**3.1.2 Principles of fast retransmission strategy**

432 Wireless Communications and Networks – Recent Advances

obtained. For HARQ schemes, a Markov model was presented to analyze the SR truncated type II HARQ scheme employing Reed Solomon linear erasure block codes in [22], where the link packet throughput, error probability, and delay performance were analyzed. In [23], a suboptimal root-finding solution was developed to solve the exhaustive search for the optimization problem formulated based on the incremental-redundancy HARQ scheme.

The delay performance of several truncated ARQ and HARQ schemes in a CD environment under the assumption of Poisson arriving packets were evaluated in detail by Boujemâa in [24]. An analytical model to quantify end-to-end performances for a CD ARQ scheme in a cluster-based multi-hop wireless network was proposed by Le *et al.* in [25]. Markov models developed to evaluate the CD system were also investigated by Mahinthan *et al.* in [26] and

While papers [24-27] have widely explored various ARQ/HARQ schemes in the CD environments, the issues regarding time constraints for delay-sensitive flows were not addressed and elaborated on. Therefore, their throughput formulas did not reflect the effective throughput that must satisfy the typical delay constraints of streaming-type or real-

Due to the aforementioned reasons, we herein propose a novel fast packet retransmission scheme, where a new approach of retransmission strategy is designed and appropriately combines the encoding/decoding mechanism presented in [18], in such a CD environment for delay-sensitive flows as a case study. In the proposed scheme, there are 2 retransmission policies that can be employed adaptively according to both the channel quality and the Application layer Protocol Data Unit (APDU) size. The retransmission is designed to be allowed only one time. Here, APDU flows in the sender are further assumed to always have a link packet ready for transmission. As a result, it is not much meaningful to analyze the packet delay involving the queueing analysis. In this paper, we only focus on the complete throughput analysis to gain the main insight of optimizing the number of channels for retransmission between the 2 proposed retransmission policies under such the CD environment. All of the derived formulas are then verified via simulations. The effective throughput of our proposed scheme is shown better than that of other CD retransmission

**3. Case study: On the effective throughput gain of cooperative diversity with** 

A general CD system model composing of a sender, a partner, and a receiver is considered, as shown in Fig. 1, where two cooperative users (i.e., sender and partner) transmit their information to the same destination (i.e., receiver). It is assumed that each user' device in this system only has one radio transceiver. Additionally, Orthogonal Frequency Division

In the present system, channels among sender, partner and receiver are modeled as nonidentical but independent Nakagami-*m* slow-fading channels corrupted by additive white Gaussian noise. The fading channels and the noise are assumed to be independent of each

by Issariyakul *et al.* in [27], respectively.

time multimedia flows in such an environment.

schemes (such as [26]) and non-CD retransmission schemes.

**3.1 System description** 

other.

**3.1.1 Cooperative diversity system** 

**a fast retransmission scheme for delay-sensitive flows [33-34]** 

Multiplexing (OFDM) is employed as the underlying transmission technique.

The design philosophy of the retransmission strategy is to improve the application layer throughput while the effective control of the transmission delay is also assured. We assume that the underlying coding scheme is HARQ and that if a packet is retransmitted, then only its complementary packet is sent.

The packet retransmission strategy can be described via the following 4 principles:


Since an OFDM system is assumed, we assume each channel only uses a subset of OFDM subchannels. For the above retransmission strategy, note that both channel-1 and channel-2 are with orthogonal subchannel set 1, while channel-3 is with orthogonal subchannel set 2. The intersection of subchannel set 1 and set 2 is arranged to be an empty set; therefore, for the receiver, the signals from channel-1 and channel-3 will not interfere with each other.

Typical retransmission operations under *policy*\_0 and *policy*\_1 are illustrated in Fig. 2 and Fig. 3, respectively. Also, we assume that the delay threshold of the considered delaysensitive APDU is set equal to the maximum of maximum delays for 2 policies. Notice that in this model the terminology *delay* only indicates the air-transmission delay component for the APDU under the proposed retransmission principle.

Fig. 2. A typical example of a fast HARQ with *policy\_*0*.* When any original link packet is found failed at the receiver, only the partner will retransmit a complementary link packet if a link packet is successfully received by the partner. Link packet i' means the complementary packet of link packet i.

Fig. 3. A typical example of fast HARQ with *policy\_*1. When any original link packet is found failed in the receiver, both the sender and the partner will retransmit a complementary link packet. Link packet i' is the complementary packet of link packet i.

