Patent Publication Number: US-8542579-B2

Title: Method and system for cooperative transmission in wireless multi-hop networks

Description:
REFERENCE TO THE RELATED PATENT APPLICATIONS 
     The present Utility Patent Application is based on the Provisional Patent Application Ser. No. 61/261,867 filed Nov. 17, 2009. 
    
    
     The U.S. Government has certain rights to the invention. The work was funded by Army Research Office under Contract Number W911NF0510246. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to wireless networks, and more in particular, to cooperative transmission in wireless networks with enhanced spatial diversity realized at the Network Protocol Layer level. 
     More in particular, the present invention is directed to cooperative transmission in wireless networks in a manner which counteracts the effects of fading, shadowing, attenuation and interference of wireless communication channels, and which capitalize on the properties of the wireless medium to enhance transmission rate and quality through the use of a concept of multi-hop relaying among source user nodes where a packet is delivered to the destination node through either a direct link between the packet generating source user node and the destination, or through multi-hop relaying by intermediate source users which have an increased probability of successful delivery if the intended packet delivery fails. 
     In overall concept, the present invention is directed to a novel technique to enhance transmission rate and transmission quality in wireless network environments through cooperative relaying of the messages at the network protocol layer level by a source user node having a channel with the highest successful delivery probability among a set of source user nodes with better channels than a respective transmitting source user node and which decoded the packet unicasted from the transmitting source user node, and which assumes the relaying function in addition to its own traffic related functions. 
     Additionally, the present invention is directed to a cooperative transmission in wireless networks implemented on the network protocol layer level but which may be cross-linked to other layers of the Open System Interconnection (OSI) model including, for example the Physical Layer, Media Access Control (MAC) Layer, etc., to further contribute to the performance gains provided by each layer of the cooperation implementation. 
     BACKGROUND OF THE INVENTION 
     Various developments in the area of wireless communication have proven that cooperative communication enhances performance in wireless environments. The idea of cooperative transmission emerged from the realization that spatial diversity may counteract the effects of fading, shadowing, attenuation and interference of wireless communication channels. For example, as presented in G. Foschini and M. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Pers. Commun., pp. 311-335, 1998; and I. Telatar, “Capacity of multi-antenna Gaussian channels,” Eur. Trans. Telecommun., vol. 10, no. 6, pp. 585-595k November/December 1999, spatial diversity was achieved in single communication links via the use of multiple antennas. 
     However, in wireless networks, the effect of multiple antennas may be realized through the combined use of antenna resources of different nodes. This observation lead to the notion of message relaying presented, for example, in A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity—Part I: system description,” IEEE Trans. Commun., vol. 51, pp. 1927-1938. November 2003; A. Sendonaris, E. Erkip, and B. Aazhang. “User cooperation diversity—Part II: implementation aspects and performance analysis,” IEEE Trans. Commun., vol. 51, pp. 1939-1948. November 2003; J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity in wireless networks: efficient protocols and outage behavior,” IEEE Trans. Inform. Theory, vol. 50, pp. 3062-3080, December 2004; G. Kramer, M. Gastpar, and P. Gupta, “Cooperative strategies and capacity theorems for relay networks,” IEEE Trans. Inform. Theory, vol. 51, no. 9 pp. 3037-3063, September 2005; G. Kramer, I. Marie, and R. D. Yates, Cooperative Communications, vol. 1, no. 3-4. “Foundations and Trends in Networking”, Flanover, Mass.: NOW Publishers Inc., 2006; A. Host-Madsen, “Capacity bounds for cooperative diversity,” IEEE Trans. Inform. Theory, fol. 52, no, 4, pp. 1522-1544. April 2006; and A. S. Avestirnehr and D. N. C. Tse. “Outage capacity of the fading relay channel in the low-SNR regime,” IEEE Trans. Inform. Theory, vol. 53, no. 4, pp. 1401-1415. April 2007. 
     The message relaying concept recently has received a great deal of attention. Most of the work on cooperative relaying has been focused on the Physical Layer, which is an actual hardware layer (lowest layer) in the Open Systems Interconnection (OSI) reference model. This model is a seven layer architecture arranged from the lower levels starting with the Physical Layer to the higher levels, including in order a Data Link Layer (which includes the Logical Linc Control (LLC) and Media Access Control (MAC) sub-layers), a Network Layer, a Transport Layer, a Session Layer, a Presentation Layer, and an Application Layer. 
     A. K. Sadek, et al. in the publication “Cognitive multiple access via cooperation: protocol design and performance analysis,” IEEE Trans. Inform. Theory, vol. 53, no. 10, pp. 3677-3697, October 2007, have provided the evidence that performance gains may be achieved even when the cooperation scheme is implemented at the Network Protocol Layer level. The Network Protocol Layer is the IP (Internet Protocol) supporting layer which routes messages (packets) across the network boundaries using the best path available between the source host to the destination host based on their addresses. 
     In Sadek, et al., a relay node is placed in between the source nodes and the destination node to relay packets from the source nodes. The system thus introduces extra relay nodes which merely perform a relaying function for the source nodes, thereby burdening the system with pure relays. 
     The extra pure relay node may not always be available. Moreover, in order for Sadek, et al.&#39;s relaying method to attain performance improvement for all source nodes, the relay node must have a better channel to the destination than all the source nodes. This has never been suggested in Sadek, et al. 
     A concept was studied in S. Biswas, et al., “Opportunistic routing in multi-hop wireless networks”, ACM SIGCOMM, vol. 34, no. 1, pp. 69-74, January 2004, which selects the best user among network users to relay the packet. However, the publication focuses on characterizing the total number of transmissions required to deliver a single packet between a pair of nodes, and therefore does not address the scheduling problem within a wireless network, since there is only a single packet at any one time in the network. No suggestion or analysis has been presented in S. Biswas, et al. for the case where the intermediate relay nodes would also have their own packets to deliver. In addition, the results of the analysis are based solely on simulation. 
     It is therefore would be highly desirable to provide a cooperative transmission technique in a more realistic environment where all source nodes are active participants transmitting their own packets and relaying packets of other source nodes with a lesser quality of the channels, and where multiple packets coexist is the system. 
     SUMMARY OF THE INVENTION 
     It is therefore an object of the present invention to provide a wireless multi-access network system with cooperative transmission feature having improved stable throughput and delay performance in which a set of source user nodes generate their packets to deliver to a common destination and which cooperate at the Network Protocol Layer level in a manner where the source users with better wireless communication channels to the destination are responsible, in addition to transmitting their own traffic, for relaying packets inadvertently received from users that have wireless communication channels of a lesser quality if these packets are not successfully received at the destination. 
     In one aspect of the present invention, there is provided a method for cooperative transmission in wireless networks in which the source user nodes are ordered according to the quality of their channels to the destination node. The channel quality may be represented by the successful delivery probability. The source user node with a better channel to the destination node is assigned with a higher index. In the subject multi-access system, a source user node  1  has the worst channel to the destination node, a source user node  2  has the second worst channel to the destination node, and every subsequent source user node i is progressively “better” than source user node (i−1), A source user node N has the best channel to the destination node. All source user nodes are notified of their rank. 
     Specifically, the subject method comprises the following steps: 
     forming a wireless multi-access system which includes a plurality N of source user nodes each generating and unicasting their respective packets to the destination node N+1, and 
     cooperatively operating the wireless multi-access system at the Network Protocol Layer level by: 
     transmitting at least one i-class packet from at least one source user node i to the destination node N+1 through the wireless communicating channel i, and, 
     if the destination node N+1 fails to successfully receive the packet transmitted by the current transmitting source user node i, but there are some source user nodes from the set {i+1, i+2, N} (which are source user nodes that have higher successful probability than source user node i) that successfully decode the transmitted packet, then a source user node j with the largest index, e.g. with the highest successful delivery probability among the source user nodes that successfully decoded the transmitted packet, will queue that packet for relaying at a later time. All other source user nodes which successfully decoded the transmitted packet will drop that packet. 
