},\tag{1}$$

5

where *C(P)* denotes the capacity region, and P is the transmission power of each source. The DoF can be seen as the pre-log factor of the achievable rate and the DoF region describes how the capacity region expands as transmission power increases.

III. PRACTICAL CHALLENGES OF INTERFERENCE ALIGNMENT

signal for transmission over the channel according to the interference alignment concept.

receiver and the transmitter. In the following, we will explain these parts in more detail.

October 14, 2014 DRAFT

At the receiver side, *channel estimation* module computes the estimation of incoming channel gains. These channel estimations can be used for recovering the transmitted message and computing the channel state information feedback signal. The *filter* module exploits estimated channel gains to recover the desired signal from interference signals according to the interference alignment concept. The *decoder* module decodes the message using an estimate of the incoming channel gain. The feedback encoder module denoted by 'f' in Fig. 2 computes the feedback signal according to the estimated channel gains. Also, there is a *synchronizer* module at the receiver to synchronize the

The structure of a canonical transmitter and receiver for the implementation of interference alignment is shown in Fig. 2. At the transmitter side, there is an *encoder* which encodes the messages to the corresponding codewords suitable for transmission over the channel. The transmission can be enhanced by the adaptation of the transmitted signal according to the received channel state infomation feedback. Specifically, in a class of communication systems that transmission powers are fixed and a maximum throughput is desired, the encoder may adapt transmission rate according to the estimate of the mutual information of the channel (computed by the *rate adaptation* module). On the other hand, in another class of systems which desire fixed-rate transmission, *power control* module should adjust transmitted power according to the channel state feedback to maintain mutual information of the channel larger than a certain level. Each transmitter has a *beamformer* which compute the proper

Fig. 2: Transmitter and Receiver Structure. **Figure 2.** Transmitter and Receiver Structure.

region expands as transmission power increases.