## **3.1.3 Cooperative diversity with fast HARQ scheme**

Two codes, a block code *C*0 and a convolutional code *C*<sup>1</sup> , are together used as the coding mechanism employed in each user (see [29], [36] for examples). For more detail description, *C*1 is a rate-1/2 convolutional code with constraint length *c* consisting of a *c*-stage shift

are with orthogonal subchannel set 1, while channel-3 is with orthogonal subchannel set 2. The intersection of subchannel set 1 and set 2 is arranged to be an empty set; therefore, for the receiver, the signals from channel-1 and channel-3 will not interfere with each other.

Typical retransmission operations under *policy*\_0 and *policy*\_1 are illustrated in Fig. 2 and Fig. 3, respectively. Also, we assume that the delay threshold of the considered delaysensitive APDU is set equal to the maximum of maximum delays for 2 policies. Notice that in this model the terminology *delay* only indicates the air-transmission delay component for

Fig. 2. A typical example of a fast HARQ with *policy\_*0*.* When any original link packet is found failed at the receiver, only the partner will retransmit a complementary link packet if

Fig. 3. A typical example of fast HARQ with *policy\_*1. When any original link packet is found failed in the receiver, both the sender and the partner will retransmit a complementary link

Two codes, a block code *C*0 and a convolutional code *C*<sup>1</sup> , are together used as the coding mechanism employed in each user (see [29], [36] for examples). For more detail description, *C*1 is a rate-1/2 convolutional code with constraint length *c* consisting of a *c*-stage shift

packet. Link packet i' is the complementary packet of link packet i.

**3.1.3 Cooperative diversity with fast HARQ scheme** 

a link packet is successfully received by the partner. Link packet i' means the

the APDU under the proposed retransmission principle.

complementary packet of link packet i.

register and two generator polynomials *G x* 1( ) and *G x* <sup>2</sup> ( ) . This code *C*1 is used as an inner code for error detection and correction. Next, the outer code *C*0 is a high rate ( ( 1), ( 1) ) *nc nc r* block code used for error detection only, where *n* is the length of each link packet that is transmitted in this scheme, and *r* is the length of parity-check bits for error detection.

When an APDU arriving at the sender, there will be *s* new information sequences *<sup>i</sup> I x*( ) , 1 *i s* , each length ( ( 1) ) *nc r* , generated in sequence. They are encoded into *<sup>i</sup> J x*( ) with *C*0 and then encoded into *V x J xG x i i* <sup>1</sup> () () () with *C*1 in sequence. Each of them will be broadcasted in sequence only one time to the partner and the receiver.

Let *V x <sup>i</sup>*( ) and *V x <sup>i</sup>*( ) be the noisy versions of *V x <sup>i</sup>*( ) arriving at the receiver and the partner, respectively. For the receiver, the syndrome of *V x <sup>i</sup>*( ) is checked in two steps. In step\_1, *V x <sup>i</sup>*( ) is regarded as a noisy version of a codeword in the ( , ( 1)) *nn c* shortened cyclic code generated by *G x* 1( ) . In step\_2, an estimate *<sup>i</sup> J x*( ) of *<sup>i</sup> J x*( ) is then checked in the high rate ( ( 1), ( 1) ) *nc nc r* block code. If the syndromes are all zero in any step, an estimate *<sup>i</sup> I x*( ) of *<sup>i</sup> I x*( ) is obtained and delivered to the *receiving buffer*, which is a buffer used for waiting other link packets back for an APDU. Subsequently, an ACK packet will be sent to the sender and the partner. However, if the aforementioned syndrome check in any step is not zero, *V x <sup>i</sup>*( ) is stored in the receiver buffer, and a NACK packet will be transmitted to the partner and the sender for possible retransmission. For the partner, if *V x <sup>i</sup>* ˆ ( ) is error-free, then either *policy*\_0 or *policy*\_1 is adopted; otherwise, it is directly dropped.

Under *policy\_*0, if *V x <sup>i</sup>*( ) is error-free, *V x <sup>i</sup>*( ) will be decoded to *V x <sup>i</sup>*( ) and then re-encode via *G x* <sup>2</sup> ( ) to *V x <sup>i</sup>* ( ) . Thereafter, *V x <sup>i</sup>* ( ) is transmitted to the receiver. Let the noisy version of *V x <sup>i</sup>* ( ) be denoted as *V x <sup>i</sup>* <sup>ˆ</sup>( ) . *V x <sup>i</sup>* ˆ( ) will be checked in the same way as in the first transmission. If *V x <sup>i</sup>* <sup>ˆ</sup>( ) is found failed, *V x <sup>i</sup>* <sup>ˆ</sup>( ) shall be combined with *V x <sup>i</sup>*( ) , to form a combined codeword, which is decoded by the Viterbi decoding. The result is checked in the high rate ( ( 1), ( 1) ) *nc nc r* block code. If the syndrome is zero, it is claimed as a correct result. Its information sequence is then estimated and delivered to the *receiving buffer*; otherwise, it is discarded and the retransmission for this link packet is stopped.

