- Research Article
- Open Access

# Cross-Layer Design in Dynamic Spectrum Sharing Systems

- A. Shadmand
^{1}, - K. Nehra
^{1}Email author and - M. Shikh-Bahaei
^{1}

**2010**:458472

https://doi.org/10.1155/2010/458472

© A. Shadmand et al. 2010

**Received:**15 January 2010**Accepted:**9 August 2010**Published:**15 August 2010

## Abstract

We consider a dynamic spectrum sharing system consisting of a primary user, whose licensed spectrum is allowed to be accessed by a secondary user as long as it does not violate the prescribed interference limit inflicted on the primary user. Assuming the Nakagami- block-fading environment, we aim at maximizing the performance of secondary user's link in terms of average spectral efficiency (ASE) and error performance under the specified packet error rate (PER) and average interference limit constraints. To this end, we employ a cross-layer design policy which combines adaptive power and coded discrete M-QAM modulation scheme at the physical layer with a truncated automatic repeat request (ARQ) protocol at the data link layer, and simultaneously satisfies the aforementioned constraints. Numerical results affirm that the secondary link of spectrum sharing system combining ARQ with adaptive modulation and coding (AMC) achieves significant gain in ASE depending on the maximum number of retransmissions initiated by the ARQ protocol. The results further indicate that the ARQ protocol essentially improves the packet loss rate performance of the secondary link.

## Keywords

- Primary User
- Secondary User
- Spectral Efficiency
- Secondary Transmitter
- Packet Loss Probability

## 1. Introduction

The rapidly growing demand for wireless services has led to deployment of the resource allocation approaches that not only provide higher data rates, but also enable the system to guarantee the quality of service (QoS) desired by various services. Cross-layer design has been considered as a promising candidate in this direction. Adaptive modulation and coding (AMC) at the physical layer is widely used to achieve high spectral efficiency (SE) [1–3], but it has to compromise between efficiency and reliability. On the other hand, the automatic repeat request (ARQ) protocol used at the data link layer increases reliability by retransmitting the erroneous packets. The systems exploiting joint design of AMC at the physical layer and ARQ at the data link layer enjoy high throughput with increased reliability as compared to those considering separate implementation of AMC and ARQ [4].

Along with efficiency and reliability, bandwidth is an important concern as the wireless applications become more and more sophisticated and widely used. However, the existing spectrum policies are not competent enough to cope with increasing spectrum access demand, and hence induce the shortage of available spectrum range. This is due to the fact that the outdated spectrum policies allow little or no sharing, and thus a large part of the useful spectrum remains idle at any given instant and location [5, 6]. The notion of spectrum sharing provides the means of efficient utilization of unused or underutilized parts of spectrum by enabling the unlicensed (secondary) users to exploit licensed (primary) spectrum bands with certain constraints on the interference imposed on licensed users.

Physical layer aspects of spectrum sharing systems have been sincerely studied in literature including [7–9]. The capacity of AWGN channels under received power constraints at the primary receiver for different scenarios, including relay networks, multiple access channels with dependent sources and feedback, and collaborative communication, was analysed in [7]. The authors in [8] derived the capacity and optimum power allocation schemes for different capacity metrics, for example, ergodic, outage, and minimum-rate in Rayleigh fading channels under average and peak received-power constraints at the primary's receiver. Spectrum sharing systems with an additional statistical delay QoS constraint along with the interference-power constraint at the primary receiver were studied in [9]. The authors determined the maximal possible arrival rate supported by the secondary user's link satisfying aforementioned constraints.

On the other hand, a substantial amount of work has been carried out in the direction of combined AMC-ARQ in the non spectrum-sharing scenario. In [4], a cross-layer design was developed combining constant-power AMC and truncated-ARQ protocol, with the aim of maximizing the spectral efficiency under target delay and packet loss constraints. Joint implementation of variable-power AMC and truncated-ARQ was proposed in [10], and it was demonstrated that combined AMC-ARQ with adaptive power outperforms that with constant-power in terms of ASE as well as packet loss rate. The authors in [11] presented power and rate adaptation policies for coded M-QAM modulation, in order to minimize the packet delay due to queuing at the data link layer, under the prescribed packet error rate constraint.

As per our best knowledge, cross-layer design combining AMC at the physical layer with the ARQ protocol at the data link layer has not been addressed so far in the context of spectrum sharing. In this paper, we study joint design of variable power AMC and truncated-ARQ protocol in the context of spectrum-sharing systems. Our aim is to devise maximum spectral efficiency of the secondary user's link under the constraints of interference-power at the primary receiver, and the target packet error rate.

