 Research
 Open Access
 Published:
Endtoend channel capacity of MACPHY crosslayer multiplehop MIMO relay system with outdated CSI
EURASIP Journal on Wireless Communications and Networking volume 2013, Article number: 144 (2013)
Abstract
For high endtoend channel capacity, the amplifyandforward scheme multiplehop multipleinput multipleoutput relay system is considered. The distance between each transceiver and the transmit power of each relay are optimized to prevent some relays from being the bottleneck and guarantee high endtoend channel capacity. According to the proposed transmission environment coefficient, the path loss can be described in a new way, and then the distance of multiplehop relay system can be optimized more simply than the original one. However, when the system has no control on media access control (MAC) layer, performance of the system deteriorates because of the presence of interference signal. Thus, the specific transmission protocol on the MAC layer for multiplehop system is proposed to reduce the power of interference signal and to obtain high endtoend channel capacity. According to the proposed transmission protocol on the MAC layer, the system indicates the tradeoff between the endtoend channel capacity and the delay time. The endtoend channel capacity of the outdated channel state information system is also analyzed.
1 Introduction
Multipleinput multipleoutput (MIMO) relay systems have been discussed in several literatures [1–3]. Additionally, ergodic capacity of the amplifyandforward relay network is discussed. The links between the relay transmitters and relay receivers are assumed to be parallel [4] and serial [5, 6]. The endtoend channel capacity based on the different number of antennas at the transmitter, the relay, and the receiver also has been evaluated [5, 6]. However, the number of relays considered there (in [5, 6]) is only one.
When the number of antennas in relay is less than the number of antennas in the transmitter and receiver, the capacity of MIMO relay system is lower than that of the original MIMO system. Moreover, when the number of antennas in relay equals that in the transmitter and receiver or more, the MIMO relay system can provide the same average capacity as an original MIMO system. In other words, although the number of antennas in relay is larger than that in transmitter and receiver, the capacity of MIMO relay system cannot exceed the capacity of original MIMO system [7–10].
Therefore, in order to achieve a high channel capacity, the multiplehop relay system is considered [11, 12]. However, in these papers, the interference signal is assumed to be absent; the performance based on a transmission protocol that only has two phases is analyzed, the signaltonoise ratio (SNR) at the receiver is assumed to be fixed, and the location as well as the transmit power of each transmitter are not dealt. In the multiplehop MIMO relay system, when the distance between the source (TX) and the destination (RX) is fixed, the distance between the TX to a relay station (RS), RS to RS, and RS to the RX called the distances between transceivers, is shortened. Consequently, according to the number of relay and the location of the relays, the SNR and the capacity are changed. Hence, to achieve the high endtoend channel capacity, the location of each relay, meaning the distance between each transceiver, needs to be optimized. We have analyzed the performance of halfduplex multiplehop relay system with the amplifyandforward strategy [13] and decodeandforward strategy [14]. However, the multiplehop relay system has been optimized on the physical layer, and the transmission of each relay is assumed to be controlled accurately. In this paper, the transmission protocol on media access control (MAC) layer is proposed and the multiplehop relay system is optimized on both physical and MAC layers, the PHYMAC crosslayer. Additionally, the system is analyzed when the outdated channel state information (CSI) at the receiver is taken into account. The channel capacity in this paper is the ergodic channel capacity.
The rest of the paper is organized as follows. We introduce the channel model of perfect CSI multiplehop MIMO relay system in Section 2. Section 3 is the analysis of the system that has interference. The specific access control on the MAC layer is described in Section 4. The endtoend channel capacity of the outdated system is analyzed in Section 5. Finally, Section 6 concludes the paper.
2 Multiplehop MIMO relay system
2.1 Channel model
We assume that there are many relay nodes, i.e., mobile phone and personal computer, arranged in a straight line from the base station to the receiver. When the receiver wants to receive the information from the base station, it transmits the request message to the base station via the relay node. After receiving the message from the receiver, the relay node detects the CSI and adds its location information into the message and transfers to the other node. When the base station receives the request message, it optimizes the distance and the transmit power based on each transmission protocol of the MAC layer. According to the location information of each relay node added into the message, the base station decides the optimized relay node and its transmit power for the multiplehop relay system. Finally, the base station starts transmitting the information to the receiver.