     The method further includes the steps of broadcasting acknowledgement signals either by the destination node N+1 or by the source user nodes j which receive the i-class packet transmitted by the source user node i. 
     In the method, each source user node j maintains a total of j virtual queues including a virtual queue i (for i=1, 2, . . . , j−1) which stores packets that are originally generated by source user node i. Each source user node j will relay some packets transmitted by source user i (for i=1, 2, . . . , j−1) in lieu of its own packets. The queuing of the i-class packets and j-class packets accumulated in the source user node j, is properly coordinated by a priority establishing mechanism. 
     An acknowledgement feedback mechanism is provided to inform the transmitters and the listening source user nodes, whether the transmitted packet is successfully decoded by the destination, or by some of the subsequent source user nodes. Then, the transmitter will decide whether to drop the packet or keep the packet in its queue. The subject cooperation protocol may be performed in determining which subsequent source user node to relay that packet. 
     When source user node i transmits a packet, it may be any of the i classes of packets, class-1, class-2, . . . , class-(j−1). Upon receiving the acknowledgement signal, either from the destination node N+1 or from any of the source user nodes whose index is greater than i on the successful receipt of the packet, the transmitting user node i discards the transmitted packet. 
     For source user nodes with index less than i, no action will be taken by these source user nodes. For a source user node j, with j&gt;i, if it does not decode the packet, no action will be taken. If the node j successfully decodes the packet transmitted by source user node i, then it will still discard the packet upon the receipt of the acknowledgement from the destination node N+1, or from any of the source user node with index greater than j. The user node j will keep the packet for relaying otherwise. 
     If, however, no acknowledgement signals are sent from the destination node, or from any of is subsequent source user nodes with index greater than i, the transmitted packet by source user node i will remain at the source user node i for retransmission. 
     The method further comprises the step of providing the buffers (virtual queues) at source user node j which contain the class-j packets generated by source user node j itself, and additional (j−1) number of buffers, which contain a total number of (j−1) classes of packets, with the i-th class of packet originally generated by source user node i, for i=1, 2, . . . , j−2, j−1. These source user nodes i, for i=1, 2, . . . , j−2, j−1 have a lesser probability of successful delivery to the destination node than the source user node j does. 
     Transmission among all classes of packets from the source user node j may be coordinated in various manners. The packet generally is allowed to be randomly chosen for transmission from any of the j buffers respective to j classes of packets at the source user node j, when the source user node j is to transmit. At each time slot, it is defined by the medium access scheduling policy which source user node will transmit. As for the case of conflict-free work-conserving mode of operation, at any time slot, (a) only one source user node which has packets in its queue will be activated to transmit, and (b) whenever there is at least one source user node that has packets in its queue, there will be a source user node activated for transmission. Alternatively, in a Time-Division-Multiple-Access (TDMA)-based schedule, there are respective time slots allocated for each of the source user nodes. Source user nodes transmit in their allocated time slots. The allocated time slot is idled if the corresponding source user node is empty. 
     In a further alternative mode of operation, the transmission of the i and j-class packets from the source user node j may be performed by assigning a higher priority to either i or j-class packets, or by assigning a higher priority to either the source user node i or source user node j, based on various criteria which may include: provision of a stable throughput, maximum throughput, system traffic delay, waiting time in the queues of the source user node j, class of service, desired priority policy, capacity of the queues in the source user node j, queue overflow threshold, etc., and combinations thereof. 
     The method further includes the steps of exchanging information on the queue(s) status between the source user nodes in the system and, subsequently, making decision on the packets transmission schedule either for different source user nodes, or for different class packets in the same source user node. 
     The decision on the transmission schedule may be made in the system either at the source user nodes themselves, or by a system scheduling controller unit (also referred to herein as Cooperative Operation Controller) which is operatively coupled to all source user nodes in the system as well as to the destination nodes. 
     A Priority Establishing Mechanism, an Acknowledgment Mechanism, as well as a Channels Ranking Mechanism are coupled both to the Cooperative Operation controller and to the source user nodes in the system to facilitate in coordination of the cooperative transmission of packets. 
     The present invention in a further aspect is a wireless multi-hop network system with an improved stable throughput and delay performance which comprises a wireless multi-access system of a plurality of interconnected source user nodes, each connected to a destination node N+1 via a respective wireless communication channel to unicast thereto respective packets, as well as a cooperative scheduling controller unit implemented at the Network Protocol Layer level of the wireless multi-access system and operatively coupled to the plurality N of the source user nodes and the destination node N+1. 
     All the N source user nodes generate their own packets to be finally delivered to the common destination node N+1, and the packets that are generated by source user node i are denoted by class-i packets. The source user nodes are ordered such that source user nodes with higher index have a higher successful delivery probability of their respective channel to the destination node. So if j&gt;i, the source user node j has a higher successful delivery probability through its direct link to the destination than source user node i has. 
     The Cooperative Scheduling Controller Unit instructs whether and which source user to relay the transmitted packet, if the destination fails to successfully receive the transmitted packet sent thereto from a source user node. 
     In order to “handle” the j-class packets generated thereat, as well as i-class packets inadvertently received due to the wireless nature of the network, the source user node j is provided with the i-queue unit with a buffer capacity sufficient to accumulate i-class packets from all participants i having a lesser delivery probability than the node j, and a dedicated j-queue with a buffer of a sufficient capacity for accumulating j-class packets generated at the source user node j. The Cooperative Scheduling Controller Unit is operatively coupled to the source user node j to coordinate transmission of the i-class packets and j-class packets from the i-queue and j-queue to the destination node via the wireless communication channel j in accordance with a predefined priority criteria. 
     The subject wireless multi-hop network system further comprises an Acknowledgement (ACK) mechanism which includes ACK transmitters at each source user node j and the destination node N+1. The destination node will broadcast acknowledgment signals upon successful receipt of any packet. The source user node j will broadcast acknowledgement signals upon successful receipt of packets transmitted by those user nodes i which have a lesser successful delivery probability (that is, those i that is less than j). 
     When a source user node i transmits a packet, if the destination node does not successfully decode the packet, but there are some user nodes from the set {i+1, i+2, . . . , N} that successfully decode the packet, then, in the case where there are more than one source user node in this set decode the transmitted packet by source user node i, the Cooperative Scheduling Controller Unit appoints a single source user node, that has the highest successful delivery probability among those that decode the packet, to keep this transmitted packet in its queue for relaying at a later time. 
     The wireless multi-hop system of the present invention further includes a cross-layer unit by which the protocol implemented at the Network Protocol Layer level is interconnected with scheduling mechanisms implemented at the Medium Access Layer, and the rank among users that are determined by the physical-layer channel properties, etc. 
     These and other features and advantages of the present invention will be apparent from the following detailed description taken in conjunction with accompanying Patent Drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic representation of the wireless multi-access system of the present invention; 
         FIG. 2  is a schematic representation of the queues arrangement of the source user nodes in the system of the present invention: 
         FIG. 3  is a schematic representation of the “Tandem” model representation of the system of the present invention; 
         FIG. 4  is a flow chart diagram of the decisions and actions process taken by the source user node i as instructed by the Cooperative Operation Controller upon an attempt of transmission by the source user node i; 
