**Joint-Design Of Link-Adaptive Modulation And Coding With Adaptive ARQ For Cooperative Amplify And Forward Relaying System**

Bhuvan Modi, O. Olabiyi and A. Annamalai

Center of Excellence for Communication Systems Technology Research, Department of Electrical and Computer Engineering, Prairie View A & M University, TX 77446 United States of America

**Abstract**

* *This paper analyzes the efficiency of a joint-design of an adaptive modulation and coding (AMC) at the physical (PHY) layer with an adaptive R^{max}-truncated selective-repeat automatic repeat request (ARQ) protocol at the medium access control (MAC) layer to maximize the throughput of cooperative non-regenerative relay networks under prescribed delay and/or error performance constraints. Particularly, we generalize the existing design model/results for cross-layer combining of AMC along with truncated ARQ in non-cooperative diversity networks in three-folds: (i) extension of the cross-layer PHY/MAC design or optimization to cooperative diversity systems; (ii) generalization/unification of analytical expressions for various network performance metrics to generalized block fading channels with independent but non-identically distributed (i.n.d) fading statistics among the spatially distributed nodes; (iii) analysis of the effectiveness of joint-adaptation of the maximum retransmission limit R^{max} of ARQ protocol and cooperative diversity order N for delay-insensitive applications. Our insightful numerical results reveal that the average throughput can be increased significantly by judiciously combining two additional degrees of freedom (N and R^{max}) that are available in cooperative amplify-and-forward (CAF) relay networks besides employing AMC at the PHY layer, especially in the most challenging low signal-to-noise ratio (SNR) regime.

*Keywords*

cross-layer design, adaptive retransmission, cooperative relay diversity, adaptive modulation and coding.

**1.Motivation**

It is well-known that the link adaptation techniques (e.g., adaptive modulation/coding) could dramatically enhance the spectral utilization efficiency of wireless networks that employ “fixed-transmission” methods. But to improve the transmission reliability/robustness at the physical (PHY) layer, one has to either increase the transmit power (thereby, decreasing the battery-life) or to reduce the transmission rate (e.g., by selecting a smaller constellation size or decreasing the code rate of forward error correction coding). Additionally, spatial/polarization diversity solutions at the physical layer (by employing multiple antenna elements at the transmitter and/or receiver) may not be reasonable on small-sized handheld portable devices or sensor nodes.An alternative way to mitigate the deleterious effects of a multipath fading is to exploit “diversity” mechanisms at higher layers of the protocol stack. For instance, ARQ is an effective strategy to achieve a high reliability of packet transmissions at the data link layer (especially in slowly time varying channels) and unlike FEC, the redundancy (packet retransmissions) are only introduced, when necessary.Similarly, the number of collaborating nodes in a CAF relay network (i.e., distributed spatial diversity order) could be increased to satisfy the prescribed average packet error rate constraint (but the reliability improvement is attained at the expense of the network capacity owing to the half-duplex operation of CAF relay networks, although this technique could overcome the practical implementation issue of packing multiple antenna elements on small-sized sensor nodes).Instead of considering AMC at the PHY layer, ARQ at the data link layer, and cooperative diversity at the network layer separately in this article, we pursue a cross-layer design that combines these three layers judiciously to maximize the spectral efficiency or throughput subject to delay and/or error performance constraints. Cross-layer design approach breaks away from conventional network design, where each and every layer of the protocol stack is optimized and operates independently. In particular, we exploit the channel knowledge at transmitter and explore the potential synergies between different protocol layers to maximize the end-to-end throughput while satisfying the prescribed delay and average packet error rate (APER) constraints. For example, by achieving a higher packet success probability with the help of cooperative diversity and ARQ, the stringent error control requirement is improved for the AMC at the PHY layer. This enables a considerable spectral efficiency gain especially in the low SNR regime. Given the maximum allowable number of retransmissions *R*^{max} (that depends on the delay constraint) in a CAF relay network, we design AMC transmissions that guarantee the required APER performance. The benefits of adapting *R*^{max }and the number of cooperating relay nodes are also investigated.