Figure 1 shows m relays that intervened in the MIMO relay system. Let M, N, and K_{ i } (i=1,…, m) denote the number of the antenna at TX, RX, and RS _{ i }, respectively. The distance between each transceiver is denoted by d_{ i } (i=0,…, m). The distance between TX and RX is fixed as d_{total}. TX and all of the relays employ the amplifyandforward strategy. Mathematical notations used in this paper are as follows: x and X are scalar variables; x and X are vector and matrix variables, respectively; (·)^{H} is the conjugate transpose.
For easy description, TX and RX are also denoted as RS_{0} and RS _{m+1}, respectively. Since path loss is taken into consideration, the channel matrix is a composite matrix and is modeled as follows: $\sqrt{{l}_{i,i+1}}$H_{ i }, i=0,…, m, of which H_{ i } represents the channel matrix between RS _{ i } and RS _{i+1}, l_{i,j} denotes the path loss between RS _{ i } and RS _{ j }. The path loss is described in detail in the following section. H_{ i } is a matrix with independent and identical distribution (i.i.d), zero mean, unit variance, circularly symmetric complex Gaussian entries.
We assume that the transmit power of TX (E_{TX}) and the total transmit power of relays (E_{RS}) are fixed and are not affected by the change in the number of relays and antennas at each relay. In order to simplify the composition of relay and demonstrate the effect of optimizing the distance and the transmit power of each relay, we assume that the transmit power of each relay is equally divided into each antenna, and the number of antennas in each relay is the same. Moreover, zeroforcing algorithm is applied in both the transmitter and the receiver. At first, the system is assumed to be controlled and the interference is absent. All relays transmit the signal at the same time, with full allocation time. Hereafter, this system is called the ideal system, and the endtoend channel capacity of the ideal system is called the ideal endtoend channel capacity. After that, the interference between every transceiver is taken into consideration, and the specific access control is proposed to obtain high endtoend channel capacity.
In the ideal system, the ideal endtoend channel capacity of forward link (from TX to RX) in multiplehop relay systems is expressed as follows. When the signal s_{i−1} is transmitted from RS _{i−1}, the received signal at RS _{ i } is expressed as follows:
where n_{ i } is the noise vector of RS _{ i } and β_{i−1} denotes the amplification factor of RS _{i−1}, which is expressed as follows:
where p_{ i } represents the transmit power of one antenna of RS _{ i }.
When m relays are intervened, the signal s_{0} is transmitted from TX, and the received signal at RX becomes
where n_{system} denotes the noise vector of the system. Therefore, the system channel matrix is written by
According to the usage of the system channel matrix H, the multiplehop MIMO relay system can be analyzed the same as the conventional MIMO system.
2.2 Ideal endtoend channel capacity
Since amplifyandforward method is applied to the channel model, the noise is also amplified and transmitted to the next relay. Therefore, the system noise vector when m relays are intervened becomes as follows:
Since ${\mathbf{\text{n}}}_{i}{\mathbf{\text{n}}}_{i}^{\mathrm{H}}\phantom{\rule{1em}{0ex}}(i=0\dots m)$ can be assumed to be a unit matrix, we have
where σ^{2} is the covariance of the noise vector in all relays and f(l_{i,i+1},p_{ j },σ^{2}) is a polynomial of l_{i,i+1},p_{ j },σ^{2}. Since σ^{2}≪1 and the covariance of noise vector are smaller than the received power, the component containing σ^{4} can be ignored. Thus, Equation 6 can be changed to the following:
Consequently, the endtoend channel capacity of the multiplehop MIMO relay system is expressed as follows:
Let
With the abovementioned definition of H_{ i }, H_{ i }H${}_{i}^{\mathrm{H}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}(i=0,\dots ,m)$ becomes a Gaussian matrix regardless of the number of relays, the distance between each transceiver, and the transmit power of each relay. It means that the endtoend channel capacity is only restricted by f_{ m }. Therefore, function f_{ m } can be considered instead of the endtoend channel capacity. In order to achieve the high endtoend channel capacity, the function f_{ m } has to be minimized.