         FIG. 5  is a flow chart diagram representing decisions and actions taken by the source user node j as instructed by the Cooperative Operation Controller upon receipt of the packet transmitted by the source user node i; 
         FIG. 6  is a schematic representation of the two-user case as a portion of the wireless multi-access system of the present invention shown in  FIGS. 1 and 3 ; 
         FIG. 7  is a diagram representing comparison of the stable throughput regions under cooperative and non-cooperative policies; 
         FIG. 8  is a diagram representing comparison of the i-class packet delay under cooperative and non-cooperative priority-based policy; 
         FIG. 9  is a diagram representing comparison of the j-class packet delay under cooperative and non-cooperative priority-based policies; 
         FIG. 10  is a diagram representing comparison of the minimum overall average delay under cooperative and non-cooperative TDMA-based policies: 
         FIG. 11  is a diagram representing comparison of the i-class packet delay under cooperative and non-cooperative TDMA-based policies; and 
         FIG. 12  is a diagram representing comparison of the j-class packet delay under cooperative and non-cooperative TDMA-based policies. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring to  FIG. 1 , a wireless multi-access system  10  of the present invention includes a plurality N of wirelessly interconnected source user nodes  12 ,  14 ,  16 ,  18 , and  20 , and a destination node  22  to which the source user nodes  12 - 20  unicast packets  24  generated at the respective source user nodes  12 - 20 . Although only nodes  12 ,  14 ,  16 ,  18 , and  20  are shown in  FIG. 1 , it is to be understood that a larger or smaller number of the source user nodes may participate in the multi-access wireless system  10  of the present invention. 
     A Cooperative Scheduling Controller Unit, also referred to herein as a Cooperative Operation Controller  26 , is schematically shown in  FIG. 1  as being implemented at the Network Protocol Layer  28  of the Open System Interconnection (OSI) reference model  30 . It is to be understood that the functions of the Cooperative Operation Controller Unit  26  includes, among others, the coordination of the packets transmission through the wireless network in accordance with the subject cooperative strategy, and may be implemented as a separate controller entity. Alternatively, its functions may be performed by the source user nodes  12 - 20  by themselves. Thus, either being designed as a main system controller, or residing on each of the source user nodes  12 - 20  and the destination node, the cooperative schedule controller unit  26  controls the operation of the wireless multi-access system  10 . For these purpose, the controller  6  includes an Acknowledgement mechanism  32 , and a Priority nit  33  which incorporates a Ranking Mechanism  34 , as well as a Establishing Mechanism  35 . The mechanisms  32 ,  34 ,  35  are schematically shown as separate entities, but they also may be implemented at the source user nodes  12 - 20  level as well. The mechanism  32 ,  34  and  35  are functionally and operationally interrelated, and operated in accord with the Cooperative Operation Controller  26 , as will be presented in detail infra herein. 
     In the wireless multi-access system  10 , there always exist source nodes that have a better channel to the destination than others. Motivated by this fact, a new network-level cooperation system has been developed which is presented herein and which implements cooperation among a plurality source user nodes  12 - 20 . This concept is implemented in the N-user multi-access system  10  where a total of N source user nodes  12 - 20  unicast to the common destination node  22  via their respective wireless communication channels  36 ,  38 ,  40 ,  42 , and  44 , which constitute direct links between the above-mentioned nodes  12 - 20  and the destination node  22 . 
     In  FIG. 1 , the node  12  is shown as the “farthest” node from the destination node  22 , and every subsequent node i ( 14 ,  16 ,  18 , and  20 ) is progressively “closer” to the destination. The node  20  is shown as the “closest” to the destination node  22 . This distance notion may either be represented as real distance in free-space communication, or a “virtual distance” that also includes all types of fading, as will be detailed infra herein. 
     For the purposes of better reflecting the “furtherness” or “closeness” of each source unit node  12 - 20  relative to the destination node  22 , these notions will be further referred to herein intermittently as a channel rank, or a successful packet delivery probability of respective wireless communication channels  36 - 44  of the source user nodes  12 - 20 . Therefore a node j, where j=2, 3, 4, . . . , N, is considered to have a better channel to the destination node  22  than a node i does, where i=1, 2, . . . , j−1, e.g., the node  20  has the best channel rank, or the highest successful delivery probability, among other source user nodes in the network. 
     In the present system  10 , the source user nodes  14 - 20  accept responsibility of relaying packets for other source users  12 - 18 , respectively, which have a lesser channel rank, in addition to handling their own traffic. This achieves substantial performance improvement without the cost of an extra node, e.g., of a pure relay node. 
     The subject cooperation concept further involves multi-hop relaying. Characterization of the stable throughput region with multi-hop relaying, will be presented further herein. 
     The erasure channel model between any two nodes is assumed in the subject system, so that a packet may be successfully decoded with a certain probability. This captures the effects of fading and attenuation at the Physical Layer, as well as the wireless multicast advantage. Under this model, nodes which are “closer” to the destination node have a higher successful probability to deliver a packet to the destination. 
     In addition, the erasure channel model permits all source user nodes  12 - 20  in the network to have some capability to decode a transmitted packet. Thus, the option is provided for the source user node j to relay packets of its predecessor nodes i=1, 2, . . . , (j−1) in lieu of its own packets if the transmission of these predecessor source user nodes i to the destination node N+1 is unsuccessful but correctly received by the node j. 
     Although it is possible to transmit packets of different lengths, for the sake of simplicity, it is assumed that packets of fixed length are generated at source user nodes according to some random stationary processes and are queued for transmission to the destination node  22 , so that the queues may be emptied with a positive probability. As will be presented in detail infra, the packet generation rate region will be described by stable throughput region. The stable throughput region is defined as the set of all arrival rate vectors (in packets/slot) to the sources such that all queues in the network  10  remain bounded. 
     For the work-conserving policies, as well as Time-Division-Multiple-Access (TDMA) policy, considered at the medium access control (MAC) layer, the analytical expressions for the stable throughput region are derived for the N-user wireless multi-access system  10  shown in  FIG. 1 . It has been shown that by following the subject cooperation strategies, all source user nodes may simultaneously increase their stable throughput rates by assuming the relay functions in addition to the source user functions. 
     The analytical expressions are derived for the delay performance of the two-user case, shown in  FIG. 6 , as a portion of the network presented in  FIG. 1 , under both the TDMA-based policy and priority-based policy, which is a special case of the work-conserving policy. The analysis reveals that the subject cooperation strategy leads to a reduced delay for both users. Further, due to a large number of interacting queues of the source user nodes operating as the source nodes for trafficking their own packets and as relays for transmitting the packets inadvertently received for other source user nodes, the methodology used in the subject Application is quite sophisticated and complex. 
     System Model 
     In the slotted multi-access system shown in  FIG. 1 , the source nodes  12 - 20 , identified also as nodes  1 ,  2 , . . . , N, unicast traffic to a common destination node (N+1). 
     Each source user node i of the source user nodes  12 - 20  generates i-class packets  24  according to a Bernoulli process with rate λi to be transmitted to the destination node  22  over their direct link therewith. The node  12  generates 1-class packets  24   1  to be transmitted over the channel  36 . The node  14  generates 2-class packets  24   2  to be transmitted via the channel  38 , etc. 
     The Bernoulli process is a finite or infinite sequence of binary random variables, and is thus a discrete-time stochastic process that takes only two values, canonically “0” and “1”. The component Bernoulli variables X i  are identical and independent. Thus, the Bernoulli processes are independent from source user node to source user node, and independently and identically distributed over time slots. Packets  24   i  generated by node i classifies as i-class packets. It is assumed that a channel with fading and attenuation also includes the effects of additive white Gaussian noise. 
     When the source user node i transmits a packet with power P, the probability that a source user node j may decode the packet is given by 
                     p     i   ,   j       =     P   ⁡     [                  h     i   ,   j            2     ⁢   P       N   0       &gt;   γ     ]               (     Eq   .           ⁢   1     )               
where
 
