General approach for the comparison of spectrum efficiency of digital mobile radio systems

Com m un ica tio n T h e ory

General Approach for the Comparison of Spectrum Efficiency of Digital Mobile Radio Systems

G. Falciasecca, C. C a i n i University of Bologna - Villa Griffone - Pontecchio Marconi (BO) Italy G. Riva, M. F r u l l o n e Fondazione Ugo Bordoni - Villa Griffone - Pontecchio Marconi (BO) Italy

Abstract. Evaluation of spectrum efficiency in mobile radio systems is often performed by different authors starting from different working assumptions; that yields results that are not easily comparable outside the "scenario" where they have been achieved. This paper attempts to settle this controversial matter providing some criteria for overcoming these difficulties. The results of this investigation allow to assess that relative capacity comparisons are fairly independent of some quality parameters, such as specified outage probability, or propagation parameters, such as the standard deviation of lognormal shadowing, so that these parameters need not complicate the comparison of competing approaches. As a consequence, a very simple scenario, providing an adequate basis for deriving constant efficiency curves, turns out to be of great relevance for comparisons. Associated with it, a graphic tool, allowing to perform quick relative comparisons among systems, is presented.

1. INTRODUCTION

Spectrum efficiency is one of the main features of a n y high capacity mobile r a d i o systems. Notwithstanding the availability of new frequency bands, the expected dramatic growth of customers enhances the importance of this aspect. A proper definition of spectrum efficiency is currently discussed in many international bodies and conferences. The topic is still under discussion in CCIR bodies (Question 47/1) and for a reference about the basic points, the CCIR Rep. 662-1 yields the relevant background. Many interesting and useful papers have been published on this subject (see for example [ 1, 2, 31): after reviewing systematically the existing literature, we have to conclude that somewhat different

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definitions of spectrum efficiency are currently in use and, most importantly, their application is usually carried out with different working assumptions. This results in a major difficulty in comparing performances of different systems. Even the authors of this paper dealt with these problems in the past, either discussing very particular solutions [4], or with a more general view [ 5 , 6 ] .Here they are dealing with the problem of analyzing how the set of adopted working assumptions (e.g. propagation characteristics, coverage strategy, spatial user distribution, etc.) influences relative capacity comparison among competing systems. To this respect, any working assumption which does not affect comparisons is useless and should be avoided. In the following a generic set of working assumptions will

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be referred to as a scenario; different scenarios Will be considered equivalent when they do not affect relative comparisons among systems, since their differences are relevant just for determining absolute values of spectrum efficiency. In [ 6 ] a Reference Plane, based on a very simple deterministic scenario, allowing to perform quick comparisons among systems has been presented. In what follows, the Reference Plane definition will be recalled and that simple scenario will be extended to include statistical effects coming from propagation and user mobility. It will be shown that relative comparisons are not affected by these more realistic working assumptions and that the Reference Plane can be used with greater generality.

2. SPECTRUM EFFICIENCY DEFINITION

In [6] the matter of the proper definition of spectrum efficiency for mobile radio systems handling voice signals was discussed. The most important points will be recalled and reconsidered here. If we assume that users -are uniformly distributed over the service area, the spectrum efficiency q can be expressed in terms of a ratio between benefit and cost as:

q A=-nR W

where n denotes the number of available channels per cell, R the bit-rate of the digital voice signal and W the available bandwidth. Let N the total number of channels; an equivalent bandwidth Wo for each channel can be defined as:

w O A-- N-W As the value of W o depends on the value of R , we can define a frequency efficiency qF, related to modulation and coding, as:

A R flF

=-

WO

(3)

In any mobile radio system a "spatial filtering action", due only to attenuation or also to antenna directivity, is always present. Actually, the well known "cellular concept" [7] is nothing but an (imperfect) space division scheme. A perfect spatial filtering action would allow to use all N channels at any location. In practical cases, the number of the available channels, n, at a given base station is reduced by a factor m with respect to N : N n=-

m

(4)

In this paper we restrict our analysis to the case of mutually orthogonal channels, so that interference is due only to active co-channel users. Cells are divided into clusters and thus m ,in (4), represents the cluster size in a usual cellular strategy, but it was shown of greater generality in [8], where it was applied also to a CDMA scheme; here we will restrict ourselves to the classical TDMAiFDMA approaches with fixed channel assignment. We define the outage probability as the percentage of territory where the CIR value needed to meet quality requirements is not guaranteed. According to the statistics assumed for the propagation and to the users distribution, it is possible to determine the carrier to interference ratio CII related to the outage probability requirement. Once the coverage layout is defined, q.(5) can be written as:

where m(Cl1,a) is the relationship between the cluster size and the CII resulting from the considered scenario, which may include statistical effects depending on both spatial user distribution and on propagation characteristics symbolized by a. In the case of deterministic propagation law, a: simply characterizes the relationship between the path length, r, and the attenuation, A : A ( r ) = ra

(7)

Typical values for a are in the range 3 to 4, even if values ranging from 2 to 6 are possible. From (6), curves with constant spectrum efficiency, 11, can be plotted on a Reference Plane qF,CII whose coordinates are the frequency efficiency qF(in terms of bit/s/Hz) and the carrier-to-interference ratio CII[dB]. Transmission systems can be characterized by a point on that plane; the abscissa is the frequency efficiency of that system whereas the ordinate is the CII required to meet the BER requirement. Comparisons among systems may be readily performed by means of the constant spectrum efficiency curves. 3. UNIFORM USER DISTRIBUTION AND LOGNORMAL SHADOWING SCENARIO

The previous section showed that the behaviour of curves with constant spectrum efficiency is strongly influenced by the relationship between cluster size and CM, expressed by m(CI1, a).