2.3 Path loss
As in Equation 8, the system channel matrix is proportional to p_{i} and l_{i,i+1}. Therefore, the path loss plays an important role in the channel model. Since there are a lot of obstacles in the propagation environment, such as huge building, it is necessary to consider the path loss as being attenuated by the reflection. The power of signal is reduced, corresponding to the transmission distance and the number of reflections. An amount of the reduction by onetime reflection is called reflection factor. Naturally, the reflection factor is changed according to the shape of obstacles, the angle of reflections, and so on. However, in this paper, the reflection factor of all reflections is assumed to be the same and denoted by a. The path loss is expressed as follows [15–21]:
where t_{ i } is the reflected number while the signal is transmitted between RS _{ i } and RS _{i+1}. Additionally, the propagation environment is specified by the propagation environment coefficient. The propagation environment coefficient W is defined as the average distance of the lineofsight distance between each transceiver. Therefore, the reflected number between each transceiver can be expressed as ${t}_{i}=\frac{{d}_{i}}{{W}_{i}}$ and the path loss in Equation 10 can be rewritten in the following new type:
According to the new type, the path loss becomes a function of the distance only. Additionally, the Taylor expression is applied into the term ${a}^{\frac{{d}_{i}}{{W}_{i}}}$, and then the path loss becomes an equation of higher degree of the distance. Therefore, the distance can be optimized easily by the mathematical method or the particle filter method that be explained in the following section.
3 System that has interference
3.1 System model
Up to now, the interference signal is assumed to be absent and the system has been analyzed. However, when the system has no control on the MAC layer or has incomplete control, the interference signal is present. The received signal at RS _{ i } is considered. RS _{ i } simultaneously receives the desired signal s_{i−1} from RS _{i−1}; the interference signal s_{i−2}, from RS _{i−2}; and the interference signal s_{i+1}, from RS _{i+1}. Actually, RS _{ i } receives the interference signal not only from the neighbor transmitters RS _{i−2} (forward link) and RS _{i+1} (backward link), but also from all of the transmitters. However, the interference signal from the other relay is weaker than the interference signal from the neighbor transmitters. Hence, the interference signals from the other relays can be ignored, and the received signal at RS _{ i } is expressed as follows:
where H_{ i j } is the channel matrix between RS _{ j } and RS _{ i }. Consequently, the endtoend channel capacity of the system has an interference that can be expressed as follows:
where
In comparison with the ideal endtoend channel capacity, the term of interference ${\sum}_{i=1}^{m}{l}_{i1,i}{p}_{i1}$ of the forward link and ${\sum}_{i=0}^{m2}{l}_{i+1,i+2}{p}_{i+2}$ of the backward link is added. Similar to the case of the ideal system, the transmit power and the distance can be optimized by mathematical method [13, 14]. However, the optimization distance of the system with difference W_{ i }, especially if the system has interference, is complicated. In order to easily optimize the distance and the transmit power simultaneously, the particle filter algorithm is applied.
3.2 Particle filter method
In this section, we propose the particle filter (PF) method to optimize both the distance and the transmit powers simultaneously for high endtoend channel capacity. The algorithm is shown in Figure 2 and explained as follows.
Let d and E denote 1×m+1 distance and transmit power vectors, respectively:

Step 1: 10,000 × random samples of d and E are generated. The function f for each sample is calculated, and the minimal value f of all samples is denoted by minf. The sample of d and E which has minf is called the optimal sample.

Step 2: 10,000 × samples of d and E are generated around the optimal sample by random function. The function f for each sample is calculated and is compared to minf.

Step 3: If there is a function f which is smaller than minf, then minf is renewed and the process returns to step 2. Otherwise, the algorithm is finished.
To evaluate the particle filter method, the function f in (14) is calculated with the parameters summarized in Table 1. Figure 3 shows the value of function f where the number of relays is 3 and 10. In the case where the number of relays is 10, the number of samples is changed, i.e., 1,000 and 10,000. As shown in Figure 3, the value of function f decreases when the number of circles increases, and the algorithm is finished when function f reaches the minimum. The minimum of function f is achieved in the system with average W[14]. Therefore, the algorithm can be finished when function f reaches the value of f in the system with average W.
As shown in Figure 3, we can recognize that the number of circles decreases when the number of relays is small and/or the number of samples is larger. However, the PF method requires a large number of samples to converge. If the number of samples is not enough, then the algorithm would not converge or it would take a huge number of circles.
3.3 Numerical evaluation for the system that has interference
The system parameter is summarized in Table 1. In order to evaluate the optimization of distance and transmit power. We assume that all relays are arranged in a straight line from the TX to the RX; the transmit power of the RX and the total transmit power of all relays are fixed.