The remainder of this paper is organized as follows. Section 2 presents the system and channel models, parameters used throughout the paper, and background of the problem addressed. Section 3 deals with the derivation of ASE of the secondary link subject to the specified constraints, and its packet loss probability. Numerical results are discussed in Section 4. Finally, the paper is concluded in Section 5.

## 2. System Model

We consider discrete-time block-fading channels for the secondary and primary users' links. The channel gains from the secondary transmitter to the primary and secondary receivers are, respectively, denoted by and . Both and are assumed to be stationary and ergodic with probability density functions (pdf's) and , respectively. Furthermore, both and are assumed to be independent and identically distributed (i.i.d.) processes, following the Nakagami- fading distribution with unit variance. The noise power spectral density and the received signal bandwidth are denoted by and , respectively; without loss of generality we assume for the simplicity of analysis [11]. Moreover, the knowledge of and is assumed to be available at the secondary transmitter. can be fed back from the secondary receiver to the secondary transmitter. can be fed back either directly from the primary receiver to the secondary transmitter or indirectly through a band manager which mediates between two parties [5].

where and denote the Nakagami fading parameters for and , respectively, , and refers to the Gamma function.

The parameters , and are transmission mode and packet-size dependent, and can be obtained by fitting the expression given in (3) to the exact obtained through simulation. The model corresponding to constant-power allocation at the secondary transmitter has been used and verified in [4].

## 3. Adaptive Coded Rate and Power Allocation with ARQ

In this section, we deal with the problem of maximizing the spectral efficiency of the secondary user under specified and average interference limit constraints. We start with determining the optimal SNR boundaries for AMC mode switching, in order to maximize the ASE under the aforementioned constraints.

### 3.1. AMC at the Physical Layer

where denotes the Gaussian hypergeometric function [12].

Value of the Lagrangian multiplier can be determined by substituting the boundary points in average interference constraint of (10) with equality sign. We use numerical methods to determine . Value of corresponds to the boundary points which satisfy the average interference constraint C1 of (10). By using maximum allowed limit ( ) in (11), becomes a function of , its pdf, and (which also can be fixed to a certain value depending upon the interference level allowed by the primary user). As shown in appendix, the optimization problem (10) is a convex optimization problem; therefore, the boundary points obtained in (14) are also optimal. Substitution of optimal boundary points in (4), and (7) yields the optimum ASE and optimum power allocated in th transmission mode, respectively. Calculation of adaptive power from (7) requires values along with the boundary values of . Based on our initial assumption of availability of at the secondary transmitter, transmit power in the th mode can be easily determined.

### 3.2. Power Adaptation and AMC Combined with ARQ

where is the maximum acceptable packet loss probability.

### 3.3. Truncated ARQ without AMC

## 4. Numerical Results

This section presents numerical results based on the analytical expressions derived in Section 3, to quantify the performance gain of the proposed scheme in terms of overall spectral efficiency and error performance. The analytical expressions have been developed for the Nakagami- block fading channel links and . However, to generate the numerical results, in this section we consider two specific cases of the Nakagami distribution namely, , which is nothing but the Rayleigh distribution, and . Adopting the approximation parameters of six-mode AMC scheme for packet length from [4, Table ], we choose the maximum allowed packet error probability for the secondary link as . The approximation parameters are determined by the AMC mode chosen corresponding to the random variable , which is the ratio of channels gains. We compare ASE resulting from optimized AMC-ARQ for the secondary link under average interference power constraint, with channel capacity of the corresponding distribution derived in [16].

## 5. Conclusion

In this paper, we developed a cross-layer design scheme in a dynamic spectrum sharing system consisting of single primary and secondary users. We considered a spectrum sharing scenario, where the secondary user can operate within the primary user's licensed spectrum, provided that the average interference power inflicted at the primary receiver does not exceed a certain average threshold. The secondary transmitter exploited cross-layer design by employing discrete AMC with adaptive power control at the physical layer, and the truncated-ARQ protocol at the data link layer. We determined AMC mode switching levels of , in order to maximize the performance of the secondary link in terms of ASE and error performance under the specified packet error rate (PER) and average interference limit constraints. Numerical results verified that the secondary link of the considered system combining ARQ with AMC achieves significant gain in ASE depending on the maximum number of retransmissions initiated by ARQ protocol. The results further lead to the conclusion that increasing the number of retransmissions improves packet loss rate probability performance of the secondary link.

## Appendix

where is given by (2). We introduce the following lemma.

Lemma 1.

For a Nakagami-m fading pdf, is a sufficient condition for convexity of both the function and constraint function in (10).

Proof.

Since , the first term in the R.H.S of (29) is positive. From discussion on convexity of function, we know that when , we have , and therefore, the second term in R.H.S of (29) is also positive and consequently , and hence function is convex.

## Authors’ Affiliations

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## Copyright

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.