Modulation and coding toolbox specifications.
Data traffic over wireless communication networks has experienced a tremendous growth in the last decade, and it is predicted to exponentially increase in the next decades . Enabling future wireless networks to fulfill this expectation is a challenging task both due to the scarcity of radio resources (e.g. spectrum and energy), and also the inherent characteristics of the wireless transmission medium. Wireless transmission is in general subject to two phenomena:
Conventional interference management strategies including time-division multiple access (TDMA) and frequency-division multiple-access (FDMA) avoid the inter-user interference by allocating orthogonal resources in time and frequency to different users, respectively. Interference 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
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 for the experimental verification of the novel interference management algorithms.
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 scheme in Section 7. Finally, Section 8 concludes the chapter.
K-user ( K>2) interference networks
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
Specifically, interference alignment for interference networks refers to “
Interference alignment can be realized in different domains such as space (across multiple antennas , ), time (exploiting propagation delays ,  or coding across time-varying channels , ), frequency (coding across different carriers in frequency-selective channels ), and code (aligning interference in signal levels ). Combinations of domains can also be used e.g. space and frequency, . In the following, we briefly introduce
2.1. Degrees of freedom region
3. Practical challenges of interference alignment
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
At the receiver side,
3.1. Channel training for interference alignment
In practice, destinations can acquire CSI through a pilot-based channel training scheme. For example, consider block fading channel model in which channel gains are constant within one fading block and change to independent values in the subsequent blocks. The length of each block coincides with the coherence time of channel denoted as
Terminals first need to learn the channels within each fading block, and next use the estimated channels to perform their transmission. A pilot-assisted interference alignment scheme is proposed in  which perform these tasks. According to this scheme, transmission within each fading block is conducted in two phases:
A more accurate estimation of the channel can be obtain by allocating more transmission power for training symbols which implies that a lower power is left for data transmission. The achievable rate region by taking into account this noisy CSI is computed in . According to Proposition 2 in , the optimum power allocation which maximizes the achievable rate region is
This result recommends that in large networks more power should be allocated to the channel training instead of the data transmission. The intuition behind this result is that in large networks the performance loss due to imperfect interference alignment as a consequence of imperfect CSI becomes more important. Thus, it is recommended to allocate more power to pilot symbols instead of data symbols to acquire CSI more accurately.
3.2. Channel state information feedback
As we have discussed in the previous section, destinations can acquire CSI through a pilot-based channel training scheme. The destinations then can send the estimated CSI to the sources via channel state feedbacks. They can transmit either un-quantized CSI (analog feedback) or quantized CSI (digital feedback) via feedback channels. In the following, we briefly review some key results for different type of feedback schemes.
This result is achieved when the number of the users selected to be active is
This recommends that, in large networks (
3.3. Iterative interference alignment
In this part we present an iterative algorithm referred to as
where each element of the vector represents an independently encoded Gaussian codeword with power . Each codeword is beamformed with the corresponding column of
If global CSI is available, the beamforming and filtering matrices can be designed such that these conditions are satisfied. However, with the lack of global CSI if we choose the beamformers and the filters randomly, with high probability only the second condition in (10) will be satisfied. Consequently, some interference remains at the destinations. The total power of interference at D
is the covariance matrix of interference at D
The solution is given in :
where denotes the
To optimize the transmitter-side beamformers the reciprocity of the channels can be exploited to obtain CSI at sources. For instance, destinations can transmit training sequences over the
4. Review on test-bed implementation of interference alignment
The idea of squeezing aligned interference signals into half of the signal space and accessing the other half of the signal space for desired transmission in an interference network is so tempting that a large body of works has been done since the introduction of interference alignment to implement this elegant approach, for instance look at , [18-26].
The first implementation of interference alignment is reported in . A hybrid version of interference alignment combined with the successive interference cancellation (IAC) in a single carrier narrow-band MIMO wireless local area network (WLAN) is tested in this paper. Several interference alignment and interference alignment-like approaches are tested in MIMO-OFDM interference channels in . This paper specifically studies the effects of poor channel conditions on the performance of interference alignment. Real-time implementation of different interference alignment scenarios are performed on different test-beds like the ones in [21-23].  identifies practical issues that degrades the interference alignment performance such as channel estimation errors or collinearity between the desired signal and interference subspaces while in , in Vienna MIMO test-bed (VMTB), the typical delay is measured.