     h ij  is the channel gain from node I to node j, 
     N o  is the noise poser level at the receiver j, and 
     γ is the Signal-to-Noise Ration (SNR) threshold required for correct decoding. 
     Packets which are not successfully decoded, are discarded immediately. The channel gain parameter may either be distance-dependent only, as in free-space communication, or it may include the effects of different types of fading represented by a random variable. 
     Channels in the system are assumed independent. It is also assumed that the source user nodes “closer” to the destination have a higher successful delivery probability, therefore, p N, N+1 &gt;p N−1, N+1 &gt; . . . &gt;p 1, N+1  as illustrated in  FIGS. 1 and 3 . 
     The reception probabilities p ij  are used herein to evaluate the performance of the subject system. It is also assumed that acknowledgements (ACKs), to be discussed in detail further herein, are instantaneous and error-free, and all source user nodes in the system “hear” the ACK signals. This relatively strong assumption is necessary and common for packet communication and establishes upper bounds to performance for both cooperative and non-cooperative cases. 
     Based on the afore-presented model, the subject Cooperation Strategy has been implemented in the system shown in  FIG. 1 . When a source user node trans s a packet generated thereat, if the destination node (N+1) successfully decodes the packet, it broadcasts an ACK signal, and every other source user node “hears” it. 
     Upon successful delivery of the packet to the destination node, the packet exits the systems. Otherwise, if the destination node does not decode the packet, but some source user nodes j from the set {i+1, i+2, . . . , N} decode the packet, the source user node with the highest quality rank among them (that is the source user node with the best channel to the destination among those that decode the packet) will keep the packet and take the responsibility to forward the packet, while all other source user nodes will then “drop” that packet. In further paragraphs, the source user node i will be considered to have a lesser channel rank than the source user node j, e.g. the source user nodes j may inadvertently receive i-class packets from the source user nodes i for relaying to the destination node. 
     Properly coordinated opera ion of the system  10  may be implemented if any of i&#39;s subsequent source user node that decodes the packet generates the ACK signals  50 . Broadcasting of ACK signals  50  upon receipt of a packet is controlled by the Acknowledgement mechanism  3  which, as shown in  FIG. 6 , includes an ACK transmitter at each source user nodes  14 ,  16 ,  18 , and  20 , and the destination user node  22  for broadcasting an ACK signal  50  upon receipt of a packet. The ACK mechanism also includes an ACK receiver at each of the source user nodes  12 - 20  for “hearing” the ACK signals  50 . The ACK mechanism operates under the control of the Cooperative Operation Controller  26  to greatly contribute to coordination of the transmission of different class packets through the entire system  10 . 
     By checking all the ACKs, if a source user node finds itself to be the node with the highest rank, it stores the packet in the buffer  54  of its queue  52 , as will be presented further herein with reference to  FIGS. 2 and 6 . Otherwise, it drops the packet. Finally, if neither the destination node nor any of i&#39;s subsequent source user nodes decodes the packet, the packet remains at i&#39;s queue for retransmission. With this form of cooperation, except node  1  which only transmits packets generated by itself, every other node j, for 2≦j≦N, will forward some packets from all its “predecessor” e.g., lower rank nodes i in addition to its own packets. 
     The subject cooperation strategy requires all N source user nodes to exchange the ACK information. Considering that only one bit is needed for each ACK to indicate successful reception, the cooperation overhead becomes negligible, and the overhead may be easily incorporated into the system analysis without affecting the results in a substantial manner. 
     The subject cooperation strategy has the effect of concentrating packets from different sources i, where iε(1, . . . , j−1), into fewer “virtual queues”, at each source user node j, where jε(2, . . . , N), where the packets in j&#39;s queue comprise a total number of (j−1) classes of relayed packets received at the source user node j plus the j-queue for the j-class packets generated at the source user node j. Given the option to schedule among multiple classes of packets, or perform inter-session network coding, the performance limit that may be approached must be an upper bound to that it can be achieved in the non-cooperative case, where packets of different classes are separated in different queues. 
     As shown schematically in  FIG. 2 , the node  12  has a queue  52 , which includes a single queue buffer  54 , accumulating 1-class packets generated at the source user node  12 . The node  14  which has a better channel rank than the node  12 , and therefore is considered for relaying the 1-class packets of the node  12 , if needed, has its queue  52   2  (which includes two virtual queues, e.g. implemented with the queue buffer  54   1 ), for accumulating 1-class packets generated and transmitted by the node  14  (but unsuccessfully delivered to the destination node  22 ) and the queue buffer  54   2  for accumulating 2-class packets generated at the node  14 . Likewise, the source user node  18 , which is the j−1 node, is provided with the queue  52   j −1 which includes j−1 virtual queues having queue buffers  54   1 ,  54   2 , . . . ,  54   j−1  for accumulating i-class packets, e.g. 1-class packets, 2-class packets, . . . , (j−1)-class packets generated at the respective i nodes  1 ,  2 , . . . , j−1, but undelivered to the destination node. 
     The node  20 , e.g. node j, which has the best probability of the successful packet delivery to the destination node in comparison with any of the group i source user nodes (i=1, 2, . . . , j−1) is best “positioned” for the relaying function than any of the nodes  1 ,  2 , . . . , j−1. For relaying purposes, the node j is provided with the queue  52   j  implemented with virtual queue  52   i  formed with the queue buffers  54   1 ,  54   2 , . . . ,  54   j−1 . In addition, the queue  52   j  of the node j has a queue buffer  54   j  for accumulating the j-class packets generated at the node j. It is clear that the queues of the nodes in the system which may accept relaying responsibilities may need to have high capacity queue buffers for storage of different classes packets transmitted through the network. 
     The following three steps define the proposed cooperation protocols: 
     Step  1 : Determine the Priority Order of the Source User Nodes. 
     The priority order is determined by the priority unit  33  which includes the Ranking Mechanism  34  which establishes the quality of the channel from each source user node to the destination node. The source user node with a better channel to the destination node is assigned a higher index. All source user nodes in the system  10  are notified of established priority order. 
     As will be presented further herein, in addition to the channel rank the priority order may also need to be established based on various priority criteria which are established by the Priority Establishing Mechanism  35 . For example, the priority of transmission of different classes of packets from the node may be based on a fullness of a respective queue buffer in the node. 
     In order to establish the priority order based on the channel quality, the Ranking Mechanism  34  instructs the system to generate pilot messages which, at the beginning of the cooperative transmission, are exchanged between the source user nodes and the destination node to estimate the user-destination channel qualities. All source user nodes will then be notified of their channel rank in the network. In the system  10 , shown in  FIG. 1 , the source user node  1  has the worst channel to the destination node, user  2  has the second worst channel to the destination, and every subsequent node i is progressively “better” than node (i−1). The source user node N has the best channel to the destination node N+1. 
     For example, in the model of the present invention shown in  FIG. 3 , the priority order assigned to the source user nodes  12 ,  14 ,  16 , . . . ,  20  is as follows: N&gt;N−1 . . . &gt;2&gt;1. This model is a “Tandem” model incorporating N sources with a single common destination. The packet reception probability is described by Eq. 1 previously presented. 
     The following steps  2  and  3  will be described herein in conjunction with the flow-charts presented in  FIGS. 4 and 5  of decisions and actions taken by each source user node as instructed by the Cooperative Operation Controller  26 , after the source user node k has attempted a transmission. 
     It is to be understood that after the source user node k transmits a packet from one of its virtual queues, no actions are taken at user for 1≦j≦k−1. 
     Step  2 : 
     Referring to  FIG. 4 , in block  60 , at an assigned time slot, when it is the source user node K&#39;s turn to transmit (Kε{1, 2 . . . N}) the user K transmits a packet from its queue  52 . As presented in previous paragraphs, the queue  52  at the source user node K consists of a total number of K virtual queues  54   1 ,  54   2 , . . . ,  54   i ,  54   j , . . . ,  54   k , where the j th  (j=1, 2, . . . , K) virtual queue  54   j  stores the j-class packets originally generated by user j, and virtual queue  54   k  stores k-class packets generated by the source user node k. Since each user k is adapted to store packets from all source user nodes with a lesser rank of the channel, it is provided with a queue buffer of ample capacity, preferably infinite size buffer. When the source user node K transmits a packet, generally user K can arbitrarily choose a packet from one of the K virtual queues  54   1 ,  54   2 , . . . ,  54   k . 
     Alternatively, the source user node k may have a priority for transmission of the packets received thereat from source user nodes of a lower rank. There may be priority criteria established for packet transmission by the Priority Establishing Mechanism  35 , which may include, but not limited to, stable throughput, maximum throughput, system traffic delay, waiting time in the queues, capacity of the queues, overflow threshold of the queues, class of service, specific priority policy, etc. Based on these criteria, the mechanism  35  may establish the priority for the order of access communication channels by source user nodes in the system. It should be understood that the Ranking Mechanism  34  and the Priority Establishing Mechanism  35  decide on the priority, order together, and operate in conjunction with the controller  26 . 
     In conjunction with the Priority Establishing Mechanism  35  and the Ranking Mechanism  34 , the Cooperative Scheduling Controller Unit  26 , (either residing on the source user nodes, or built as a separate entity), establishes priority policies, and operates the system in lieu of the priority criteria, thus controlling the operation of the system  10 . 
     There are two issues which the Cooperative Scheduling Controller Unit  26  considers when instructing nodes to operate: (1) which node to transmit, and (2) which virtual queue to serve at the transmitting node. 
     Regarding the issue (1), both conflict-free work-conserving policies and Time-Division-Multiple-Access policies (TDMA) are considered further herein. A specific Medium Access Control (MAC) policy is to decide which source user node is to access the channel at a time slot so that the stable throughput performance is not deteriorated. 
     According to the conflict-free work-conserving policy, as long as only one backlogged user is activated at each time slot and no time slot will be wasted (if there are packets in the system), any deterministic or probabilistic policy (or even arbitrary policy) in selecting one backlogged user to transmit may achieve a satisfactory stable throughput performance. 
     According to the TDMA policy, users are assigned to transmit in disjoint fractions of time slot, and user K transmits in its assigned time slots. But different policies in deciding which user to transmit may affect the delay performance of the entire system. 
     Regarding the issue (2), it has been shown that the priority policy in deciding which virtual queue to serve at a source user node does not affect the stable throughput region. However, the priority policy will affect the delay performance of individual packet class. 
     Step  3 : 
     At the end of the time slot of user K&#39;s transmission, source user nodes will perform different actions according to their rank in the network. Specifically, (a) referring to  FIG. 4 , the source user node K in block  62 , the source user node K checks if the destination node sends back an acknowledgement (ACK) message indicating successful reception. If the acknowledgement message is received, the packet is dropped by user K in block  64 , and there is no further action needed for user K. 
     If the acknowledgement message is not received, the following action will be commanded by the controller unit  26 : 
     In block  66 , the source user node K checks if there is ACK from any of K&#39;s subsequent nodes, that is, if ACKs were sent by at least one node j, with j&gt;K. If so, the logic passes to block  64 , and the packet is dropped by user K. If not, the flow chart passes to block  68  instructing the node K to keep the packet in its own queue  54   k  for retransmission. 
     Referring to  FIG. 5 , upon transmission of the packet by the source user node K, the following actions and decisions are performed at user node j, for K+1≦j≦N: 
     If user j does not decode the packet successfully in block  70 , the logic instructs the source user node j to take no actions in block  74 . However, if in block  70 , the source user node j decodes the packet successfully, user j in block  72  will first broadcast an acknowledgement to the entire network. Then, user j will decide whether to drop or keep the decoded packet according to the following criterion: 
     User j checks in block  76  if there is at least one ACK sent by either the destination node, or, as instructed in block  80 , from a node with a higher channel rank than j. If so, user j is instructed in block  78  to drop the decoded packet. If not, the user j then is instructed in block  82  to keep the packet in the corresponding virtual queue for retransmission at a later time. 
     The acknowledgements (ACKs) are assumed to be error-free and broadcast to the entire network. Considering that only one bit is needed by each ACK to indicate successful reception, the cooperation overhead is negligible and the assumption of instantaneous and error-free acknowledgement is reasonable. 
     If more than one source user node j have similar channel ranks, the controller unit  26  along with the Priority Establishing and Ranking mechanisms  34 ,  35  make decisions based on additional criteria, for example, fullness of the queues and appoint the node for transmission which is best positioned for this purpose. 
     Cooperative Communication Policies 
     At the Medium Access Control (MAC) layer the conflict-free work-conserving policy and TDMA policy have been considered regarding the issue of which node to transmit as presented in previous paragraphs. The MAC Layer of the OSI reference model is used to coordinate the sending of data between computers, and is basically concerned with hardware addressing. These are centralized MAC policies, and hence are not very practical to be implemented in real networks. However, the results presented herein may serve as the baseline for designing more practical policies, and may provide an upper performance bound to the latter. Together with the subject cooperation system and method of the present invention the cooperative communication policies are described as follows: 
     Work-Conserving Cooperative Communication Policy 
     
