Multihop relaying and multiple antenna techniques: performance tradeoffs in cellular systems
 Kevin R. Jacobson^{1, 2} and
 Witold A. Krzymień^{1, 2}Email author
https://doi.org/10.1186/16871499201165
© Jacobson and Krzymieńń; licensee Springer. 2011
Received: 2 September 2010
Accepted: 18 August 2011
Published: 18 August 2011
Abstract
Two very important and active areas of wireless research are multihop relaying and multiple antenna techniques. Wireless multihop relaying can increase the aggregate network data capacity and improve coverage of cellular systems by reducing path loss, mitigating shadowing, and enabling spatial reuse. In particular, multihop relaying can improve the throughput for mobiles suffering from poor signal to interference and noise ratio at the edge of a cell and reduce cell size to increase spectral efficiency. On the other hand, multiple antenna techniques can take advantage of scattering in the wireless channel to achieve higher capacity on individual links. Multiple antennas can provide impressive capacity gains, but the greatest gains occur in high scattering environments with high signal to interference and noise ratio, which are not typical characteristics of cellular systems. Emerging standards for fourth generation cellular systems include both multihop relaying and multiple antenna techniques, so it is necessary to study how these two work jointly in a realistic cellular system. In this paper, we look at the joint application of these two techniques in a cellular system and analyze the fundamental tradeoff between them. In order to obtain meaningful results, system performance is evaluated using realistic propagation models.
Keywords
I Introduction
The key goals for future broadband cellular systems are: reliable data transmission up to 1 Gb/s at high spectral efficiency, good coverage throughout the cells, and the ability to reliably serve a large number of mobile users. However, the wireless channel is a very difficult communications channel over which to achieve reliable high speed data transmission. Due to numerous impairments, such as multipath propagation, random fading, high signal losses, and interference, a strongly attenuated and corrupted signal appears at the receiver. In order to overcome this problem, wireless systems must use sophisticated transmission and receiver processing techniques in order to achieve satisfactory throughput at an acceptable error rate. Cellular systems are interference limited by design in order to maximize their capacity. As a result, mobile users suffer from low signal to interference and noise ratio (SINR), especially when they are at cell edges. This work considers two techniques that hold promise to further improve spectral efficiency of cellular systems while preserving their wide area coverage: multihop (MH) relaying and multipleinput multipleoutput (MIMO) antenna techniques.
MIMO transmission can improve capacity within a given bandwidth by taking advantage of the rich scattering in a typical wireless channel [1, 2]. MIMO spatial multiplexing uses uncorrelated spatial signatures of signals at the receiver to create a number of spatial channels to greatly increase capacity. This approach requires complex physical layer processing at the transmitter and/or receiver, and in order to approach potential capacity, full knowledge of the channel gains between all pairs of transmit and receive antennas. Under some circumstances, channel state information must be known at both the transmit and receive ends. Multiple antennas also create diversity that may be exploited to increase reliability of transmissions. Both of these techniques provide the greatest gains in richly scattering channels described by a Rayleigh model. A Rayleigh channel is a channel in which no direct line of sight (LOS) exists, so all of the transmitted energy is scattered (and highly attenuated as a result) prior to reception. MIMO can provide great capacity gains, but essentially, it requires a poor channel to do so. When scattering in the channel is not sufficient (e.g., in some Ricean channels), multiple antennas at the transmitter can be used for beamforming, in which the transmitted beam is steered toward the intended receiver. MIMO spatial multiplexing provides the greatest capacity gains at high SINR; however, cellular systems typically operate at low SINR, with users at cell edges suffering from the poorest SINR.
Multihop relaying [3–5], on the other hand, strives to mitigate transmission impairments by reducing the path loss between transmitter and receiver with the addition of intermediate wireless relays. With a short link hop, the path loss is greatly reduced, and obstacles can be avoided so that the SINR is increased and random signal fluctuations due to both shadowing and scattering are reduced. Higher link capacities and improved reliability can thus be obtained. With the higher SINR provided by multihop relaying, it is expected that MIMO techniques may perform better.