The endtoend channel capacity of the system in which the transmission of all relays is controlled or not is shown in Figure 4. The endtoend channel capacity of the system that has interference is much lower than the ideal endtoend channel capacity. Therefore, in order to obtain the high endtoend channel capacity, the access control on the MAC layer should be considered
4 Specific access control on MAC layer
4.1 Multiplephase transmission
In this paper, the transmission protocol of all relays is assumed to be controlled on time domain. The transmission of all relays is divided into multiple phases of time domain. The relay in the same phase transmits the signal in the same allocation time that is denoted by t_{ i }. The other relay that will be divided into different phases keeps the silence or receives the signal. Since the neighbor relay transmits the signal in different phases, the interference signal is weaker than that of the system that has no control. Therefore, the endtoend channel capacity can be respected to be higher.
Figure 5 shows two and three phases of transmission protocol. The twophase transmission protocol is explained as follows. The evennumber relays and the oddnumber relays transmit the signal in phases 1 and 2, respectively. Therefore, in the twophase transmission protocol, the closest interference relays of the backward and forward links to RS _{ i } are RS _{i+1} and RS _{i−3}, respectively.
The endtoend channel capacity of the system with n phases can be written as follows:
where
Compare the interference component of the system, it has no control (14) to that of the system with nphase transmission protocol (16), the distance from the interference relay is longer, and the number of interference relay is also larger. Hence, we can say that according to the control on MAC layer, the power of interference decreased; thus, the endtoend channel capacity is expected to be higher.
4.2 Numerical evaluation for multiplephase transmission
The allocation time for each phase is assumed to be 1 s, and the system model is the same as the one mentioned. In order to evaluate the transmission protocol on the MAC layer, the distance between each transceiver and the transmit power of each relay are assumed to be equal. Figure 6 shows the endtoend channel capacity in case the access of all relay is controlled on the MAC layer.
For all cases, such as in phases 1 to 4, we find the optimum number of relays which achieves the highest endtoend channel capacity. The reason is that, similar to the ideal system, when the number of relay increases, the distance between each transceiver becomes shorter; thus, the power of desired signal increases and the endtoend channel capacity increases. However, the interference signal is taken into account. When the number of relays is small, the distance between each transceiver is large; therefore, the power of interference signal is low and the endtoend channel capacity is high. Moreover, when the number of relays is large, the power of interference signal increases. Therefore, the signaltointerference noise ratio (SINR) decreases, and the endtoend channel capacity decreases.
The endtoend channel capacity of onephase and twophase transmission protocols is almost the same. The reason is that, compare to twophase transmission protocol in Subection 4.1, in onephase transmission protocol, the closest interference relays of backward link and forward link to RS _{ i } are RS _{i+1} and RS _{i−2}, respectively. Therefore, the power of interference signal to each relay in both phase transmission protocols is almost the same.
The optimum number of relays and the highest endtoend channel capacity are different for each phase. Since the power of interference signal decreases when the number of phases increases, the endtoend channel capacity of the higher number of phases is higher than that of lower number of phases. In order to evaluate the multiplehop relay system, the system without relay node, meaning the direct link from the TX to the RX, is taken into consideration. In the case of direct link, the transmit power of TX is 200 mW (the sum of transmit power of TX and all relay nodes); the other parameters are the same as those in the multiplehop relay system (Table 1). The channel capacity of direct link is 6×10^{−4} bit/s/Hz, which is much smaller than that of the multiplehop relay system (Figure 6). The reason can be that the signal power is reduced by the distance to the power of 2 and the number of reflections; compared to the direct link, the distance of the multiplehop relay system is shorter and the number of reflections is smaller. Therefore, although the interference signal is present, the SINR of the multiplehop relay system is higher than the SNR of the direct link. Since the channel capacity of direct link is much smaller than that of the multiplehop relay system in the proposed propagation environment, hereafter, only the channel capacity of the multiplehop relay system is considered. However, the delay time of each scenario should be considered. The delay time is defined as the delay of transmitted signal to the RX compared to the original MIMO system (the direct link). The delay time of the signal transmitted from the TX to the final receiver RX is described in Figure 7. We can recognize that the delay time increases when the number of relays as well as the number of phases increase. It is the tradeoff between the endtoend channel capacity and the delay time.
As shown in Figures 4 and 6, the endtoend channel capacity of the system that has control on the MAC layer is higher than that of the system that has no control. However, it is smaller than the ideal endtoend channel capacity. In order to obtain the higher endtoend channel capacity, the distance and the transmit power should be optimized based on each transmission protocol on the MAC layer or the MACPHY crosslayer.