Under *policy*\_1, a complementary link packet *V x <sup>i</sup>* ( ) via *G x* <sup>2</sup> ( ) of *V x <sup>i</sup>*( ) will be transmitted from the sender to the receiver, and let the noisy version be denoted as *V x <sup>i</sup>*( ) . Meanwhile, if *V x <sup>i</sup>*( ) is error-free, *V x <sup>i</sup>*( ) will be decoded to *V x <sup>i</sup>*( ) and then re-encode via *G x* 2( ) to *V x <sup>i</sup>* ( ) . Let the noisy version of *V x <sup>i</sup>* ( ) be denoted as *V x <sup>i</sup>* <sup>ˆ</sup>( ) . Following that, *V x <sup>i</sup>*( ) and *V x <sup>i</sup>* ˆ( ) will be checked via the two-step decoding procedure, respectively. If the syndrome of any one is zero, it is claimed as a correct result, its information sequence is then estimated and delivered to the *receiving buffer*; otherwise, *V x <sup>i</sup>*( ) shall be combined with *V x <sup>i</sup>* <sup>ˆ</sup>( ) and *V x <sup>i</sup>*( ) , respectively, to form two combined codewords, which are decoded by the Viterbi decoding. If any result is successful, its information sequence is then estimated and delivered to the *receiving buffer*; otherwise, a new codeword, *V x i mrc* , <sup>ˆ</sup> ( ) , will be further generated based on the Maximal Ratio Combining (MRC) (see [31] for more details) technique via *V x <sup>i</sup>* <sup>ˆ</sup>( ) and *V x <sup>i</sup>*( ) . The syndrome of the new codeword is checked in the same concept of the two-step decoding procedure. If the result is successful, the estimated information sequence will be delivered to the *receiving buffer*; otherwise, it is discarded and the retransmission for this link packet is stopped.

#### **3.2 Throughput analysis**

Performances of the application layer throughput for the present scheme will be first analyzed in detail in this Section. It is assumed that the time axis is partitioned into equal size slot. In each time slot, it is separated into two parts. That is to say, the main part of a time slot is used for link packets transmissions and the rest of the time slot is reserved for ACK/NACK packets transmissions. Here, the SNR is assumed staying constant in a time slot. In addition, the *M*-ary, *M <sup>b</sup>* 2 where *b* is even, the Quadrature Amplitude Modulation (QAM) scheme is assumed in the OFDM subchannels of the proposed model.

#### **3.2.1 Link packet error probability**

For *M*-ary QAM in Nakagami-*m* slow-fading channels, the average BERs for channel-*j*, *j*=1,2,3, denoted as *<sup>j</sup>* , can be derived by

$$\overline{\varpi}\_{j} = \bigcap\_{0}^{\infty} p\_{j}(\boldsymbol{\gamma}\_{j}) \varepsilon\_{\text{ins},j}(\boldsymbol{\gamma}\_{j}) d\boldsymbol{\gamma}\_{j} \text{ , j=1,2,3,} \tag{1}$$

where, in channel-*j*, *ins*, *j j* ( ) is the instantaneous BER conditional on *<sup>j</sup>* for *M*-ary QAM, *j* is the instantaneous SNR per bit, *<sup>j</sup>* <sup>0</sup> , *<sup>j</sup> <sup>j</sup> <sup>m</sup> m m <sup>m</sup> jj j <sup>j</sup> p me m* <sup>1</sup> ( ) ( ) is the probability density function (pdf) of *<sup>j</sup>* in Nakagami-*m* fading given in [28], *m* 1 2 , ( ) is the gamma function, and *<sup>j</sup>* is the average SNR per bit. The instantaneous BER *ins*, *j j* ( ) was previously derived in [30], [32] as