**1.1 Literature Review/Prior Work**

While the literature on performance analysis of non-adaptive (i.e., fixed-rate and/or fixed-power) cooperative diversity systems and adaptive transmission techniques for non-cooperative wireless networks are quite extensive that span over four decades, most prior focused only on the improvement of the link layer performance. The art of adaptive link layer for cooperative wireless networks especially in a cross-layer design framework is still in its infancy. For instance, in [1]-[3] (and references therein), the authors have studied extensively the design and implementation of AM and coding at the PHY layer, wherein the transmission rates are matched to the time-varying channel conditions in a non-cooperative wireless system. Author in ref. [4] investigates the efficiency of a truncated ARQ protocol scheme for a cooperative amplify-and-forward system with fixed modulation. Authors in ref. [5]-[9] have considered Adaptive Modulation and/or optimal power allocation amongst collaborating nodes in cooperative relay systems. Whereas authors in ref. [10] studied the effectiveness of cross-layer combining of the ARQ and the AMC for non-cooperative diversity systems in a Nakagami-m fading channel. Authors in [11] analyzed the performance of a cross layer design in terms of spectral efficiency, which combines cooperative diversity with truncated ARQ in Ad-hoc wireless networks, but without link adaptation in the Rayleigh fading channel. Ref. [12],[13] studied the spectral efficiency analysis of Joint AMC and Cooperative ARQ for a single incremental relay in the Rayleigh fading channel. In [14], authors considered a cross-layer combination of a cooperative hybrid ARQ with adaptive modulation in wireless ad-hoc networks by assuming a single retransmission request under the Rayleigh fading environment.Motivated by above observations/discussions, our contributions in this paper can be summarized as follows.

1.Motivated by the appreciable improvement in the data link layer throughput by judiciously combining a truncated ARQ protocol with adaptive modulation and coding (AMC) over the simple concatenation of ARQ to fixed modulation/coding schemes, we consider a design methodology similar to [10] but with two additional degrees of freedom for providing the desired level of rate-reliability trade-off via cooperative diversity and adaptive *R*^{max } In addition, we developed a novel unified analytical framework (based on the marginal MGF of the end-to-end SNR) to compute the average spectral efficiency, outage probability and APER performance metrics over fading channels (viz., since the MGF of the end-to-end SNR is much easier to compute and/or readily available for CAF relay networks compared to its probability density function, while the marginal MGF can be computed efficiently using this MGF in conjunction with Fixed-Talbot method [15]). Our proposed mathematical framework is satisfactorily general to exemplify the performance of adaptive-link non-regenerative relay networks over a extensive range of fading distributions (i.e., it is not only restricted to the Rayleigh or independent identically distributed (i.i.d) Nakagami-m fading channel) with independent and non-identically distributed (i.n.d) fading statistics across the spatially distributed diversity paths and can be efficiently apply to the wireless system composed of large number of relays.

2.Moreover,we propose an interesting approach for maximization of throughput by joint adaptation of two parameters, one with cooperative diversity order *N* and second with adaptive *R ^{max}* scheme (see Fig. 8). To the best of our knowledge a similar approach which focuses on throughput optimization by jointly adaptation of both

Figure 1. System Model: Link-adaptive cooperative diversity system with ARQ technique[1]

**2. SYSTEM MODEL**

**2.1 COOPERATIVE DIVERSITY MODEL**

Figure 1 shows combined link-adaptive and ARQ based cooperative diversity system with a source node S communicates with a destination node D via a direct-link and through N amplify-and-forward relays, Ri, in two transmission phases. During the initial Phase I, S broadcasts signal x to D and to the relays Ri, where channel fading coefficients between S and D, S and the i-th relay node Ri, Ri and D are denoted by , and , respectively. In the second segment of cooperation, each of the N relays re-transmits the received signal after amplification via orthogonal transmissions (using TDMA in a round-robin fashion and/or FDMA). If a maximum ratio combiner (MRC) process is deployed at the destination node D to coherently merge all the signals received during these two transmission phases, the effective end-to-end SNR is given by [17],[16]