It has been observed that a cellular capacity wall of 350 Mb/s/cell [6] is on the horizon. Therefore, it is necessary to use smaller cells in order to achieve a higher spectral efficiency over an area (b/s/Hz/km^{2}). One method of achieving this is to divide the larger cell, typically 1 to 2 kilometer in radius, into smaller subcells in which relay stations (RSs) serve mobile stations (MSs) closest to them. Numerous researchers have looked at the various approaches to MH relaying in cellular systems [7–12]. Two proposals under consideration for 4G IMTAdvanced [13–15]: IEEE 802.16m [16, 17] and LTEAdvanced [18, 19] will include relaying as options. Clearly, relaying requires more complicated system level algorithms (medium access control MAClayer and higher) in order to achieve good results in a network of wireless stations. Also, MH relaying requires additional system resources (time or frequency slots), and hence the spectral efficiency (measured in b/s/Hz) may suffer under some conditions. It seems natural to combine MIMO and relaying techniques in order to improve the performance of a cellular system, but it is necessary to determine how well they work together and what tradeoffs exist in combining them. In addition, it is necessary to use a system model that captures the radio frequency (RF) propagation of a typical cellular system accurately.
There exists a theoretical analysis of MH MIMO systems [20]. However, some results in it have been derived under simplifying assumptions, and the complexity of a deployable MH MIMO system makes it difficult to predict its realistic performance. Thus, we have focussed on simulating and calculating system performance using realistic cellular environments, with parameters and models recommended in emerging standards such as 802.16 [21] and established ones of the 3rd generation partnership project (3GPP) [22]. In particular, the measure of success of MIMO combined with MH relaying depends greatly on the physical environment in which the system operates. We consider typical urban scenarios, at first analyzing a onedimensional system and then looking at twodimensional cellular systems with both hexagonal and Manhattan topologies.
Our work studies a cellular system combining decode and forward (DF) MH relaying with multiple antenna techniques with the goal of achieving higher data carrying capacity simultaneously with good system coverage. Much research has emerged recently on MH relaying and multiple antennas, which means there are a large number of considerations in the design of such a system. Our initial results in that area were presented in conference papers [23, 24]. This paper provides a more complete description of the system model used, additional more detailed results, their more extensive and much more insightful discussion and resulting conclusions, which may be of great value to cellular system designers.
The remainder of this paper is structured as follows: Section II provides details on the system model used for the MIMO link, a simple onedimensional MH MIMO network and a twodimensional cellular MH MIMO network. Section III gives calculated results for numerous scenarios. Section IV provides some detailed discussion of the results and Section V concludes the paper.
II System model
The MH model used in this paper is an extension of the single antenna MH relaying work in [25–27], in which typical cellular topologies and system parameters are used to calculate network throughput achievable using MH relaying. In the present paper, which presents and extends the research presented in [23, 24], we include the benefits of multiple antenna techniques. The model is necessarily complex, taking into account both physical layer (PHY) and medium access control (MAC) layer considerations. A dual slope path loss model with distance and other parameters typical of cellular systems is used. We capture both nonline of sight (NLOS) Rayleigh and line of sight (LOS) Ricean aspects, which are selected as a function of distance.
A PHY layer model
1) MIMO Link
2)Onedimensional multihop relaying system
where x is distance, and b is the distance breakpoint, below which a NLOS path becomes LOS (typically 300 m in urban areas). A lognormal random variable, ψ_{dB}, is optionally added in (7) to model random shadowing effects. ψ_{dB} has zero mean, and its standard deviation, σ_{ψ dB}, is typically 10 dB in an urban NLOS microcell, and 4 dB in an urban LOS microcell [22].
From (7) and (8), we can see that the channel matrix elements are modeled as Rayleigh random variables when b < x < 5, 000 m and Ricean (with K_{ r } > 0) when 20m < x < b. This is a general and simple method of modeling the channel for the purposes of studying the interaction of MH relaying and MIMO in this paper. The precise RF propagation characteristics of a system will depend on the specific location, and a more accurate RF propagation simulation would be required. However, we believe that this simple model will enable sufficient insight into the system behaviour.
When calculating the SINRs for the hops, interference from all other transmitting stations is included, at levels determined by their transmit powers, distances from the receiver, and antenna gains (see [25–27] for the detailed parameters). In MH relaying, interfering stations are usually far enough away that their signals experience the higher NLOS path loss.
Model parameters
Carrier frequency, f_{ c }  5.8 GHz 

