J.J. Biebuma, S.I. Orakwe, C.C. Ejidike

Department of Electrical/Electronics Engineering, University of Port Harcourt, Port Harcourt




 This paper presents an improved signal reception in mobile communication system using space diversity technique. Using two transmit antennas and one receive antenna the scheme provides the same diversity order as maximal-ratio receiver combining (MRRC) with one transmit antenna, and two receive antennas. It is also shown that the scheme may easily be generalized to two transmit antennas and M receive antennas to provide a diversity order of 2M.


Keywords: Diversity, maximal ratio combining, bit error rate, signal to noise ratio, wireless communications.



The next-generation wireless systems are required to have high voice quality as compared to current cellular mobile radio standards and provide high bit rate data services (up to 2Mbits/s). At the same time, the remote units are supposed to be small lightweight pocket communicators. In other words, the next generation systems are supposed to have better quality and coverage, good power and bandwidth improved utilization, and be deployed in diverse environments.

Figure 1:          Multi-path propagation


Maximal ratio combining is known to be optimal in the sense that it yields the best statistical reduction of fading of any linear diversity combiner. This work is only concentrating on Maximal ratio combining method of achieving diversity. The two parameters considered in this work are signal to noise ratio (SNR) and bit error rate (BER).  Bit error ratio is a performance measurement that specifies the number of bit corrupted or destroyed as they are transmitted from its source to its destination (Song, 1999). BER can be expressed mathematically as:


BER =                                                                                         (1)


Signal to noise ratio is defined as the ratio of a signal power to noise power and it is normally expressed in decibel (dB) and can be mathematically expressed as:


In the next generation of mobile communication systems there is a need for higher performance of signal reception, accomplished by increasing capacity or reducing multi-path interference. Multi-path interference in the mobile communication is anything which alters, modifies, or disrupts a signal as it travels along a channel between a transmitter and a receiver. This paper focuses on solving the following problem:

·         Rayleigh fading or multi-path fading involving irregular signal strength variations.

·         Path loss which increases with distance between base station and mobile.

·         Performance degradation shown in the difference between the mean signal - to - noise ratio (SNR) and non - fading signal.

Signal fading due to the multi-path propagation can be reduced using space diversity techniques considering signal to noise ratio (SNR) and bit error rate (BER) as parameters.

When the mechanisms that caused fading in communication channels were first modelleled in the 1950s and 1960s, the principles developed were primarily applied to over the horizon communication covering a wide range of frequency bands. This paper emphasizes on Rayleigh fading, primarily in the UHF band that affects mobile systems, such as cellular and personal communication systems (PCS). In the analysis of communication systems performance, the classical (ideal) additive-white-Gaussian-Noise (AWGN) channel, with statistically independent Gaussian noise samples corrupting data samples free of intersymbol interference (ISI), is the usual starting point for developing basic performance results (Sklar, 2002). In a wireless mobile communication system, a signal can travel from transmitter to receiver over multiple reflective paths. This phenomenon, referred to as multipath propagation, can cause fluctuations in the received signals amplitude, phase and angle of arrival, giving rise to the terminology multipath fading.  


Diversity schemes

Diversity is a commonly used technique in mobile radio systems to combat signal fading. The basic principle of diversity is as follows. If several replicas of the same information-carrying signal are received over multiple channels with comparable strengths, which exhibit independent fading, then there is a good likelihood that at least one or more of these received signals will not be in a fade at any given instant in time, thus making it possible to deliver adequate signal level to the receiver.


There are several techniques for obtaining diversity branches, the most important of these are: Space, frequency, polarization and time diversity.

Space diversity is the most common form of diversity technique in mobile radio base stations. It is easy to implement and does not require additional frequency spectrum resources. Space diversity is exploited on the reverse link at the base station receiver by spacing antennas apart so as to obtain sufficient decorrelation. The key for obtaining minimum uncorrelated fading of antenna outputs is adequate spacing of the antennas. In frequency diversity, signals are transmitted over different frequencies. The frequency separation between carriers should be larger than the coherence bandwidth. They are not commonly used. In Polarization diversity, two orthogonally polarized (transmit or receive) antennas are used, Orthogonal polarization exhibits uncorrelated fading (scattering angle relative to each polarization is random), only two-branch diversity is possible. It is not commonly used. Time diversity is the transmission of the same information in time slots separated by channel coherence time, has low efficiency and it is useless for stationary users.

Several diversity combining methods are known. The three main methods are: selection combining, maximal ratio combining, and equal gain combining. They can be used with each of the diversity techniques discussed above.


In selection combining technique, one of the two diversity branches with the highest signal-to-noise ratio (SNR) is connected to the output of the receiver. The first signal above a given threshold is used. The signal is used until it falls below the threshold. At any time only one signal branch is used and co-phasing is unnecessary. In Maximal Ratio Combining (MRC) technique, the M diversity branches are first co-phased and then weighted proportionally to their signal level before summing Fig. 3. The distribution of the maximal ratio combiner has been shown to be

Prob                                                          (3)

MRC is known to be optimal in the sense that it yields the best statistical reduction of fading of any linear diversity combiner, the mean SNR of the combined signal may be easily shown to be

Mean =  = M Γ                                                                                                     (4)

Therefore, combiner output mean varies linearly with M. This confirms the intuitive result that the output SNR averaged over fades should provide gain proportional to the number of diversity branches. In some applications of Equal Gain Combining (EGC), it may be difficult to estimate the amplitude accurately, the combining gains may all be set to unity, and the diversity branches merely summed after co-phasing.  The distribution of equal gain combiner does not have a neat expression and has been computed by numerical evaluation. Its performance has been shown to be very close to within a decibel to maximal ratio combining (Goldsmith, 2005).