Table I

**2.2 ADAPTIVE MODULATION AND CODING (AMC) SCHEME**

Suppose that the multiple transmission modes are available at the PHY layer, and each associated with a specific AMC scheme. In practice, link-adaptation is performed at the frame level (which is the processing unit at the PHY layer) and the AMC controller at the transmitter (i.e., source node S) selects a particular mode for transmission based on the feedback of channel side information (e.g., effective SNR) acquired by the destination node D. But APER evaluation (required for MAC layer throughput calculation) through the average bit error rate using may not be always accurate especially for higher order constellations (since information bits in a symbol incur different error probabilities) and coded transmissions over slow fading channels (since bit errors are not uncorrelated). Moreover, this form does not provide the averaging problem over the fading SNR density function that arises in the performance evaluation of AMC systems. In this article, we will utilize an exponential-type approximation for the instantaneous packet error rate (PER) provided in [10]. At the physical layer, following two sets of transmission modes are considered (listed in Table I[1]): TM1- is uncoded, with *M _{n}*-ary rectangular/square QAM modes (where

**2.3 Selective-Repeat Arq Protocol Scheme**

The selective-repeat ARQ protocol is implemented at the data link layer with a retransmission limit *R*^{max} (while only finite delays and buffer sizes can be afforded in practice), and hence error-free delivery is not guaranteed. The value of *R*^{max} can be determined by dividing the maximum permissible network delay by the round-trip delay required for each retransmission. If a packet is not received correctly after *R*^{max} retransmissions, it will be dropped and we declare packet loss. In our cross-layer design, our design objective is to select an appropriate modulation scheme that ensures that the packet loss after *R*^{max} retransmissions is no larger than the target packet loss probability, *P*_{loss}.

Figure 2. Illustration of packet and frame structures

The packet and frame structures are depicted in Fig. 2. It is considered that, at the data link layer, each packet consists of *N _{p}* bits that, contains a payload, serial number, and cyclic redundancy check (CRC) bits for error detection. Each packet is mapped into a block consisting of

**3. Cross-Layer Combining Of AMC With Truncated ARQ Over Fading Channel**

In this section, we discuss our cross-layer design which combines AMC at the PHY layer with an adaptive ARQ at the data link layer for multi-relay two-hop CSI-assisted CAF networks. We also outline the development of our unified expressions (i.e., that involves computing the difference between two “CDF” terms as in (6) in conjunction with closed-form formulas for the MGF of or ) for calculating the APER, average spectral efficiency and outage probability performance metrics. Moreover, extension this to blind relays and cooperative decode-and-forward relay system is quite straight-forward [19].

**3.1 Performance Requirement At The PHY Layer**

Let us assume that the sum of transmit powers from all cooperating nodes is constant and the range of effective end-to-end SNR (1) is partitioned into *T *+ 1 non-overlapping consecutive intervals with boundary points denoted as. For instance, mode *n* is chosen whenand the transmission will be ceased (no payload bits will be sent) when to avoid deep channel fades. Remaining task now is to determine the boundary points (switching SNR thresholds) required to attain *P*_{target}.Since our system uses packets as processing units, we rely on the following exponential-type PER approximation to simplify the AMC design [10], viz.,

**3.3. Outage Probability**

When the total received SNR falls below the region boundary threshold ( is obtained by substituting and from Table I in (5)), the source node S ceases transmission, because the prescribed target PER cannot be satisfied even with the smallest constellation size. The Probability of such an outage event is given by where the CDF term can be evaluated efficiently using [15], viz.,

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