Implementation of interference alignment in frequency domain over measured channels is considered in  where the different variants of interference alignment are compared with frequency planning scenarios. The significant superiority of interference alignment performance in terms of average sum rate is reported at high SNRs in this paper.
In all previously mentioned papers, the effects of hardware impairments are ignored. In , the effects of such impairments on the performance of interference alignment and coordinated multi-point CoMP is an approach similar to interference alignment with this main difference that in CoMP all the sources know the information to be transmitted to all destinations.
CoMP is an approach similar to interference alignment with this main difference that in CoMP all the sources know the information to be transmitted to all destinations.
5. KTH four-multi test-bed setup
5.1. Hardware setup
The current version of the test-bed consists of six nodes where three of them are fixed and take the role of transmitting sources while the other three are movable receiving destinations. All the nodes are equipped with two vertically polarized dipole antennas spaced 20 cm apart which is 1.6 times of the carrier’s wavelength. Twelve Ettus Research USRP N210 (see www.ettus.com) are used to govern the twelve antennas in the network. The source USRPs are equipped with the standard Ettus XCVR2450 RF dautherboards while the destination USRPs use custom boards to achieve sufficient noise figure and dynamic range. The output signal of each source USRP is amplified by a ZRL-2400LN power amplifier. Two Linux computers control all the USRPs in the network. The network structure of KTH four-multi test-bed is illustrated in Fig. 3.
The network is designed to work at 2.49 GHz center frequency with 12 MHz bandwidth. Synchronization of the network is performed in three levels, namely time, frequency and transmit-receive synchronizations. The time and transmit-receive synchronizations are done by means of a pulse-per-second (PPS) signal (0-5 V, 1 Hz square wave) and a national marine electronics association (NMEA) signal (an ASCII protocol that provides hour-minute-second time), respectively. Both signals are generated by an EM406A GPS module and distributed through the network. The frequency synchronization is also performed by helps of 10 MHz reference clocks (CLK). All the source’s local oscillators are locked to the same clock while a separate clock is provided for each of the destinations. In a real implementation the same synchronization would be achieved using common control and synchronization channels (cellular systems) or from the burst preambles (wireless local area networks). In a system with interference alignment, transmitter will in any case need some kind of back-haul to provide a common time reference and disperse scheduling decisions.
5.2. Software setup
The four-multi software framework has been developed in C++(see http://fourmulti.sourceforge. net/). It runs on two Linux computers separately. One of the computers controls the three source nodes while the other one controls the three destination nodes connected to them via Ethernet connections. The sources’ computer generates the transmitted frames and feeds them to the source nodes while the destinations’ computer process the received frames at the destination nodes. A TCP/IP connection between the source and the destination computers provides the feedback links. Backhaul communication among the source nodes is also implemented by the help of TCP/IP connections between the source computer and the source nodes.
The framework contains a toolbox for coding and modulation (AMC and OFDM1) which was used in the implementations of the next two sections. The KTH four-multi Modulation and coding toolbox includes an LDPC channel encoder/decoder, a QAM modulator/demodulator and an OFDM modulator/demodulator. The specification of these built-in functions is summarized in Table 1.
|FFT length||80||Coding rates||1/2, 5/8, 3/4|
|Cyclic prefix length||12||Codeword length||1520|
|Number of null subcarriers||42||QAM modulation orders||4, 16, 64, 256|
|Subcarrier spacing (KHz)||312.5|
6. Test-bed implementation of the iterative transceiver filter design and power control
We, in this section, first present an iterative algorithm for joint transceiver filter design and power control proposed in  and then explain how this algorithm is implemented on KTH four-multi test-bed and finally present measurement results.