$$\begin{aligned} \varepsilon\_{\text{ins},j}(\boldsymbol{\gamma}\_{j}) &= \\ \frac{1}{\sqrt{M}\log\_{2}\sqrt{M}} \sum\_{z=1}^{\log\_{2}\sqrt{M}} \sum\_{t=0}^{f(z,M)} \left\{ \,\_{erf} \mathrm{cf}((2t+1)\sqrt{\mathbf{g}\boldsymbol{\gamma}\_{j}}) f(t,z,M) \right\}, & j = 1,2,3, \end{aligned} \tag{2}$$

where *<sup>z</sup> f zM* ( , ) (1 2 ) 1 *<sup>M</sup>* , *g MM* <sup>2</sup> 3log (2 2) ,

$$f(t, z, M) = (-1)^{\frac{t^2 2^{z-1} \sqrt{M}}{2} \left\lfloor \left\lfloor 2^{z-1} - \left\lfloor \begin{array}{c} t2^{z-1} \left/ \sqrt{M} + 1/2 \end{array} \right\rfloor \right\rfloor \right\rfloor}, \text{and } \operatorname{erfc}(\cdot) \text{ is the error function.} $$

The average link packet error probability in a single transmission in channel-*j*, *j*=1,2,3, denoted as *Pj*,*<sup>e</sup>* , can be given by

$$\overline{P}\_{j,\varepsilon} = \int\_0^\infty p\_j(\boldsymbol{\gamma}\_j) (1 - (1 - \varepsilon\_{\mathrm{ins},j}(\boldsymbol{\gamma}\_j))^n) d\boldsymbol{\gamma}\_j \ , j = 1, 2, 3. \tag{3}$$

Furthermore, the average link packet error probability after the Viterbi decoding conditional on the event that both *V x <sup>i</sup>* <sup>ˆ</sup>( ) and *V x <sup>i</sup>*( ) are corrupted, denoted as *Pf* ,0 , can be approximately by (see eq. (28) in [29])

$$\overline{P}\_{f,0} \equiv 1 - (1 - p\_b)^{n - (c - 1)}\,,\tag{4}$$

where *<sup>b</sup> p* is the corresponding bit error probability obtained via the Viterbi decoding. As shown in [29], *<sup>b</sup> p* is bounded by

$$p\_b \le \frac{1}{2} \frac{\left. \widetilde{\varepsilon} T(X, Y)}{\left. \widetilde{\varepsilon} Y} \right|\_{X = 2\sqrt{\widetilde{\varepsilon}^{\left(1 - \widetilde{\varepsilon}^{\right)}}}, Y = 1} \, \, \tag{5}$$

where ' , the upper bound of the conditional BERs given that the two-step (mentioned in Section 3.1.3) decoding syndromes in channel-1 and channel-3 are non-zero, is given by

$$\varepsilon^{'} = \max\left\{ \frac{\varepsilon\_1}{1 - \left(1 - \varepsilon\_1\right)^{n'}}, \frac{\left(1 - \varepsilon\_2\right)\varepsilon\_3}{1 - \left(1 - \left(1 - \varepsilon\_2\right)\varepsilon\_3\right)^{n}} \right\},\tag{6}$$

and *T(X,Y)* is the generating function of the convolutional code. In addition, *Pf* ,1 , the average link packet error probability after the Viterbi decoding conditional on the event that both *V x <sup>i</sup>*( ) and *V x <sup>i</sup>*( ) are corrupted, can be given by (4)-(6) together with ' replaced by *n* 1 1 (1 (1 ) ), which is the conditional BER given that the two-step decoding syndrome in channel-1 is non-zero.

Last, but not least, the average link packet error probability after the MRC decoding, under *policy\_*1, denoted as *Pmrc* , can be given by

$$\overline{P}\_{mrc} = \int\_0^\infty \tilde{p}(\chi\_b) (1 - (1 - \varepsilon\_{mrc}(\chi\_b))^\pi) d\chi\_b \tag{7}$$

where *<sup>b</sup>* is the instantaneous SNR per bit at the output of the MRC decoder, *<sup>b</sup> p*( ) represents the pdf of *<sup>b</sup>* , *<sup>b</sup>* 0 , and *mrc b* ( ) is the instantaneous BER conditional on *<sup>b</sup>* for *M*-ary QAM after the MRC decoding. According to [28], [30], *m m m b c m bb c <sup>p</sup> me m* 2 21 2 / ( ) (2 ) , where *<sup>c</sup>* means the equivalent average SNR for each channel. The instantaneous BER *mrc b* ( ) can be given by (2) with *<sup>j</sup>* replaced by *<sup>b</sup>* .