4.3 Numerical evaluation for MACPHY crosslayer
For MACPHY crosslayer, for each transmission protocol on the MAC layer, the distance and the transmit power are optimized simultaneously by particle filter method (Subsection 3.2). The allocation time for each phase is assumed to be 1 s, and the system model is the same as mentioned. The endtoend channel capacity of the MACPHY crosslayer is shown in Figure 8.
Similar to the system that only has control on the MAC layer, there is the optimum number of relays which achieves the highest endtoend channel capacity and the tradeoff of channel capacitydelay time. However, comparing to the system that has equal distance and transmit power (Figure 6), the endtoend channel capacity of the system with MACPHY crosslayer is much higher.
Up to now, since the transmission of relay node is assumed to be isotropic, there is the interference from both forward link and backward link. However, the MIMO relay node can use the beamforming technique to transmit the signal to the next relay. It means that the signal is transmitted to the forward link only and that the interference from the backward link is absent. Figure 9 shows the endtoend channel capacity of system that only has the forward link interference.
As shown in Figure 9, the endtoend channel capacity increases when the transmission phase increases. Additionally, the tradeoff of the channel capacitydelay time can be applied to this scenario. However, comparing to the system that has interference from both forward link and backward link (Figure 8), the endtoend channel capacity of the system that only has the forward link interference (Figure 9) is much higher. It means that there is the tradeoff between complication and channel capacity. The beamforming of MIMO can be applied in the scenario that the higher channel capacity is requested and that the device is large enough to equip the MIMO beamforming.
Up to now, the allocation time of each phase is assumed to be 1 s. Thus, there is the tradeoff between the channel capacity and the delay time. However, when the transmission time is normalized, it means that the time to transmit the signal from the TX to the final receiver RX is fixed at 1 s and the allocation time of each phase is changed, depending on the number of phases. The larger the number of phases, the smaller the allocation time of each phase becomes. The system model is the same as mentioned, and the relationship between the endtoend channel capacity and the number of relays when the transmission time is normalized, as shown in Figure 10. In this system, we also assume that MIMO beamforming is applied for all relays; therefore, only the interference from the forward link is taken into account.
As shown in Figure 10, there are the optimal numbers of relays in the sense of maximal endtoend channel capacity of each number of phases. Additionally, the maximal endtoend channel capacity and the optimal number of relays are changed, depending on the transmit power of TX, the total transmit power of RS, the transmission environment (W), and so on. In the case where the number of relays is small, the optimization of the system has no control on the MAC layer (all relays transmit the signal at the same time, one phase) which can reach the higher endtoend channel capacity than in other scenarios. Moreover, in the case where the number of relays is large, the higher number of phases can obtain the higher endtoend channel capacity. Hence, to obtain the high endtoend channel capacity, the appropriate number of relays, the number of phases, and so on should be adopted.
5 Outdated CSI system
5.1 System model
Up to now, the performance of the system is analyzed under the assumption of a perfect CSI at both the transmitter and receiver. However, in actuality, the perfect CSI assumption is not always practical due to channel estimation errors, feedback channel delay, and noise. Compared to channel estimation errors, the CSI imperfection introduced by feedback channel delay is sometimes more significant and inevitable.
To characterize the outdated CSI at the RS _{ i }, the channel time variation is described by the firstorder Markov process:
where τ denotes the total delay caused by signal processing, feedback, and other system delays, ρ=J_{0}(2π f_{ D }τ) is the time correlation coefficient, J_{0}(·) is the zeroorder Bessel function of the first kind and f_{ D } denotes the maximum Doppler frequency shift. k denotes $\sqrt{1{\rho}^{2}}$. The innovation term ${\stackrel{\u0304}{\mathbf{H}}}_{i}$ also has i.i.d entries, zero mean, and unit variance. For notation brevity, we drop off the time index:
where ${\widehat{\mathbf{H}}}_{i}$ denotes the outdated channel matrix while H_{ i } is the true one.