The spectrum efficiency definition now becomes:

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General Approach for the Comparison of Spectrum Efficiency of Digital Mobile Radio Systems

Even if the analysis could be extended to more complicate cases, in this paper we adopted only the following essential hypotheses: - negligible effects of thermal noise; - hexagonal cellular coverage; - omnidirectional base station antennas, located in the center of the cells: - no power control. Hereinafter the influence of two typical factors, namely user mobility and propagation conditions, will be analyzed, in order to verify how they affect m(Cl1.a) and hence comparisons among competing systems. User mobility should be characterized by many parameters, such as location distribution, mobile velocity distribution, hand-over probability and so on; here we restrict our analysis to the effects of a uniform distribution of the mobile locations. As far as the propagation conditions are concerned, it is well known that in the mobile radio channel the attenuation is subject to fast fluctuations around a slowly varying mean value [9]. While the short term fluctuations are caused by multipath propagation, the slow variations of the mean value are due to the shadowing effects of buildings and hills. The contribution of the shadowing in determining the CII is of great importance since it affects the mean value. This phenomenon can be well characterized if the fast variations due to multipath effects (see next sections) are averaged over some wavelengths. It was experimentally found that in this case any signal X can be considered as a log-normally distributed random variable [9], whose median value follows the deterministic law given (7). Therefore we have:

where 5 represents a zero mean gaussian variable, whose standard deviation CJ is usually in the range 4 to 9 dB. A realistic comparison among mobile radio systems can therefore be performed considering both the effects of lognormal shadowing and user mobility. A rigorous analytical approach is hardly feasible; therefore this complete analysis has been carried out by means of a simulation program; but we choose to slightly delay the presentation of these results. First we want to examine a very special and idealized case, with o =0 dB, outage probability Pout=O, and no user mobility. Later on, this choice will be fully justified, since we will show that, in spite of its simplicity, this approach is sufficient for making relative efficiency comparisons. For these reasons and for its usefulness, we will refer to this case as the Reference Case. Let us now present the relative model: the useful

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unit is at the border of its cell while the six nearest interferers are at the center of their own cells; mobile to base link is considered. The function m (U1.a)can be easily evaluated, as reported for example in [6]:

(9) The subscript R stands for the Reference Case: the resulting evaluations are graphically represented in Fig. 1. From (6) and (9), we note the relevant influence of the propagation parameter a on the Reference Plane curves: it determines the slope of the straight lines representing the curves with constant spectrum efficiency: a change in the parameter a does therefore result in a modification of relative comparisons among systems.

.

PSK

*QAM I

+

1

GMSK =3.5 a=2

*a

10

qF Fig.1 - Comparison of spectrum efficiencies of different modulation schemes under different propagation conditions. Curves relative to propagation parameter a=2 and a=3.5 are plotted in the Reference Plane and provide the relationship between C/1 and q~ values leading to the same spectrum efficiency of a classical 2-PSK scheme in those propagation conditions. Points representing 2-PSK. GMSK and QAM performance refer to a BER=10-5 under the hypothesis that the effect of the interfering signals is the same as Gaussian noise.

Let us now come back to the results relative to the realistic case with distributed mobiles and lognormal shadowing: we assume d equal to 6 dB and an outage probability Pout=lO%. In Fig. 2 we have represented the CIR corresponding to this case against cluster size, for different values of a.The curves obtained by simulation are plotted together with the corresponding curves of the Reference Case, showing a constant downward shift, depending only on a. Any working assumptions change leading to a simple shift of curves with constant spectrum efficiency does not affect relative comparisons; as a matter of fact, two systems with equal spectrum

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efficiency (whose representative points lie on the same curve), will keep having an equal spectrum efficiency (their representative points will lie on a new curve which is still the same for both). Therefore, we can conclude that the considered scenario with distributed mobiles and lognormal shadowing with Pout= 10% cp does not alter relative comparisons with respect to the I! Reference Case. h Even different values of outage probability do not @ 0 affect relative comparisons. As a matter of fact, Fig. 3 5 shows that the deviation of CIR with respect to the 10% value is fairly independent of the cluster size, and u this results in a simple translation of the curves with constant efficiency: the simple Reference Case can therefore still be useful for comparison purposes, no c 0 . I matter which outage probability value is required. .y rd It is worth noting that if the approximation reported in [ l o ] is extended to this case, an analytical 5 computation is possible, whose results are well in agreement with our simulations and, of course, with the concluding remarks. Previous results have been obtained with reference to the case -6 dB; let us now examine the effects of this parameter on the spectrum efficiency comparisons among systems.

-

-n

3

6

9

12

15

18

21

Cluster size Fig. 3 - Deviation of carrier-to-interference ratio from values relative to 10%outage probability (a= 2 ; 3 3 , when both user mobility and log-normal fading. d = 6 dB, is considered. The curves refer to 1% and 5% outage probability.

In Fig. 4 the reference curves obtained by applying (9) are plotted together with the curves achieved (by means of analytical computations) in the special case cr = 0 dB; curves represent the CIR corresponding to an outage probability equal to 10% (now due only to unfavourable user locations). It is worth noting that the difference between them and the reference curves can be considered negligible (