#### **3.2.2 Throughput**

436 Wireless Communications and Networks – Recent Advances

Performances of the application layer throughput for the present scheme will be first analyzed in detail in this Section. It is assumed that the time axis is partitioned into equal size slot. In each time slot, it is separated into two parts. That is to say, the main part of a time slot is used for link packets transmissions and the rest of the time slot is reserved for ACK/NACK packets transmissions. Here, the SNR is assumed staying constant in a time slot. In addition, the *M*-ary, *M <sup>b</sup>* 2 where *b* is even, the Quadrature Amplitude Modulation

For *M*-ary QAM in Nakagami-*m* slow-fading channels, the average BERs for channel-*j*,

 

is the instantaneous BER conditional on *<sup>j</sup>*

<sup>1</sup> ((2 1) ) ( , , ) 1,2,3, log

where *<sup>z</sup> f zM* ( , ) (1 2 ) 1 *<sup>M</sup>* , *g MM* <sup>2</sup> 3log (2 2) ,

The average link packet error probability in a single transmission in channel-*j*, *j*=1,2,3,

, and *erfc* ( ) is the error function.

*j*

 

( 1)

, *j*=1,2,3. (3)

<sup>ˆ</sup>( ) and *V x <sup>i</sup>*( ) are corrupted, denoted as *Pf* ,0 , can be

,0 1 (1 ) , (4)

, *j*=1,2,3, (1)

<sup>0</sup> , *<sup>j</sup> <sup>j</sup> <sup>m</sup> m m <sup>m</sup>*

is the average SNR per bit. The instantaneous BER *ins*, *j j*

 is the

*jj j <sup>j</sup> p me m* <sup>1</sup> ( ) ( ) 

in Nakagami-*m* fading given in [28], *m* 1 2 , ( ) is

for *M*-ary QAM,

 ( ) 

(2)

*j jj ins jj j p d* ,

*erfc t g f t z M , j M M*

*<sup>n</sup> Pj <sup>e</sup> j j ins jj j <sup>p</sup> <sup>d</sup>* , , <sup>0</sup> ( )(1 (1 ( )) )

*n c P p f b*

Furthermore, the average link packet error probability after the Viterbi decoding conditional

 () () 

0

*Mf zM*

*z t*

log ( , )

2

2 1 0

*<sup>z</sup> t M z z ftzM t M* <sup>1</sup> <sup>2</sup> 1 1 ( , , ) ( 1) ( ) 2 2 12

(QAM) scheme is assumed in the OFDM subchannels of the proposed model.

**3.2 Throughput analysis** 

**3.2.1 Link packet error probability** 

 ( ) 

probability density function (pdf) of *<sup>j</sup>*

was previously derived in [30], [32] as

( )

*ins j j*

,

denoted as *Pj*,*<sup>e</sup>* , can be given by

on the event that both *V x <sup>i</sup>*

approximately by (see eq. (28) in [29])

is the instantaneous SNR per bit, *<sup>j</sup>*

, can be derived by

*j*=1,2,3, denoted as *<sup>j</sup>*

*j* 

where, in channel-*j*, *ins*, *j j*

the gamma function, and *<sup>j</sup>*

 

> For the fast HARQ scheme with *policy*\_0, the application layer throughput in APDU/slot, denoted as *T*<sup>0</sup> , can be derived as

$$T\_0 = \frac{1}{s} (1 - \overline{P}\_{1,\epsilon} \overline{P}\_{2,\epsilon} - \overline{P}\_{1,\epsilon} (1 - \overline{P}\_{2,\epsilon}) \overline{P}\_{3,\epsilon} \overline{P}\_{f,0})^s,\tag{8}$$

where 1 /*s* represents the average number of the APDUs transported per slot, and the second term indicated the success probability of an APDU transmission.

Next, for the fast HARQ scheme with *policy*\_1, the application layer throughput in APDU/slot, denoted as *T*<sup>1</sup> , can be derived as

$$T\_1 = \frac{\alpha}{s} (1 - \overline{P}\_{1,\varepsilon}^2 \overline{P}\_{2,\varepsilon} \overline{P}\_{f,1} - \overline{P}\_{1,\varepsilon}^2 (1 - \overline{P}\_{2,\varepsilon}) \overline{P}\_{3,\varepsilon} \overline{P}\_{f,0} \overline{P}\_{f,1} \overline{\overline{P}}\_{mrc})^s,\tag{9}$$