Channel bandwidth, W  10 MHz 
Receiver noise figure, F  8 dB 
Maximum transmit power, P_{ TX }  30 dBm 
Omni antenna gain, G_{ TX }, G_{ RX }  9 dBi 
Directional antenna gain, G_{ TX }, G_{ RX }  17.5 dBi 
Directional antenna frontback ratio, G_{ FB }  25 dB 
Link margin, M  5 dB 
PHY mode  802.16 OFDM256 
BS antenna height  32 m 
Subcell RS antenna height  10 m 
MS antenna height  1.5 m 
Building height  12 m 
Mixed MH MIMO case
N _{ T }  N _{ R }  

BS  4  4 
RS  3  3 
MS  2  2 
3) Twodimensional multihop cellular system
MSs will be served by the closest RS or BS, handing off as necessary to a closer station as the MS moves. As a result, some MSs will obtain service directly from the BS (one hop), some MSs will be served by RSs via two or more hops depending on their locations. MSs at the cell edge will be served via the maximum number of hops in the cell. Wireless transport links exist between the BS and its closest RSs, and between adjacent RSs, and access links exist between a MS and its serving RS or BS. We consider only decode and forward relaying, in which the data stream is decoded and reencoded at RSs before transmitting on the next hop. All relay stations are wireless and may not transmit and receive simultaneously (halfduplex). We can calculate the signal to interference and noise ratio (SINR) at each station's receiver and then find the rate attainable on each hop using a process similar to that described for the onedimensional network.
B MAC layer
The previous section described the calculation of PHY layer capacities of each hop. But the key measure of performance of MH MIMO in a cellular system is the overall achievable network capacity, R_{Net}. The MAC layer coordinates transmissions as the data propagates from BS through RSs to the destination MSs, and so we must now consider networkwide scheduling of these transmissions in order to determine network capacity.
As a first step, we consider nonspatial reuse scheduling, in which only one station in the entire macrocell is allowed to transmit in a channel at a particular time. This is not an efficient use of bandwidth, so we also consider spatial reuse in which simultaneous transmissions occur in the macrocell. In order to avoid interstation interference and to ensure that a station is guaranteed not to be transmitting at the same time it is receiving (Laneman's halfduplex constraint [34]), stations close to (one hop away from) a transmitting station must remain silent.
1) Onedimensional multihop relaying
where p ≤ n_{hops} is an odd integer and q ≤ n_{hops} is an even integer.
2) Twodimensional multihop cellular system
R_{Net} in a twodimensional system can be calculated knowing the data rates achievable on each of the links, and by considering the spatial reuse schedule imposed by the medium access control layer (MAC). With spatial reuse, data transmission can occur simultaneously in numerous subcells within the cell. The details of spatial reuse as applied to MH relaying have been presented in [27]. Expressions for R_{Net} have been derived for up to fourhop hexagonal and Manhattan cellular topologies. These expressions are used to obtain the results presented here.
III Results
A Single MIMO hop
Cellular systems generally operate at a fairly low SINR. It is easy to see from this figure that the rate advantage due to MIMO is relatively low at low SINR. We can increase the SINR on each hop by adding relays, but this may increase K_{ r } , which reduces the MIMO capacity gain, until at K_{ r } = ∞, there remains only 6 dB array gain due to multiple receive antennas. From (8) we find that K_{ r } is still about 10 at a fairly short distance of 100 m, and so MIMO gain, although reduced at this distance, is not completely lost.
B Onedimensional multihop relaying
Figure 8 clearly shows the importance of spatial reuse in MH relaying. When there are more than two hops, channels (time or frequency slots) can be reused at stations that are adequately separated in space, which provides great increases in networkwide spectral efficiency despite the introduction of interference between subcells. Without spatial reuse, interference is lower, but MH relaying is more wasteful of spectrum. As shown in Figure 8a, no spatial reuse case, R_{Net}, decreases beyond 6 hops since relaying is increasingly wasteful of resources. With fewer than 6 hops, the addition of relays is slightly beneficial since the increase in SINR afforded by shortening the hop distances increases the MIMO gain. In Figure 8b, with spatial reuse, R_{Net} continuously increases with the number of hops. With more relays, there is more opportunity for channel reuse in distant parts of the cell.
Cumulative distribution functions of MH MIMO network capacity for some cases are shown in Figure 9. The figure demonstrates the drastic capacity increase that MH relaying can achieve by avoiding NLOS propagation and enabling spatial reuse, and the gradual increase in capacity afforded by MIMO.
C Twodimensional multihop cellular system
In this section, we extend the calculations to a cellular system with tesselated Manhattan and hexagonal cells with one to four hops using the results of [27].
Universal frequency reuse is used among the cells for all cases. We assume the use of omnidirectional (in the horizontal plane) antenna elements for the MIMO arrays since they provide the greatest spatial spread.
Hop distances: 500 m radius hexagonal cell
Distance per hop (m) and path type (NLOS/LOS)  

