Endtoend channel capacity of MACPHY crosslayer multiplehop MIMO relay system with outdated CSI
 Pham Thanh Hiep^{1}Email author,
 Nguyen Huy Hoang^{2},
 Sugimoto Chika^{1} and
 Kohno Ryuji^{1}
https://doi.org/10.1186/168714992013144
© Thanh Hiep et al.; licensee Springer. 2013
Received: 17 December 2012
Accepted: 15 May 2013
Published: 29 May 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 The endtoend channel capacity of the outdated channel state information system is also analyzed.
Keywords
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.
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.
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
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
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
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

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.
Numerical parameters
Antenna elements at TX, RX, RS  4 

Transmit power of TX (mW)  100 
Total transmit power of RS (mW)  100 
Noise power (mW)  6.12e011 
Reflection factor  0.38 
Distance between TX and RX (m)  3,000 
Average LOS W (m)  500 
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.
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.
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
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.
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
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.
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.
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.
where ${\widehat{\mathbf{H}}}_{i}$ denotes the outdated channel matrix while H_{ i } is the true one.
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:
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.
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.
Declarations
Authors’ Affiliations
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