We assume that the transmitter adds the CSI in the data packet and transmits to the receiver; thus, the receiver knows both H_{ i } and ${\widehat{\mathbf{H}}}_{i}$. After receiving the data packet, the receiver feedbacks the CSI to the transmitter immediately. However, the transmitter should wait some phases to transmit the signal; therefore, this CSI becomes the outdated CSI. It means that the transmitter only knows the outdated CSI ${\widehat{\mathbf{H}}}_{i}$, while the receiver knows both H_{ i } and ${\widehat{\mathbf{H}}}_{i}$. In an SVDbased MIMO system, the relay RS _{ i } steers the modulated signal vector s_{ i } within the eigenspace spanned by the right singular vectors contained in ${\widehat{\mathbf{E}}}_{i}^{t}$:
The relay RS _{i+1} receives the signal the same way as that in Subsection 2.1:
and it preprocesses ${\mathbf{s}}_{i+1}^{r}$ using ${\widehat{\mathbf{E}}}_{i+1}^{r}$:
We can also use mode complex algorithms such as minimum mean squared errors or maximum likelihood to achieve better performance at the cost of higher complexity. A basic conclusion is that the more complex methods do perform better in outdated CSI condition. However, the improvement is limited and is at the cost of higher complexity. We use this method for its low complexity and ease of analysis. The l th component of vector x and the l th row of matrix x are denoted by x(l) and x(l), respectively. The componentwise form is expressed as follows:
where the received signal consists of three components: the informationcarrying term, the interference term, and the noise term. The correlation matrix is approximate to the unit matrix. Therefore, the endtoend channel capacity of n phase outdated CSI system is changed as follows:
where [t]
for the system that has interference from both forward link and backward link.
for the system that has interference from only forward link (using MIMO beamforming).
Compared to the system that has perfect CSI at both the transmitter and the receiver (14), in the endtoend channel capacity of the system that has outdated CSI at the transmitter (25), the cochannel interference by outdated CSI is added.
5.2 Endtoend channel capacity of outdated CSI system
The distance and the transmit power of the outdated CSI system is optimized by particle method (Subsection 3.2). The system model is the same as the one mentioned. The parameter is summarized in Table 1. As explained, the endtoend channel capacity is changed depending on the number of relays. However, in this section, the endtoend channel capacity, depending on the outdated CSI, is examined. Therefore, we fix the number of relays.
Figures 11 and 12 show the endtoend channel capacity of the system that only has the interference from the forward link (using the MIMO beam forming) where there are four numbers of relays. The endtoend channel capacity of the system in the case where the transmission time is normalized is shown in Figure 12.
As shown in Figures 11 and 12, the endtoend channel capacity is decreased when the term f_{ D }τ increases. It can be explained that when the term f_{ D }τ increases, the power of interference signal is increased; therefore, SINR decreases. The decrease of endtoend channel capacity in each number of phases is different regardless of how large the endtoend channel capacity is in the case of the perfect CSI system. The higher the number of phases, the larger the delay time becomes. Therefore, the endtoend channel capacity of the system has the higher number of phases that decreased more rapidly. It means that the onephase transmission protocol is the most robust regardless of the number of relays. Figure 13 shows the endtoend channel capacity of eight relay systems. Although the endtoend channel capacity of the onephase system in the case of the perfect CSI (or when the term f_{ D }τ is small) is lower than that of the higher number of phase systems, it becomes higher than the other higher number of phase systems when the term f_{ D }τ increases.
6 Conclusions
In this paper, we analyzed the endtoend channel capacity of multiplehop MIMO relay system with MACPHY crosslayer. Compared to the system that has no control on the MAC layer, the endtoend channel capacity of the system that has control on the MACPHY crosslayer is higher. It means that the tradeoff of channel capacitycomplication is indicated. There is the optimum number of relays for each access control on the MAC layer that achieves the maximal endtoend channel capacity. However, there is the tradeoff between channel capacity and delay time. The system with outdated CSI is also analyzed, and the endtoend channel capacity of the low number of phases is more robust than that of the higher number of phases regardless of the number of relays.
However, in this paper, the ergodic channel capacity has been analyzed, and we only proposed the MAC layer protocol; the appropriate modulation and code word were not considered. In the future, realtime channel capacity, the appropriate modulation, and code word will be examined. In addition, the optimal combination of the MAC layer and physical layer will be analyzed.
References
 1.
Wang B, Zhang J, hostMadsen A: On the capacity of MIMO relay channel. IEEE Trans. Inf. Theory 2005, 51(1):2943.
 2.
Shiu DS, Foschini GJ, Gans MJ, Kahn JM: Fading correlation and its effect on the capacity of multielement antenna systems. IEEE Trans. Commun 2000, 48(3):502513. 10.1109/26.837052
 3.