n  r _{ 1 }  r _{ 2 }  r _{ 3 }  r _{ 4 } 
1  500NLOS       
2  333NLOS  167LOS     
3  200LOS  200LOS  100LOS   
4  143LOS  143LOS  143LOS  71LOS 
SINR: 500 m radius hexagonal cell
SINR per hop (dB)  

n  Hop 1  Hop 2  Hop 3  Hop 4 
1  5.4       
2  12.9  19.4     
3  28.9  19.8  17.4   
4  32.5  27.9  18.4  16.1 
It is useful to observe how distances, path losses, and SINRs change as relays are added to this system. The nonlinear path loss model used, combined with the effect of scheduling transmissions among subcells within a cell, gives some nonlinear and somewhat surprising results.
With no relays (n = 1), an MS at the cell edge is 500 m from the BS, which gives a NLOS channel according to the path loss model (7). In this case, reception at the MS suffers from high cochannel interference from adjacent cells and a very poor SINR since we are considering universal frequency reuse among cells. The twohop (n = 2) hexagonal case has six RSs around the BS that gives two hops between the BS and any MS at the cell edge. The first hop, between the BS and any RS, is about 333 m and therefore is Rayleigh/NLOS according to the dual slope model. The second hop, between any RS and a celledge MS, is about 167 m and Ricean/LOS. The firsthop link suffers from high path loss, and experiences high cochannel interference from numerous RSs in other cells. In fact, there are three interfering RSs in other cells that are the same distance away as the BS. The interference is particularly bad from those RSs since the scheduling of RS transmissions in the other cells is not coordinated with the BS and RSs in the studied cell. Interference from within the studied cell is eliminated by scheduling. The second hop has a much better SINR since that link enjoys a much reduced path loss due to LOS, yet interfering signals are a greater distance away and experience higher losses due to NLOS.
Adding 12 more RSs creates a threehop hexagonal system. All three hops to an MS at the cell edge are LOS channels but the interfering channels are still NLOS. Also, RSs within the studied cell can be scheduled to minimize cochannel interference. Interfering RSs in other cells, uncoordinated with transmissions in the study cell, are now a much greater distance away and so have much less impact than in the twohop case. The resulting improvement in SINR on the links is dramatic.
The next step, creating a fourhop hexagonal system, shortens the hops a little more. However, the incremental improvement over threehop is less dramatic since LOS links were already obtained by the threehop system. Notice that the SINR has improved on the first hop fairly significantly since the inner RSs become more insulated from the interfering transmissions from other cells. The last hop does not improve much in SINR because it is still quite near interfering subcells in the adjacent cells.
Rates: 500 m radius hexagonal cell, single antenna
R per hop (b/s/Hz)  R_{net} (b/s/Hz)  

n _{ hops }  Hop 1  Hop 2  Hop 3  Hop 4  
1  0.30        0.30 
2  0.058  6.2      0.067 
3  9.3  6.3  5.5    5.2 
4  10.5  8.9  5.8  5.1  7.7 
Rates: 500 m radius hexagonal cell, (3 × 3) MIMO on each hop
R per hop (b/s/Hz)  R_{net} (b/s/Hz)  