         
         
           
             A policy is defined to be conflict-free work-conserving if it holds that:
           (1) It does not idle the time slot whenever there are packets in the system; and   (2). At most, one backlogged source user node transmits in each time slot.   
         
           
         
       
    
     Therefore, the source user nodes can access the channel via countless disciplines as long as they do not violate any of the above-listed conditions. This is an unspecified policy. It will be shown in further paragraphs that any conflict-free work-conserving policy yields the same stable throughput region. 
     When a backlogged node k accesses the channel, it may randomly pick up a packet from its queue for transmission. The packet may be its own packet, or a packet it relays for any of its “predecessor” nodes e.g., nodes with a lower ranking.
         If the destination node receives the packet successfully, it sends back an ACK signal, and the packet is removed from the system.   If the destination fails to receive the packet, but there is at least one source user node in the set {k+1, k+2, . . . , N} that decodes the packet, the source user node with the largest rank index (e.g., having a best probability of the successful delivery of the packet to the destination node) queues the packet. Then all other source user nodes drop (disregard) the packet.   If none of the source user nodes from (k+1) up to (N+1) decodes the packet, the packet remains in the queue of the source user node k for retransmission.
 
TDMA-Based Cooperative Communication Policy
   Source user nodes access the channel via a TDMA-based schedule, where each source user node is allocated a fraction of time in each frame to access the channel.       

     Let Ω=(ω 1 , ω 2 , . . . , ω N ) denote the resource-allocation vector for the N nodes, all feasible resource-allocation vectors should satisfy 
                 ∑     t   =   1     N     ⁢     ω   i       ≤   1.         
At the beginning of the source user node k&#39;s assigned time slot, the source user node k transmits a packet from its queue if it is backlogged. If the queue of the source use node k is empty, the slot is not utilized.
         If the destination receives the packet successfully, the packet is removed from the system.   If the destination fails to receive the packet, then, if there are some source user nodes among k&#39;s subsequent source user nodes that decode the packet, only the source user node with the largest rank index among them queues the packet for retransmission.   If none of the source user nodes from (k+1) up to (N+1) decodes the packet, the packet remains in the queue of the source user node k for retransmission.       