Gesbert D, Bolcskei H, Gore DA, Paulraj AJ: MIMO wireless channel: capacity and performance prediction. Proc. GLOBECOM 2000, 2: 10831088.
 4.
Liang Y, Veeravalli V: Gaussian Orthogonal relay channels: optimal resource allocation and capacity. IEEE Trans Inf. Theory 2005, 51(9):32843289. 10.1109/TIT.2005.853305
 5.
Lee K, Kim J, Caire G, Lee I: Asymptotic ergodic capacity analysis for MIMO amplifyandforward relay networks. IEEE Trans. Commun 2010, 9: 27122717.
 6.
Jin S, McKay M, Zhong C, Wong K: Ergodic capacity analysis of amplifyandforward MIMO dualhop systems. IEEE Trans. Inf. Theory 2010, 56(5):22042224.
 7.
Gastpar M, Vetterli M: On the capacity of large Gaussian relay networks. IEEE Trans. Inf. Theory 2005, 51(3):765779. 10.1109/TIT.2004.842566
 8.
Tsuruta M, Karasawa Y: Multikeyhole model for MIMO repeater system evaluation. IEICE Trans. Commun 2006, J89B(9):17461754.
 9.
Chizhik D, Foschini GJ, Gans MJ, Valenzuela RA: Keyholes, correlations, and capacities of multielement transmit and receive antennas. IEEE Trans. Wireless Commun 2002, 1(2):361368. 10.1109/7693.994830
 10.
Levin G, Loyka S: On the outage capacity distribution of correlated keyhole MIMO channels. IEEE Trans. Inf. Theory 2010, 54(7):32323245.
 11.
Giindiiz D, Khojastepour M, Goldsmith A, Poor H: Multihop MIMO relay networks: diversitymultiplexing trade off analysis. IEEE Trans. Wireless Commun 2010, 9(5):17381747.
 12.
Razaghi P, Yu W: Parity forwarding for multiplerelay networks. IEEE Trans. Inf. Theory 2009, 55(1):158173.
 13.
Hiep P, Kohno R: Optimizing position of repeaters in distributed MIMO repeater system for large capacity. IEICE Trans. Commun 2010, E93B(12):36163623. 10.1587/transcom.E93.B.3616
 14.
Hiep PT, Fumie O, Ryuji K: Optimizing distance, transmit power and allocation time for reliable multihop relay system. EURASIP Journal on Wireless Communications and Networking 2012, 2012: 153. 10.1186/168714992012153
 15.
ITUR: Radiowave Propagation. In Recommendation ITUR P.5268: propagation by diffraction. Geneva: ITUR; 2003.
 16.
ITUR: Radiowave Propagation. In Recommendation ITUR P.6769: attenuation by atmospheric gases. Geneva: ITUR; 2001.
 17.
ITUR: Radiowave Propagation. In Recommendation ITUR P.8382: Specific attenuation model for rain for use in prediction methods. Geneva: ITUR; 2001.
 18.
ITUR: Radiowave Propagation. In Recommendation ITUR P.10571: probability distributions relevant to radiowave propagation modelling. Geneva: ITUR; 2001.
 19.
ITUR: Radiowave Propagation. In Recommendation ITUR P.12383: propagation data and prediction methods for the planning of indoor radiocommunication systems and radio local area networks in the frequency range 900 MHz to 100 GHz. Geneva: ITUR; 2003.
 20.
ITUR: Radiowave Propagation. In Recommendation ITUR P.14112: propagation data and prediction methods for the planning of shortrange outdoor radiocommunication systems and radio local area networks in the frequency range 300 MHz to 100 GHz. Geneva: ITUR; 2003.
 21.
Kita N, Yamada W, Akio S: Path loss prediction model for the overrooftop propagation environment of microwave band in suburban areas. (in Japanese) IEICE Trans.Commun, J89B(2) 2006, 115125.
Author information
Additional information
Competing interests
The authors declare that they have no competing interests.
Authors’ original submitted files for images
Below are the links to the authors’ original submitted files for images.
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Hiep, P.T., Hoang, N.H., Chika, S. et al. Endtoend channel capacity of MACPHY crosslayer multiplehop MIMO relay system with outdated CSI. J Wireless Com Network 2013, 144 (2013). https://doi.org/10.1186/168714992013144
Received:
Accepted:
Published:
Keywords
 Medium Access Control
 Channel State Information
 Relay Node
 Path Loss
 Channel Capacity