where /*s* represents the average number of the APDUs transported per slot, and similar to the concept in (8), the second term means the success probability of an APDU transmission. In (9), *Pmrc* is the average link packet error probability after the MRC decoding conditional on *V x <sup>i</sup>* <sup>ˆ</sup>( ) and *V x <sup>i</sup>*( ) all found failed. Since *Pmrc* is the unconditional probability of a link packet error after the MRC decoding and the result will be correct after the MRC decoding as long as there is at least a link packet that is correct, *Pmrc* can be derived as *P P P PP mrc mrc e e e* <sup>2</sup> /( (1 ) ) 1, 2, 3, by the definition of conditional probability [35]. Moreover, in (9) can be obtained via the equality

$$
\overline{P}\_{1,e}\alpha = 1 - \alpha \tag{10}
$$

since the average number of retransmission link packets generated per slot should equal the average number of retransmission completed, after normalization.

Last, but not least, for delay-sensitive flows, the maximum air-transmission delay of an APDU allowed is usually subject to a specific QoS requirement. In this case, based on the similar derivation and argument in [18], one can appropriately tune the key parameter, namely, *s*, in the system to achieve the highest effective throughput under a given delay constraint.

#### **3.3 Analytical and simulation results**

In this section, the considered CD environment with a sender, a partner, and a receiver remains the same as shown in Fig. 1. We assume that an APDU is composed of 5 link packets. A 16 QAM modulation scheme is adopted. The coding mechanism is referred to Section 3.1.3. Also, we set *r* 6 bytes, *c* 9 , and *n* 257 bytes. The ACK/NACK packet size for ARQ related schemes is set equal to 25 bytes and for HARQ related schemes is set equal to 26 bytes. The link speed is set equal to 10Mbps. Besides, excluding the errorcorrecting codes, the ratio of the additional header overhead associated with the lower layer protocols from the application one is set equal to 0.04.

First, we will evaluate and compare the performance results among all schemes to see main potential insights of our proposed scheme by considering the ideal case that the channel between the sender and the partner is error-free. Next, we further investigate the impact on the system performance when there is an error probability on the channel between the sender and the partner.

#### **3.3.1 With an error-free channel-2**

For the fast retransmission scheme, based on (8)-(9), analytical results of application throughputs under 1 , with *P*3,*<sup>e</sup>* 0.9 and *P*3,*<sup>e</sup>* 0.1 , in the Nakagami-3 slow-fading environment, are depicted in Fig. 4 and Fig. 5, respectively. In Fig. 4, it can be found that if 2 1 0.4 10 , the optimal throughput can be achieved with only 1 channel for retransmission (via the partner); if <sup>2</sup> 1 0.4 10 , it can be achieved by parallel retransmissions via 2 channels (via both sender and partner). However, in Fig. 5, it is seen

to the concept in (8), the second term means the success probability of an APDU transmission. In (9), *Pmrc* is the average link packet error probability after the MRC

probability of a link packet error after the MRC decoding and the result will be correct after the MRC decoding as long as there is at least a link packet that is correct, *Pmrc* can be

since the average number of retransmission link packets generated per slot should equal the

Last, but not least, for delay-sensitive flows, the maximum air-transmission delay of an APDU allowed is usually subject to a specific QoS requirement. In this case, based on the similar derivation and argument in [18], one can appropriately tune the key parameter, namely, *s*, in the system to achieve the highest effective throughput under a given delay

In this section, the considered CD environment with a sender, a partner, and a receiver remains the same as shown in Fig. 1. We assume that an APDU is composed of 5 link packets. A 16 QAM modulation scheme is adopted. The coding mechanism is referred to Section 3.1.3. Also, we set *r* 6 bytes, *c* 9 , and *n* 257 bytes. The ACK/NACK packet size for ARQ related schemes is set equal to 25 bytes and for HARQ related schemes is set equal to 26 bytes. The link speed is set equal to 10Mbps. Besides, excluding the errorcorrecting codes, the ratio of the additional header overhead associated with the lower layer

First, we will evaluate and compare the performance results among all schemes to see main potential insights of our proposed scheme by considering the ideal case that the channel between the sender and the partner is error-free. Next, we further investigate the impact on the system performance when there is an error probability on the channel between the

For the fast retransmission scheme, based on (8)-(9), analytical results of application

environment, are depicted in Fig. 4 and Fig. 5, respectively. In Fig. 4, it can be found that if

0.4 10 , the optimal throughput can be achieved with only 1 channel for

retransmissions via 2 channels (via both sender and partner). However, in Fig. 5, it is seen

1 

, with *P*3,*<sup>e</sup>* 0.9 and *P*3,*<sup>e</sup>* 0.1 , in the Nakagami-3 slow-fading