6.1. Iterative transceiver filter design and power control algorithm
In an interference network, each user can affect the received SINR at its corresponding destination through the choice of beamforming and receiving filters as well as the transmitting power. Considering single stream transmissions, the received SINR at the
where is the minimum required SNR in an AWGN channel. The total power of the interference,
Inspired by Max-SINR algorithm and the aforementioned power control algorithm, an iterative transceiver design and power control algorithm was proposed in . A brief version of the algorithm is presented on the next page for the sake of completeness. The algorithm is composed of three update phases in each iteration such that the receiving filters, transmission powers and beamforming filters are sequentially updated. The receiving and beamforming filters are optimized to deliver the maximum SINR at the destinations in the forward communication direction and at the sources in the reverse direction, respectively according to the concept of Max-SINR algorithm. On the other hand, in the power update phase, the powers are set to the minimum values needed for maintaining a fixed rate communication. The transmission power is upper bounded by
Set beamforming vector and
6.2. Transmitted frame structure
The air interface of the network is designed based on OFDM modulation using KTH four-multi’s modulation and coding toolbox. Coding rate of 1/2 and 16QAM modulation was chosen for transmitting fixed-rate data streams though the air interface. The transmitted frame structure is depicted in Fig. 4. In our experiment, each frame consists of 20 payload symbols and either two or three reference signals (RS) (i.e. pilot symbols). The payload symbols are
Three types of RS are employed in the network, which are referred to as
CSI-RS: The received noisy CSI-RS at the destinations are exploited to estimate the corresponding channel matrices to enable execution of Algorithm 1. The CSI-RS are transmitted
DM-RS: The DM-RS are used to compute the effective channel by taking into account the transmit and receive filters. Therefore they need to be stream-dedicated and be processed by the same pre-coder as the payload symbols of the corresponding stream. In this way, their power is not fixed and is set by the power control algorithm.
P-RS: Algorithm 1 is constructed to select the minimum possible transmission power to minimize the interference at the destinations. This hence reduces the power of DM-RS and may lead to a poor estimation of cross-channels, which is not favorable. To tackle this problem, P-RS is introduced where the amplitudes of the CSI-RS are scaled after the pre-coder by a scaling factor α. In each frame, the scaling factor is computed as
6.3. Measurement results
The test-bed measurement was performed in KTH signal processing department which floor map is illustrated in Fig. 5. The measurement environment is categorized as an indoor office. In this experiment only non-line-of-sight (non-LOS) scenarios were investigated by placing source and destination nodes in the corridor and inside the nearby offices, receptively. The receive antenna gains also decreased by connecting 10 dB attenuators to them in order to avoid saturation of receive power amplifiers. The measurement was done in 100 batches. In each batch a random placement of the destination nodes in the area marked by colored circles in the figure were measured. The signals transmitted according to two different schemes were measured sequentially in each batch. In the first scheme, referred to as
High power may push the terminals’ power amplifier to work in their non-linear region. Non-linearities in the transmit-receive chain degrades the performance of the system by introducing
Table 2 shows the average performance of the two schemes for the 100 measurement batches. In this measurement the PC scheme’s target SINR
|Average power (dBm)||-12.9||-3.4||1.1||7.1||-1|
|BER||0.0815||0.0124||0.0020||0.0030||2.2 × 10−4|
|Average SINR (dB)||10.9||20||24.3||26.7||18.5|
Empirical cumulative distribution function (CDF) of the received SINR for two schemes is plotted in Fig 6. This plot reveals the reason for the low BER of PC scheme, despite its low transmit power. The received SINRs in this scheme are concentrated around the target value while in the noPC scheme they are distributed over a wider range. Having SINR higher than the target value while the transmit rate is fixed leads to the waste of energy and on the other hand SINRs lower than the target increase the probability of error and therefore the BER.
The benefit of power control in the PC scheme is in fact two-fold. By decreasing the transmit power, while retaining the target SINR, not only less interference is received at the destinations but also the distortion noise due to transceiver impairments decreases.