     Stable Throughput Region 
     The stable throughput region has been characterized under the proposed cooperative communication policies, starting with the definition of queuing stability. 
     A. Queuing Stability 
     Let X k   t  denote number of arrivals in slot t to queue k, and Y k   t  denote departures from queue k. The queue length evolution of queue k has the following form
 
 Q   k   t+1   =[Q   k   t   −Y   k   t ] +   +X   k   t   (Eq. 2)
 
     As defined in W. Szpankowski, “Stability conditions for some distributed systems: Buffered random access systems,” Adv. Appl. Probab., vol. 26, pp. 498-515, 1994, queue k is stable if 
     
       
         
           
             
               
                 
                   
                     
                       lim 
                       
                         t 
                         → 
                         ∞ 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       P 
                       ⁡ 
                       
                         [ 
                         
                           
                             Q 
                             k 
                             t 
                           
                           &lt; 
                           x 
                         
                         ] 
                       
                     
                   
                   = 
                   
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                     ⁡ 
                     
                       ( 
                       x 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     The system is stable if and only if all the queues are stable. Under the subject model, the queue length vector Q t ={Q 1   t , Q 2   t , . . . . , Q N   t } forms an irreducible, aperiodic Markov chain. Queuing stability is equivalent to the positive recurrence of the Markov chain. 
     An important tool to determine stability is Loynes&#39; Theorem, which states that, if the arrival and service processes of a queue are jointly stationary, the queue is stable if and only if the average arrival rate is strictly less than the average service rate. The criterion in D. Bertsekas, et al., “Data Network”, 2 nd  ed. Englewood Cliffs, N.J., Prentice-Hall, 1992, has been used which establishes that in a work-conserving system, the system is stable if the proportion of time the system is busy is less than 1. The stable throughput region has been characterized as the union of all sets of arrival rate vectors (λ 1 , λ 2 , . . . , λ N ) such that all queues in the system remain stable. Under the TDMA-based policy, the stable throughput region is obtained as the set of all arrival rates (λ 1 , λ 2 , . . . , λ N ) such that there exists (ω 1 , ω 2 , . . . , ω N ) which stabilizes the system. 
     B. Main Results 
     The main results are outlined with respect to the stable throughput analysis. Proofs of the following Theorems 1 and 2, as well as proofs of Propositions 1 and 2, may be found in B. Rong and A. Ephremides. “Protocol-Level Cooperation “Wireless Networks: Stable Throughput and Delay Analysis”. 
     Theorem 1: 
     Λ=(λ 1 , λ 2 , . . . , λ N ) is the Bernoulli arrival rate vector. The stable throughput region under both the work-conserving and TDMA-based cooperative communication policies is the same, and is characterized by: 
     
       
         
           
             
               
                 
                   = 
                   
                     
                       { 
                       
                         
                           Λ 
                           ⁢ 
                           
                             : 
                           
                           ⁢ 
                           
                             
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                                 = 
                                 1 
                               
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                             ⁢ 
                             
                               
                                 r 
                                 k 
                               
                               
                                 
                                   ∏ 
                                   
                                     i 
                                     = 
                                     
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                                       + 
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                                     + 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                     
                                 
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                                   ( 
                                   
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                         &lt; 
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                     ⁢ 
                     
                         
                     
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                     where 
                   
                 
               
               
                 
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                                       ⁢ 
                                       
                                           
                                       
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                                   ⁢ 
                                   
                                       
                                   
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     Theorem 2: 
     Nodes in the network are ordered such that p N, N+1 &gt;P N−1, N+1 &gt; . . . &gt;p 1, N+1 . With such ordering, the stable throughput region of the cooperative system strictly contains the stable throughput region when cooperation is not used. The maximum stabilizable arrival rates of nodes from 1 up to (N−1) strictly increase, while the maximum stabilizable arrival rate of node N remains unaffected. 
     Delay an Analysis 
     It is known that delay analysis of more than two interacting queues is next to impossible. Thus, the effort has been focused on the case of two users. M. Sidi, et al., in “Two interfering queues in packet-radio networks”, IEEE Trans. Commun., vol. Com-31. No. 1, pp. 123-129. January 1983, analyzed delay of interfering queues in packet-radio networks under the collision channel model. The technique relies on solving the moment-generating function of the joint stationary queue lengths. From Theorem 1, it is seen that any conflict-free work-conserving policy yields the same stable throughput region. However, the delay performance depends on specific work-conserving policy. Therefore, the delay performance of the TDMA policy, as well as a special work-conserving policy, e.g., priority-based policy are investigated. The priority rule assigns higher priority to class-1 packets. First, this priority-based cooperative communication policy is described in the two-user case shown in  FIG. 6 :
         Source user node  12  has a higher priority than source user node  14  to access the channel. When the source user node  12  is backlogged, it transmits a packet. If the destination node  22  decodes the packet, the packet exits the system. Otherwise, if the source user node  14  decodes the packet, the source user node  14  queues the packet for retransmission and the source user node  12  drops the packet. If neither the source user node  14  nor the destination node  22  decodes the packet, the packet remains at user  12 .   When the source user node  12  is empty, then the source user node  14  accesses the channel. If there are both class-1 and class-2 packets in its queue, the source user node  14  picks up a packet belonging to class 1 and transmits that packet first. If there are only class-2 packets, the source user node  14  transmits a packet of class 2. If the packet is successfully decoded by the destination node  22 , the packet exits the system. Otherwise, the packet stays in the queue at the source user node  14 .       

     It is assumed that on a control sub-channel  90 , source user nodes  12  and  14  share their queue status information in order for this policy to be implementable. According to the stated priority-based cooperative policy, there are three queues involved in analysis, as shown in  FIG. 6 : 
     1) Q 1  at the node  12  which contains the packets generated by the source user node  12  itself; 
     2) Q 21  at the node  14  which contains the packets that are relayed from the source user node  12 ; 
     3) Q 22  at the node  14  which contains the packets generated by the source user node  14  itself. 
     Q 21  and Q 22  are merged at the node  14  and are denoted by Q 2 . For the system shown in  FIG. 6  the following Proposition has been attained: 
     Position 1: 
     Under the priority-based cooperative communication policy, if the system is stable. 
     (a) The average delay of class-1 packet is given by 
                     D   1     =         N   1     +     N   21         λ   1               (     Eq   .           ⁢   6     )               
(b) The average delay of class-2 packet is given by
 
                     D   2     =         N   2     -     N   21         λ   2               (     Eq   .           ⁢   7     )               
where,
 
1) N 1 , the average queue length of Q 1 , is given by
 
                     N   1     =         -     λ   1   2       +     λ   1           p     1   ,   2       +     p     1   ,   3       -       p     1   ,   2       ⁢     p     1   ,   3         -     λ   1                 (     Eq   .           ⁢   8     )               
2) N 21 , the average queue length of Q 21 , is given by
 
                           ⁢       N   21     =           f   ⁢           ⁢     λ   1   2       +     g   ⁢           ⁢     λ   1             a   ⁢           ⁢     λ   1   2       +     b   ⁢           ⁢     λ   1       +   c       ⁢           ⁢   with               (     Eq   .           ⁢   9     )                 f   =       (       p     1   ,   2       -       p     1   ,   2       ⁢     p     1   ,   3           )     ⁢     (           p     2   ,   3       -     p     1   ,   3             p     1   ,   2       +     p     1   ,   3       -       p     1   ,   2       ⁢     p     ,   13             -     p     1   ,   2       -     p     2   ,   3       +       p     1   ,   2       ⁢     p     1   ,   3           )         ⁢     
     ⁢           ⁢     g   =       (       p     1   ,   2       -       p     1   ,   2       ⁢     p     1   ,   3           )     ⁢     (       p     1   ,   2       +     p     1   ,   3       -       p     1   ,   2       ⁢     p     1   ,   3           )         ⁢     
     ⁢           ⁢     a   =       p     1   ,   2       +     p     2   ,   3       -       p     1   ,   2       ⁢     p     1   ,   3             ⁢     
     ⁢           ⁢     b   =       (       p     1   ,   2       +     p     1   ,   3       -       p     1   ,   2       ⁢     p     1   ,   3           )     ⁢     (       -     p     1   ,   2         -     2   ⁢     p     2   ,   3         +       p     1   ,   2       ⁢     p     1   ,   3           )         ⁢     
     ⁢           ⁢     c   =         p     2   ,   3       ⁡     (       p     1   ,   2       +     p     1   ,   3       -       p     1   ,   2       ⁢     p     1   ,   3           )       2               (     Eq   .           ⁢   10     )               
3) N 2 , the average queue length of Q 2 , is given by
 