The effectiveness of diversity is usually presented in terms of diversity gain (DG). Diversity Gain can be defined as the improvement in time-averaged signal-to-noise ratio (SNR) from combined signals from a diversity antenna system, relative to the SNR from one single antenna in the system, preferably the best one.


Where the instantaneous SNR of the diversity in combined signal is     is the mean SNR of the combined signal, is the highest SNR of the diversity branch signals,  is the mean value of and   is a threshold or reference level.

The probability P is dependent on the number of branches M in the diversity system.

Maximal ratio combining

Maximal ratio combining (MRC) combines the information from all the received branches in order to maximize the ratio of signal to noise power, which gives it its name. All branches are weighted according to their individual voltage to noise power ratios and then summed and the weightings are designed so as to give maximum SNR (Andrews, 2002).

Fig. 1 shows the baseband representation of the classical two-branch classical maximal-ratio receive combining (MRRC) scheme. At a given time, a signal is sent from the transmitter.  The channel between the transmit antenna and the receive antenna zero is denoted by   and between the transmit antenna and the receive antenna one is denoted by   where



 Noise and interference are added at the two receivers. The received baseband signals are


Where and  represent complex noise and interference. Assuming  and  are Gaussian distributed, the maximum likelihood decision rule at the receiver for these received signals is to choose signal  if


Where  is the squared distance between signals  and  calculated by the following expression:


The receiver combining scheme for two-branch MRRC is as follows:                                     



Expanding (8) and using (9) and (10) we get


Fig.2.   Two-branch MRRC.



Where  is the energy of the signal. The maximal-ratio combiner may then construct the signal , as shown in Fig. 1, so that the maximum likelihood detector may produce   , which is maximum likelihood estimate of  (Sklar, 2002).



Two-branch transmit diversity with receivers

There may be applications where a higher order of diversity is needed and multiple receive antennas at the remote units are feasible. In such cases, it is possible to provide a diversity order of 2  with two transmit and receive antennas.

            Fig.3.   the new two-branch transmit diversity scheme with two receivers.

Table 1

The definition of channels between the transmit and receive antennas


Rx antenna 0

Rx antenna 1

Tx antenna 0

Tx antenna 1


Table 2

The notation for the received signals at the two receive antennas


Rx antenna 0

Rx antenna 1




 Fig. 3 shows the baseband representations of the new scheme with two transmit and two receive antennas.


Table 1 defines the channels between transmit and receive antennas, and Table 2 defines the notation for the received signal at the two receive antennas. Where   are receivers at different points and  are complex random variables representing receiver thermal noise and interference. The combiner in Fig. 3 builds the following two signals that are sent to the maximum likelihood detector:                                                                    


 Substituting the appropriate equations we have:   



 We may hence conclude that, using two transmit and  receive antennas, we can use the combiner for each receive antenna and then simply add the combined signals from all the receive antennas to obtain the same diversity order as –branch MRRC.


Simulations result

The diversity gain is a function of many parameters, including the modulation scheme and FEC coding.



Fig:      4

Fig:      5

Fig. 4 and 5: The BER performance comparison of coherent BPSK with MRRC and two-branch transmit diversity in Rayleigh fading.


 Fig. 4 and 5 shows the BER performance of uncoded coherent BPSK for MRRC and the new transmit diversity scheme in Rayleigh fading. It is assumed that the total transmit power from the two antennas for the new scheme is the same as the transmit power from the single transmit antenna for MRRC. It is also assumed that the amplitudes of fading from each transmit antenna to each receive antenna are mutually uncorrelated Rayleigh distributed and that the average signal powers at each receive antenna from each transmit antenna are the same. Further, we assume that the receiver has perfect knowledge of the channel. Although the assumptions in the simulations may seem highly unrealistic, they provide reference performance curves for comparison with known techniques. As shown in Fig. 4 and 5, the performance of the new scheme with two transmitters and a single receiver is 3 dB worse than two-branch MRRC. The 3-dB penalty is incurred because the simulations assume that each transmit antenna radiates half the energy in order to ensure the same total radiated power as with one transmit antenna. If each transmit antenna in the new scheme was to radiate the same energy as the single transmit antenna for MRRC, however, the performance would be identical (Goldsmith, 2005). In other words, if the BER was drawn against the average SNR per transmit antenna, then the performance curves for the new scheme would shift 3 dB to the left and overlap with the MRRC curves. Nevertheless, even with the equal total radiated power assumption, the diversity gain for the new scheme with one receive antenna at a BER of 10-4   is about 15 dB. As stated before, these performance curves are simple reference illustrations. The important conclusion is that the new scheme provides similar performance to MRRC, regardless of the employed coding and modulation schemes.


Conclusions and discussions

An improved signal reception in mobile communication system has been presented. It is shown that, using two transmit antennas and one receive antenna, the signal reception provides the same diversity order as MRRC with one transmit and two receive antennas. It is further shown that the technique may easily be generalized to two transmit antennas and M receive antennas to provide a diversity order of 2M. An obvious application of the technique is to provide diversity improvement at all the remote units in a wireless system, using two transmit antennas at the base stations instead of two receive antennas at all the remote terminals (Cavers, 1991). The scheme does not require any feedback from the receiver to the transmitter and its computation complexity is similar to MRRC. When compared with MRRC, if the total radiated power is to remain the same, the transmit diversity scheme has a 3-dB disadvantage because of the simultaneous transmission of two distinct symbols from two antennas. Otherwise, if the total radiated power is doubled, then its performance is identical to MRRC. Moreover, assuming equal radiated power, the scheme requires two half-power amplifiers compared to one full power amplifier for MRRC, which may be advantageous for system implementation. The scheme also requires twice the number of pilot symbols for channel estimation when pilot insertion and extraction is used (Alamouti, 1998).






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