n _{ hops }  Hop 1  Hop 2  Hop 3  Hop 4  
1  1.0        1.0 
2  0.2  17.3      0.24 
3  23.0  14.3  11.0    12.1 
4  25.6  21.1  12.4  9.8  18.0 
Rates: 500 m radius hexagonal cell, mixed MIMO case
R per hop (b/s/Hz)  R_{ net }(b/s/Hz)  

n _{ hops }  Hop 1  Hop 2  Hop 3  Hop 4  
1  0.72        0.72 
2  0.21  12.4      0.25 
3  23.7  14.3  8.9    11.6 
4  26.3  21.1  12.4  7.9  17.5 
IV Discussion
Results of this work show that there is a fundamental capacity tradeoff when using MIMO and MH relaying jointly. This may seem obvious, since the two techniques actually work using conflicting assumptions: MIMO works by exploiting the randomly scattering channel, while MH relaying attempts to mitigate that random behaviour. A key effect is the loss of MIMO's diversity and spatial multiplexing gains as relaying is introduced. This is apparent from (2) since, with r_{LOS} = 1, the rank of H decreases and MIMO capacity gain is lost as the Rice factor, K_{ r } , increases. However, multiple antennas provide advantages due to receive array gain, and due to minimization of cochannel interference with conventional transmit beamforming methods. Also, the use of MH relaying shortens the hop distances, which increases the SINR. So although scattering is reduced, SINR is increased. Increasing the SINR provides higher spatial multiplexing gain, but reducing scattering reduces spatial multiplexing gain. To put this another way, MIMO's spatial multiplexing and diversity gains are achieved at the expense of SINR: the uncorrelated signal that is key to MIMO gains occurs because the signal experiences rich scattering associated with high path loss.
One might expect that MH relaying should work best since it addresses the real root of the problema weak received signalwhile MIMO tries to make the best of a bad situation by collecting and making best use of randomly scattered signals. Consider the ultimate MH system, in which there are an infinite number of relays spaced at zero distance. The signal received at the end destination at any distance from the sender would be perfect, but the cost of relay placement would be infinite, the delay long, and the algorithms and signaling overhead for routing prohibitively complicated. Hence, a sensible application of MIMO with MH relaying in a cellular system may exploit the following approaches.

Add just enough relays to achieve LOS and low path loss between stations. The resulting small subcells enable higher spectral efficiency per unit area (b/s/Hz/km^{2}).

Use universal frequency reuse among the cells to increase spectral efficiency per unit area.

Use spatial reuse scheduling among subcells throughout the cell in order to increase spectral efficiency per unit area.

Beamforming with multiple antennas at the transmit side may reduce cochannel interference.

Multiple antennas at the receiver will provide array gain.
V Conclusions
We have assembled a realistic model for MH MIMO in a cellular system. This model was used to determine the network capacity and investigate the tradeoffs associated with the combination of MH relaying and MIMO techniques. MIMO spatial multiplexing can provide great gains in capacity, but only when rich scattering occurs, as is the case when the channel is NLOS. Multihop relaying provides great advantage by relaying around obstacles, reducing the path loss by creating LOS conditions, and enabling spatial reuse of spectrum. We have shown that there is some tradeoff in using these methods simultaneously, but by understanding the nature of this tradeoff in a typical cellular system, we can leverage the benefits of both MH relaying and MIMO. MH relaying can drastically increase SINR, but it still suffers from cochannel interference from neighboring uncoordinated cells. It is expected that network MIMO techniques, in which BSs in different cells coordinate their transmissions, may be used in conjunction with MH relaying. This is the subject of our current work.
Endnotes
Endnote A. We use equal power allocation in our work in which all transmit antennas transmit with equal power. This is simpler and more realistic since knowledge of the channel at the transmitter is not needed. With such knowledge, the use of waterfilling on each hop can increase the hop rates, but this will not change any fundamental conclusions.
Declarations
Acknowledgements
This work was supported by funding from the Natural Sciences and Engineering Research Council (NSERC) of Canada, TRLabs, Rohit Sharma Professorship, TELUS Communications, and Engineers Canada. The work was presented in part at the 10th International Symposium on Wireless Personal Multimedia Communications (WPMC07), Jaipur, India, 3  6 Dec 2007, and at GLOBECOM 2008, New Orleans, LA, USA, 30 Nov  4 Dec 2008.
Authors’ Affiliations
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