     
       
         
           
             
               
                 
                   
                       
                   
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                     12 
                   
                   ) 
                 
               
             
           
         
       
     
     Under the TDMA-based cooperative communication policy, when the network is stable, the analytical delay expressions are derived as functions of the reception probabilities as well as the allocation vector (ω 1 , ω 2 ). Among all allocation vectors that stabilized the system, the optimal allocation vector (ω* 1 , ω* 2 ) is solved that minimizes the average delay over all packets. The minimum average delay is given in the following Proposition: 
     Proposition 2: 
     Under the TDMA-based cooperative communication policy, if the network is stable, the minimum average delay over all packets that can be achieved by the optimal (ω* 1 , ω* 2 ) is: 
                       D   Avg   *     ⁡     (   TDMA   )       =         (           b   1     ⁡     (       -     r   2   2       +     r   2     +       αλ   1     ⁢     λ   2         )         +         b   2     ⁡     (       -     r   1   2       +     r   1       )           )     2         (       λ   1     +     λ   2       )     ⁢     (         b   1     ⁢     b   2       -       b   1     ⁢     r   2       -       b   2     ⁢     r   1         )                 (     Eq   .           ⁢   13     )               
with (ω* 1 , ω* 2 ), the average delay of class-1 packet is
 
                       D   1     ⁡     (   TDMA   )       ⁢            (       ω   1   *     ,     ω   2   *       )     =           (       -     r   1       +   1     )     ⁢     (       b   2     ⁢           b   1     ⁢       b   2     ⁡     (     (       -     r   2   2       +     r   2     +       αλ   1     ⁢     λ   2         )     )           (       -     r   1   2       +     r   1       )           )             b   1     ⁢     b   2       -       b   1     ⁢     r   2       -       b   2     ⁢     r   1           +         α   ⁡     (       -     r   2   2       +     r   2     +       αλ   1     ⁢     λ   2         )       ⁢     (       b   1     +           b   1     ⁢       b   2     ⁡     (       -     r   1   2       +     r   1       )             -     r   2   2       +     r   2     +       αλ   1     ⁢     λ   2               )           r   2     ⁡     (         b   1     ⁢     b   2       -       b   1     ⁢     r   2       -       b   2     ⁢   r       )                       (     Eq   .           ⁢   14     )               
the average delay of class-2 packet is:
 
                       D   2     ⁡     (   TDMA   )       ⁢            (       ω   1   *     ,     ω   2   *       )     =           (       -     r   2   2       +     r   2     +       αλ   1     ⁢     λ   2         )     ⁢     (       b   1     +           b   1     ⁢       b   2     ⁡     (       -     r   1   2       +     r   1       )             -     r   2   2       +     r   2     +       αλ   1     ⁢     λ   2               )           r   2     ⁡     (         b   1     ⁢     b   2       -       b   1     ⁢     r   2       -       b   2     ⁢     r   1         )         ⁢           ⁢   with                 (     Eq   .           ⁢   15     )                       ⁢         r   1     =     λ   1       ⁢     
     ⁢           ⁢       r   2     =             p     1   ,   2       ⁡     (     1   -     p     1   ,   3         )           p     1   ,   2       +     p     1   ,   3       -       p     1   ,   2       ⁢     p     1   ,   3             ⁢     λ   1       +     λ   2         ⁢     
     ⁢           ⁢       b   1     =     1   -       (     1   -     p     1   ,   2         )     ⁢     (     1   -     p     1   ,   3         )           ⁢     
     ⁢           ⁢       b   2     =     p     2   ,   3         ⁢     
     ⁢           ⁢     α   =         p     1   ,   2       ⁡     (     1   -     p     1   ,   3         )           p     1   ,   2       +     p     1   ,   3       -       p     1   ,   2       ⁢     p     1   ,   3                         (     Eq   .           ⁢   16     )               
Results
 
     In  FIG. 7 , the stable throughput regions of the cooperative policies are compared with the non-cooperative policies in the two-user case shown in  FIG. 6 . In this plot, the reception probabilities of the user-destination channels are chosen to be p 1,3 =0.3, p 2,3 =0.8. For the inter-user channel three channel conditions were studied with reception probabilities: p 1,2 =0.4, 0.6, 0.85 (note that p 1,2  affects the performance of the cooperative case only). The stable throughput region of the cooperative policies is found to strictly contain the non-cooperative policies, and the region increases as the inter-user channel condition improves. 
     The benefit of cooperation in delay performance for class-1 packets and class-2 packets respectively, under the priority-based policy is demonstrated in  FIGS. 8 and 9 . The channel reception probabilities are the same as described above. Using the same technique, the delay performance under the non-cooperative priority-based policy is derived as: 
     (a) The average delay of class-1 packet is: 
                     D   1     ⁢            non   ⁢     -     ⁢   cooperative     =         -     λ   1       +   1         p     1   ,   3       -     λ   1                     (     Eq   .           ⁢   17     )               
(b) The average delay of class-2 packet is:
 
     
       
         
           
             
               
                 
                   
                     D 
                     2 
                   
                   ⁢ 
                   
                      
                     
                       
                         non 
                         ⁢ 
                         
                           - 
                         
                         ⁢ 
                         cooperative 
                       
                       = 
                       
                         
                           
                             
                               ( 
                               
                                 
                                   - 
                                   
                                     p 
                                     
                                       1 
                                       , 
                                       3 
                                     
                                   
                                 
                                 + 
                                 
                                   p 
                                   
                                     2 
                                     , 
                                     3 
                                   
                                 
                                 - 
                                 
                                   
                                     p 
                                     
                                       1 
                                       , 
                                       3 
                                     
                                   
                                   ⁢ 
                                   
                                     p 
                                     
                                       2 
                                       , 
                                       3 
                                     
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               λ 
                               1 
                             
                           
                           - 
                           
                             
                               p 
                               
                                 1 
                                 , 
                                 3 
                               
                               2 
                             
                             ⁢ 
                             
                               λ 
                               2 
                             
                           
                           + 
                           
                             
                               p 
                               
                                 1 
                                 , 
                                 3 
                               
                             
                             ⁢ 
                             
                               λ 
                               1 
                             
                             ⁢ 
                             
                               λ 
                               2 
                             
                           
                           + 
                           
                             p 
                             
                               1 
                               , 
                               3 
                             
                             2 
                           
                         
                         
                           
                             ( 
                             
                               
                                 
                                   p 
                                   
                                     2 
                                     , 
                                     3 
                                   
                                 
                                 ⁢ 
                                 
                                   λ 
                                   1 
                                 
                               
                               + 
                               
                                 
                                   p 
                                   
                                     1 
                                     , 
                                     3 
                                   
                                 
                                 ⁢ 
                                 
                                   λ 
                                   2 
                                 
                               
                               - 
                               
                                 
                                   p 
                                   
                                     1 
                                     , 
                                     3 
                                   