7. Test-bed implementation of the interference alignment with compressed feedback
In this section we describe the implementation of interference using limited digital feedback (see Section 3.2). Rather than using a uniform quantizer, we use a modified form of the MIMO matrix compression of the IEEE802.11ac standard. The propagation scenario and test-bed is the same as the one used in Section 6 i.e. a system with three (
The section is organised as follows. Section 7.1 describes the feedback compression of the CSI assuming a system with
7.1. Compression of IEEE802.11ac and adaptation to interference alignment
The feedback scheme described in the standard IEEE802.11ac resembles the feedback method for slowly time-varying single-user MIMO channels presented in . In this scheme a singular value decomposition (SVD) of the MIMO channel
The destination then feeds back, in compressed form, the complex unitary matrix
In the case of centralised interference alignment, knowledge of the channels between all sources and destinations is required to obtain all the beamformers
To overcome this problem, in the system implementation we have based the feedback from destination
Thus destination Dk now feedback a compressed version of the right-hand side eigenvectors of
The size of matrix
The IEEE 802.11ac feedback compression scheme starts by rotating the phase of the columns of
Since we use OFDM there is one
The number of bits can be reduced by a further (
Since the signals from source,
The elements of
A practical problem which occurred during the early experimentation was that the SNR sometimes exceeded 53.75 dB. This happened due to the high transmission power and short range. First this was handled by reporting the maximum value 53.75 dB whenever this happened. However, this resulted in making the reconstructed channel at the transmitter high-rank although the estimated channel at the receiver were in fact low-rank-which was very detrimental to the performance. To circumvent this problem, an offset is subtracted from SNR values when this condition happens.
In addition to interference alignment By interference alignment we are here referring to the modified form of interference alignment known as Max-SINR, see Section 3.3. However, measurements we have performed have shown that the performance difference between the original interference alignment and Max-SINR is neglible in our scenario.
By interference alignment we are here referring to the modified form of interference alignment known as Max-SINR, see Section 3.3. However, measurements we have performed have shown that the performance difference between the original interference alignment and Max-SINR is neglible in our scenario.
When the channel is changing the performance of interference alignment will inevitably be degraded due the channel mismatch between the channel at the feedback time and the channel at the actual transmission. The amount of degradation depends on the time delay and the level of movement in the environment. In  using measurements we showed that the throughput of interference alignment dropped 6.4% when two passers-by were walking in the measurement environment and the feedback delay interval was 23 ms. With this delay interval the overhead of performing the feedback scheme above with Ng=8 is 2.5%, assuming that the feedback scheme of IEEE802.11ac is used.
The channel may also change due to the existence of the users at the destinations. This effect was studied by measuring the performance with and without a user located close to the destination nodes. The results were obtained using eight destination positions. The performance of interference alignment dropped 4.9% while the performance of single-user MIMO was unaffected.
These results show that interference alignment can still deliver a net performance gain of sum throughput some 15% over single-user MIMO in a WiFi scenario with three access points and three users, even when feedback overheads and mobility is taken into account.
We have reviewed the concept of interference alignment, with theoretical results regarding power and time allocation between training and payload data transmission, and previous works within experimentation on interference alignment. We further present implementation efforts addressing the combination of iterative interference alignment and power control and using compressed channel state feedback based on a modified form of the MU-MIMO feedback scheme of IEEE802.11ac. Our experimental results show that the iterative interference alignment and power control scheme is able to provide better FER/BER performance (16QAM code rate 0.5), than an implementation without power control. The results using the modified IEEE802.11ac feedback scheme, show that interference alignment can bring an improvement in throughput when considering the loss of bandwidth needed for feedback of the channel state information even for channels with realistic indoor mobility.
The research leading to these results has received funding from Swedish Foundation for Strategic Research (SSF) under RAMCOORAN project and ACCESS Linnaeus Center under graduate course wireless experimentations. The measurements were performed within the framework of the HIATUS project. The project HIATUS acknowledges the financial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission under FET-Open grant number: 265578.
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- CoMP is an approach similar to interference alignment with this main difference that in CoMP all the sources know the information to be transmitted to all destinations.
- By interference alignment we are here referring to the modified form of interference alignment known as Max-SINR, see Section 3.3. However, measurements we have performed have shown that the performance difference between the original interference alignment and Max-SINR is neglible in our scenario.