0.4 10 , it can be achieved by parallel

*P*1,*<sup>e</sup>* 1 

/*s* represents the average number of the APDUs transported per slot, and similar

<sup>ˆ</sup>( ) and *V x <sup>i</sup>*( ) all found failed. Since *Pmrc* is the unconditional

, (10)

<sup>2</sup> /( (1 ) ) 1, 2, 3, by the definition of conditional probability [35].

where 

Moreover,

constraint.

sender and the partner.

throughputs under 1

1 

2

**3.3.1 With an error-free channel-2** 

retransmission (via the partner); if <sup>2</sup>

decoding conditional on *V x <sup>i</sup>*

derived as *P P P PP mrc mrc e e e*

**3.3 Analytical and simulation results** 

protocols from the application one is set equal to 0.04.

in (9) can be obtained via the equality

average number of retransmission completed, after normalization.

that the throughput of *policy\_*0 is always better than that of *policy\_*1. Because the average link packet error probability of channel-3 is small, the retransmission of duplicated link packet on channel-1 via *policy\_*1 will waste bandwidth.

Fig. 4. Application throughputs under typical 1 with *P*3,*<sup>e</sup>* 0.9 under a fast HARQ scheme.

Fig. 5. Application throughputs under typical 1 with *P*3,*<sup>e</sup>* 0.1 under a fast HARQ scheme.

In what follows, we compare the throughput of our proposed scheme with that of the previous work [26] and non-CD HARQ scheme under 1 , with <sup>3</sup> 3 10 in Nakagami-3 slow-fading channels, as shown in Fig. 6. Notice that in Fig. 6, the *CD with optimized fast HARQ* scheme represents the case that the retransmission policy is adaptively adjusted to be optimal on the basis of the channel quality in the CD environment. For a fair comparison among all schemes, all throughput results are in bit/second, and other 2 schemes are modified to allow only 1 retransmission and time slots for those discarded retransmissions are then used for new transmissions. Notice due to this modification, their throughput formulas are modified versions of (9) with the unused parameters removed. In details, one should set *Pf* ,1 1 and replace the parameter *n* in (3) by *n-*(*c-*1) for the scheme in [26], and set *P*2,*<sup>e</sup>* 1 for the non-CD HARQ scheme. With the help of Fig. 6, it can be found that better performance is achieved by the optimized fast HARQ scheme except when 1 is extremely small due to the additional overhead of the HARQ.

Fig. 6. Application layer throughput (in bit/sec.) comparison among various schemes under Nakagami-3 slow-fading channels when channel-2 is error-free.

Notice that, generally speaking, BER=0.001 is fairly high (in our parameter setting, which is about equal to the packet error rate =0.9 when without employing any error correcting mechanism), that is to say, the channel condition is extremely bad. Here, the reasons for setting channel-3's BER=0.001 are explained as follows. Although the sender would like to select the neighboring partner having good channel condition for helping transmission, in the worst case when the partner is far away from the receiver and both of them are at the edge of a cell such that the channel-3's condition degrades. In this case, with the validation of analytical and simulation results, the performance result of our scheme is much better than that of other schemes. It means our scheme is very powerful. Thus, it can be easily reasoned that when channel-3's BER decreases, our scheme still remains the best although the performance results for these schemes will all be improved.

Furthermore, taking <sup>3</sup> 1 2 10 and <sup>3</sup> 3 10 as an example, effective throughput performances of these schemes under different Nakagami-*m*, *m*=1/2, 1, 3, slow-fading channels in the CD environment are compared, as listed in Table 1. From Table 1, both analytical results based on (8)-(9) and simulation results show that the optimized fast HARQ scheme always achieves better throughput performance than other schemes since the optimized fast HARQ scheme can adaptively adjust the retransmission policy according to the channel quality. Again in Table 1, it is found that the analytical results are slightly lower than the simulation ones for both the optimized fast HARQ scheme and the non-CD HARQ scheme since the Viterbi decoding mechanism via (5) is employed for them. Note that the upper bound in (5) is tight and can be regarded as an excellent approximation when the BER is lower than <sup>2</sup> 10 [36].


Table 1. Comparisons of the application layer throughputs (in bit/second) at <sup>3</sup> 1 2 10 and <sup>3</sup> 3 10 among various schemes under different Nakagami-*m*, *m*=1/2, 1, 3, slowfading channels.

