Space Alignment for Cognitive Transmission in MIMO Uplink Channels
© Ioannis Krikidis. 2010
Received: 5 July 2010
Accepted: 2 November 2010
Published: 3 November 2010
This paper investigates a new transmission technique for cognitive access in multiple-input multiple-output (MIMO) uplink channels with waterfilling power allocation- (WPA-) based primary transmission. The proposed technique allows a cognitive node to access the common destination simultaneously with the primary node, without affecting the MIMO primary performance. By using an appropriate precoding design, the cognitive node aligns its transmitted signal to the unused primary eigenmodes and ensures an orthogonality between the primary and the cognitive links. In order to overcome the limitation of the conventional WPA at high signal-to-noise ratios, a modified WPA enables the primary node to release some eigenmodes in order to provide a positive cognitive rate for all the cases.
Cognitive radio (CR) is introduced as an efficient technique in order to use the radio spectrum more efficiently . It is characterized by the capability of the cognitive radios (secondary or unlicensed nodes) to coexist with the spectrum owners (primary or licensed nodes) and share the same frequency band in an opportunistic fashion. The opportunistic access enables the cognitive nodes to use the spectrum when it is idle (spectrum holes) and makes the CR network transparent to the primary network. However, for scenarios with high primary traffic, the number of spectrum holes becomes limited, and thus a positive cognitive data rate cannot be supported.
In order to overcome this limitation of the conventional CR concept, several approaches have been proposed in the literature. In , a dirty-paper coding (DPC) approach allows both the primary and the secondary nodes to simultaneously access the channel (interference channel) and protects the primary receiver from interference. However, the DPC design requires a knowledge of the primary signal at the CR as well as a global instantaneous channel knowledge which correspond to a high implementation complexity. On the other hand, in  the primary node exchanges its transmission silence with a cooperative (relaying) assistance from the cognitive node in order to increase both the primary and the cognitive performance. However, this approach requires a cooperation between primary and CR nodes which is not always possible in a "strict" cognitive context where the primary network is not aware of the CR nodes. Another approach incorporates the interference alignment concept [4, 5] with a multiple-input multiple-output (MIMO) waterfilling power allocation (WPA) [6, 7] in order to achieve orthogonality between primary and cognitive networks. This approach uses an appropriate precoding technique in order to align the cognitive transmitted signal to the unused eigenmodes of the primary channel. However, the original work in [6, 7] focuses on an interference channel (2 Tx-2 Rx) and cannot guarantee a cognitive transmission at high signal-to-noise ratios (SNRs), where the number of the unused eigenmodes is limited.
In this paper we extend the technique presented in  for a MIMO uplink channel with CR. An appropriate space alignment design enables the CR node to access the common destination simultaneously with the primary node without affecting the primary performance by using the unused primary eigenmodes. We show that due to the uplink topology the cognitive space alignment corresponds to a parallel symmetric Gaussian channel where the number of subchannels is equal to the number of unused primary eigenmodes. In addition, in order to ensure a positive cognitive data rate for high SNRs, a modified WPA that allows the primary node to control its transmitted power for each subchannel is proposed. We show that an appropriate power threshold can release some primary eigenmodes for cognitive transmission without significantly affecting the primary performance. The average achievable rate for both the primary and the secondary networks is evaluated via theoretical and analytical results. To the best of our knowledge the space alignment design for CR uplink channels as well as the modified WPA scheme are reported in this paper for the first time.
The rest of this paper is organized as follows. In Section 2 we present the system model, and we introduce the main assumptions required for our analysis. In Section 3 we describe the proposed CR space alignment design, and we discuss its achievable rate performance. Numerical results are shown and discussed in Section 4, followed by concluding remarks in Section 5.
Upper case and lower case bold symbols denote matrices and vectors, respectively. denotes the trace of a matrix , denotes the identity matrix of order , denotes the logarithm of base 2, represents the expectation operator, and the superscript denotes hermitian transposition operation.
2. System Model
As for the channel side information (CSI), we assume that both the primary and the secondary networks have a global knowledge of their channels (a similar assumption is considered in [2, 6, 7]). More specifically, we assume that the instantaneous primary channel is perfectly known at the nodes , and the receiver while the instantaneous secondary channel is perfectly known at the cognitive node . It is worth noting that although this assumption provides an upper bound on the achievable rate for both the primary and the cognitive networks, several techniques make this assumption reasonable: (a) in some contexts channel reciprocity can be exploited to acquire CSI at the transmitters (Time Division Duplex (TDD) mode), (b) feedback channels are often available in wireless communications (in several modern wireless standards, e.g., Long Term Evolution (LTE)), and (c) learning mechanisms  can be exploited to iteratively track the required CSI. The impact of an imperfect channel knowledge on the achievable rates is beyond the scope of this paper and will be considered for future investigation.
3. A Space Alignment Technique for Cognitive Access
In this section we introduce a space alignment technique that enables the cognitive node to communicate with the common destination , simultaneously with the primary node, without affecting the MIMO primary network. The performance of the system is determined in terms of the achievable data rate for both the primary and the secondary networks.
3.1. Primary Network
where , the parameter is chosen to satisfy the total power constraint , is a constant, and the noise power is equal to 1. In contrast to the conventional WPA technique, which corresponds to and maximizes the achievable rate, the introduced modified waterfilling policy gives the primary node the flexibility to control the power allocated at each eigenmode. More specifically, the system parameter depends on the degradation tolerance (maximum degradation level without affecting the required system quality of service (QoS)) that characterizes the system and enables the primary node to release some spatial directions without significantly affecting its performance (e.g., if , the release of the th spatial channel does not modify the achievable performance).
where denotes the maximum achievable primary rate corresponding to . Due to the iterative nature of the WPA , the above optimization problem can be solved by using a simple iterative algorithm that continuously increases (with a constant step) until the constraint in (7) is satisfied. Although a further theoretical analysis of is beyond the scope of this paper, an interesting remark holds for the high SNR regime. More specifically, given that the WPA converges to a uniform PA scheme at high SNRs, a parameter with (where ) ensures the release of primary eigenmodes for all the cases. The parameter is introduced as a critical system parameter, and its importance is evaluated via simulation results in the next section.
3.2. Primary Network
where the above expression is based on the ordered singular values of the matrix as well as the WPA applied on the primary network. The probability in (14) can be evaluated numerically, and its general closed form is beyond the scope of this paper. (For small values of a closed form expression is possible; for example, for , the joint probability density function of the ordered eigenvalues is  which results in .) It is worth noting that, due to the channel inversion that is involved in the cognitive precoder matrix in (10), the achievable cognitive rate is independent of the channel and the related fading/shadowing effects.
4. Numerical Results
Computer simulations were carried out in order to evaluate the performance of the proposed scheme. The simulation environment follows the system model of Section 2 and the adopted performance metric is the average data rate expressed in bits per channel use (BPCU).
A new cognitive transmission technique for MIMO uplink channels has been proposed. The new technique incorporates space alignment with WPA and results in an orthogonality between primary and cognitive transmissions. We have shown that a conventional WPA provides an efficient cognitive performance for intermediate SNRs but results in a zero cognitive data rate for high SNRs. A modified WPA that allows the primary node to release some eigenmodes without affecting its required QoS and ensures a positive cognitive data rate for all the cases has been also investigated.
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