                                 
                                 ⁢ 
                                 
                                   p 
                                   
                                     2 
                                     , 
                                     3 
                                   
                                 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 λ 
                                 1 
                               
                               - 
                               
                                 p 
                                 
                                   1 
                                   , 
                                   3 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     18 
                   
                   ) 
                 
               
             
           
         
       
     
     λ 1 =λ 2 =λ and λ varies to obtain the presented plots. It has been shown that when cooperation is used, both class-1 and class-2 packets experience less average delay. And when the inter-user channel quality improves, cooperation leads to more performance gains to both users. 
     The benefit of cooperation in terms of delay performance under the TDMA-based communication policy is presented in  FIGS. 10-12 . Using the same technique, the minimum overall delay achievable under the non-cooperative TDMA-based policy is: 
     
       
         
           
             
               
                 
                   
                     
                       D 
                       Avg 
                       * 
                     
                     ⁡ 
                     
                       ( 
                       TDMA 
                       ) 
                     
                   
                   ⁢ 
                   
                      
                     
                       
                         non 
                         ⁢ 
                         
                           - 
                         
                         ⁢ 
                         cooperative 
                       
                       = 
                       
                         
                           1 
                           
                             
                               λ 
                               1 
                             
                             + 
                             
                               λ 
                               2 
                             
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       
                                         p 
                                         
                                           1 
                                           , 
                                           3 
                                         
                                       
                                       ⁢ 
                                       
                                         
                                           λ 
                                           2 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             
                                               λ 
                                               2 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                   + 
                                   
                                     
                                       
                                         p 
                                         
                                           2 
                                           , 
                                           3 
                                         
                                       
                                       ⁢ 
                                       
                                         
                                           λ 
                                           1 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           
                                             1 
                                             - 
                                             
                                               λ 
                                               1 
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                               2 
                             
                             
                               
                                 
                                   p 
                                   
                                     1 
                                     , 
                                     3 
                                   
                                 
                                 ⁢ 
                                 
                                   p 
                                   
                                     2 
                                     , 
                                     3 
                                   
                                 
                               
                               - 
                               
                                 
                                   p 
                                   
                                     1 
                                     , 
                                     3 
                                   
                                 
                                 ⁢ 
                                 
                                   λ 
                                   2 
                                 
                               
                               - 
                               
                                 
                                   p 
                                   
                                     2 
                                     , 
                                     3 
                                   
                                 
                                 ⁢ 
                                 
                                   λ 
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     19 
                   
                   ) 
                 
               
             
           
         
       
     
     Meanwhile the average delay of class-1 packet and class-2 packet are given by 
     
       
         
           
             
               
                 
                   
                     
                       D 
                       1 
                     
                     ⁡ 
                     
                       ( 
                       TDMA 
                       ) 
                     
                   
                   ⁢ 
                   
                      
                     
                       
                         non 
                         ⁢ 
                         
                           - 
                         
                         ⁢ 
                         cooperative 
                       
                       = 
                       
                         
                           1 
                           - 
                           
                             
                               λ 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   p 
                                   
                                     2 
                                     , 
                                     3 
                                   
                                 
                                 + 
                                 
                                   
                                     p 
                                     
                                       1 
                                       , 
                                       3 
                                     
                                   
                                   ⁢ 
                                   
                                     
                                       
                                         
                                           p 
                                           
                                             2 
                                             , 
                                             3 
                                           
                                         
                                         ⁢ 
                                         
                                           
                                             λ 
                                             2 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               
                                                 λ 
                                                 2 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           p 
                                           
                                             1 
                                             , 
                                             3 
                                           
                                         
                                         ⁢ 
                                         
                                           λ 
                                           ⁡ 
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               
                                                 λ 
                                                 1 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               p 
                               
                                 1 
                                 , 
                                 3 
                               
                             
                             ⁢ 
                             
                               p 
                               
                                 2 
                                 , 
                                 3 
                               
                             
                           
                           - 
                           
                             
                               p 
                               
                                 1 
                                 , 
                                 3 
                               
                             
                             ⁢ 
                             
                               λ 
                               2 
                             
                           
                           - 
                           
                             
                               p 
                               
                                 2 
                                 , 
                                 3 
                               
                             
                             ⁢ 
                             
                               λ 
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     20 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       D 
                       2 
                     
                     ⁡ 
                     
                       ( 
                       TDMA 
                       ) 
                     
                   
                   ⁢ 
                   
                      
                     
                       
                         non 
                         ⁢ 
                         
                           - 
                         
                         ⁢ 
                         cooperative 
                       
                       = 
                       
                         
                           1 
                           - 
                           
                             
                               λ 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   p 
                                   
                                     1 
                                     , 
                                     3 
                                   
                                 
                                 + 
                                 
                                   
                                     p 
                                     
                                       2 
                                       , 
                                       3 
                                     
                                   
                                   ⁢ 
                                   
                                     
                                       
                                         
                                           p 
                                           
                                             1 
                                             , 
                                             3 
                                           
                                         
                                         ⁢ 
                                         
                                           
                                             λ 
                                             1 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               
                                                 λ 
                                                 1 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           p 
                                           
                                             2 
                                             , 
                                             3 
                                           
                                         
                                         ⁢ 
                                         
                                           λ 
                                           ⁡ 
                                           
                                             ( 
                                             
                                               1 
                                               - 
                                               
                                                 λ 
                                                 2 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               p 
                               
                                 1 
                                 , 
                                 3 
                               
                             
                             ⁢ 
                             
                               p 
                               
                                 2 
                                 , 
                                 3 
                               
                             
                           
                           - 
                           
                             
                               p 
                               
                                 1 
                                 , 
                                 3 
                               
                             
                             ⁢ 
                             
                               λ 
                               2 
                             
                           
                           - 
                           
                             
                               p 
                               
                                 2 
                                 , 
                                 3 
                               
                             
                             ⁢ 
                             
                               λ 
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                     ⁢ 
                     21 
                   
                   ) 
                 
               
             
           
         
       
     
       FIG. 10  shows that the minimum overall delay achieved by the cooperative TDMA policy is strictly less than that by the non-cooperative TDMA policy. It is also seen that the delay for both the class-1 packet and class-2 packet improves over that of the non-cooperative case, as illustrated in  FIGS. 11 and 12 . A better inter-user channel helps reduce delay under the cooperative communication policy. 
     The cooperation among the sets of users at the Network Protocol Layer level in a wireless multi-access system attains the higher stable throughput for all users in the network simultaneously. Results of the analysis for the delay performance indicate that users may experience reduced average delay when cooperation is used. In lieu of the subject cooperative transmission, it is possible to consider more general system models which allow simultaneous transmissions and multi-packet reception. The subject system and method may be extended also to include diverse traffic demands (unicast, multicast, broadcast) and more general network topologies. It is possible to consider different network-level cooperation disciplines through a cross-layer, as shown in  FIG. 1 , and confirm the expectation that performance would improve. 
     It is contemplated in the scope of the present invention that a cross-connection between the subject cooperative strategy implemented on the network protocol layer and other layer, e.g. Physical Layer, Data Line Layer (LIC and MAC), Transport Layer, Session Layer, Presentation Layer, and Application Layer may be designed to further benefit performance characteristics of the wireless multi-access networks. 
     Although this invention has been described in connection with specific forms and embodiments thereof, it will be appreciated that various modifications other than those discussed above may be resorted to without departing from the spirit or scope of the invention as defined in the appended claims. For example, equivalent elements may be substituted for those specifically shown and described, certain features may be used independently of other features, and in certain cases, particular applications of elements may be reversed or interposed, all without departing from the spirit or scope of the invention as defined in the appended claims.