### **3.3.2 With a non-error-free channel-2**

440 Wireless Communications and Networks – Recent Advances

In what follows, we compare the throughput of our proposed scheme with that of the

slow-fading channels, as shown in Fig. 6. Notice that in Fig. 6, the *CD with optimized fast HARQ* scheme represents the case that the retransmission policy is adaptively adjusted to be optimal on the basis of the channel quality in the CD environment. For a fair comparison among all schemes, all throughput results are in bit/second, and other 2 schemes are modified to allow only 1 retransmission and time slots for those discarded retransmissions are then used for new transmissions. Notice due to this modification, their throughput formulas are modified versions of (9) with the unused parameters removed. In details, one should set *Pf* ,1 1 and replace the parameter *n* in (3) by *n-*(*c-*1) for the scheme in [26], and set *P*2,*<sup>e</sup>* 1 for the non-CD HARQ scheme. With the help of Fig. 6, it can be found that better performance is achieved by the optimized fast HARQ scheme except when 1

Fig. 6. Application layer throughput (in bit/sec.) comparison among various schemes under

Notice that, generally speaking, BER=0.001 is fairly high (in our parameter setting, which is about equal to the packet error rate =0.9 when without employing any error correcting mechanism), that is to say, the channel condition is extremely bad. Here, the reasons for setting channel-3's BER=0.001 are explained as follows. Although the sender would like to select the neighboring partner having good channel condition for helping transmission, in the worst case when the partner is far away from the receiver and both of them are at the edge of a cell such that the channel-3's condition degrades. In this case, with the validation of analytical and simulation results, the performance result of our scheme is much better than that of other schemes. It means our scheme is very powerful. Thus, it can be easily

 , with <sup>3</sup> 3 

10 in Nakagami-3

is

previous work [26] and non-CD HARQ scheme under 1

extremely small due to the additional overhead of the HARQ.

Nakagami-3 slow-fading channels when channel-2 is error-free.

Due to the fundamental physical characteristics of wireless channels, there often exists an error probability for each transmission channel in the real-world environment. However, in order to take the advantage of CD, the sender usually selects the neighboring partner having good channel condition between them. Thus, we herein set <sup>4</sup> 2 10 for demonstrating performance results. The throughput comparisons of various schemes under 1 , with 4 2 10 and <sup>3</sup> 3 10 in Nakagami-3 slow-fading channels, are shown in Fig. 7.

It is found in Fig. 7 that the performance of the optimized fast HARQ scheme obviously degrades when the BER of channel-1 is smaller than <sup>3</sup> 3 10 when compared with that in Fig. 6. Because there exists an error probability on channel-2 and *policy*\_0 only uses the cooperative path (i.e., channel-2 together with channel-3) for retransmissions, the power of *policy\_*0 decreases. However, the throughput result of the optimized fast HARQ scheme in Fig. 7 is also shown better than that of the other 2 schemes. In addition, it can be observed that when <sup>3</sup> 1 3 10 , the performance results of the first 2 good schemes are almost the same as those in Fig. 6 due to the fact that MRC is much powerful.

Fig. 7. Application layer throughput (in bit/sec.) comparison among various schemes under Nakagami-3 slow-fading channels when channel-2 is not error-free.

Last, for completeness, we take <sup>3</sup> 1 2 10 , <sup>4</sup> 2 10 , and <sup>3</sup> 3 10 , as an example, to illustrate the effective throughput results for various schemes under different Nakagami-*m*, *m*=1/2, 1, 3, slow-fading channels, and summarize the results in Table 2. From Table 2, it can be found that both analytical results based on (8)-(9) and simulation results of the optimized fast HARQ scheme also always have better throughput results than those of other schemes as in Table1. The results of the non-CD HARQ scheme for both Table 1 and Table 2 are the same since its performance only depends on channel-1's BER. We also notice that throughput improvement of our scheme is significant even with <sup>4</sup> 2 10 in the sender-topartner channel.

In summary, based on Figs. 6 and 7 and Tables 1 and 2, we can thus conclude that the fast HARQ scheme is an excellent approach for transporting delay-constrained streaming-type or real-time multimedia flows in CD environments even when there is an error probability on the cooperative path. It is for the reasons that the retransmission strategy can be adaptively adjusted according to the channel condition and that the decoding procedure involving MRC and the Viterbi decoding are appropriately designed.


Table 2. Comparisons of the application layer throughputs (in bit/second) at <sup>3</sup> 1 2 10 , 4 2 10 , <sup>3</sup> 3 10 among various schemes under different Nakagami-*m*, *m*=1/2, 1, 3, slow-fading channels.
