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MINIMUM BIT ERROR RATE MULTI USER DETECTION FOR SDMA SYSTEM
1,*
Divya Morla, 1Ravi Sankar Chandu, 1Habibulla Khan, 1B.T.P.Madhav,
1K.Ramakrishna, 1G.Sasi Kumari & 1Mahesh Sonti
1Department of ECE, K L University, Guntur DT, AP, India
*Email: [email protected]
ABSTRACT
In this paper a space-time decision feedback equalization (ST-DFE) scheme with Multi User Detection (MUD) for multiple receiver antenna aided space division multiple access systems is used to achieve minimum bit error rate(MBER). The MBER multi user detection is capable of improving bit error rate performance and enhancing the attainable system capacity. In this paper we show that the BER performance of a system is improved over that of the standard minimum mean square error (MMSE) design. The implementation of the MBER ST-DFE assisted MUD is proposed using a stochastic gradient- based least bit error rate algorithm hence achieving a lower computational complexity than the LMS algorithm. The simulation results demonstrate that the MBER ST-DFE assisted MUD is robust to channel estimation errors as well as to potential error propagation imposed by decision feedback errors, compared to the MMSE ST-DFE assisted MUD.
Keywords:Decision Feedback Equalizer, Minimum Mean Square Error, Multiple Input Multiple-Output,Multi User Detection, Space-Division Multiple Access, Space-Time Processing.
1. INTRODUCTION
In order to further increase the system capacity, antenna arrays can be employed for supporting multiple users in a space-division multiple access (SDMA) communications scenario [1]-[3]. We investigate space-time (ST) decision feedback equalization (DFE) assisted multiuser detection (MUD) scheme designed for multiple receiver antenna aided SDMA systems. To interpret the multiuser-supporting capability of such a novel SDMA system, it is useful to relate it to classic code-division multiple access (CDMA) multiuser systems. In a CDMA system, each user is separated by a unique user-specific spreading code.
Whereas an SDMA system differentiates each user by the associated unique user-specific channel impulse response (CIR) encountered at the receiver antennas. In a simplistic but conceptually appealing interpretation, the unique user-specific CIR plays the role of a user-specific CDMA signature. In this analogy, the CIR-signatures are not orthogonal to each other, but this is not a serious limitation, because even orthogonal spreading codes become non- orthogonal upon convolution by the CIR. However, owing to the non-orthogonal nature of the CIRs, an effective multiuser receiver is required for separating the users in an SDMA system.
The most popular SDMA-receiver design is constituted by the minimum mean square error (MMSE) MUD [4].
However in a CDMA context and in an adaptive beam forming-based MUD scenario, a better strategy is to choose the detector’s coefficients by directly minimizing the system’s bit error ratio (BER). For the single-user single- antenna system, the minimum BER (MBER) equalization design has become popular, and it has been shown that the MBER DFE is less sensitive to the error propagation due to decision feedback errors compared to the MMSE DFE[5]-[10]. For the base station employing multiple transmit antennas, an MBER multiuser transmission scheme has been proposed, while for the multiple antenna assisted receiver, an MBER rake receiver has been discussed.
Against this background, the novelty of this paper is that the MBER ST DFE assisted MUD (ST-DFE-MUD) is proposed for the first time in the literature in the context of SDMA. In addition to the theoretically MBER ST-DFE- MUD, which is unachievable in practice, the adaptive least bit error rate (LBER) aided ST-DFE-MUD is proposed for its practical implementation and characterized in terms of its steady-state BER and convergence performance.
Least mean square (LMS)-based ST-DFE-MUD has a lower computational complexity than the latter in the case of the binary phase-shift keying (BPSK) modulation scheme. Simulation results are also provided in support of the theoretical analysis. The modulation technique can readily be extended to the QPSK scheme with multiple bits per symbol. In this paper, it is shown that the MBER ST-DFE-MUD design results in an enhanced BER performance in comparison to the standard MMSE design. Unlike the MMSE design, whose performance degrades significantly owing to decision feedback errors in the presence of multiuser feedback loops, the MBER ST-DFE-MUD is robust
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to the error propagation, as will be demonstrated by our simulation study. An adaptive implementation of the MBER ST-DFE-MUD is considered based on a stochastic gradient learning algorithm referred to as the LBER technique. It is demonstrated that LBERST-DFEMUD consistently outperforms the least quadrature phase-shift keying (QPSK) scheme [11]-[12] and other modulation schemes with multiple bits per symbol.
2. SYSTEM MODEL.
Consider the multiple antenna aided SDMA system which supports M-users as shown in Figure 1, where each is user is equipped with a single transmit antenna and the receiver is assisted by an L-element antenna array. The received signal samples xl(k) at the symbol rate for 1≤l≤ L are given by
(1)
Figure 1. Schematic of an antenna array aided SDMA uplink scenario, where each of the M users is equipped with a single transmit antenna and the base station’s receiver is assisted by an L-element antenna array.
Where nl(k) is an independently identically distributed complex valued Gaussian white noise process with,, , denotes the noise-free part of the lth receive antenna’s output, sm(k) is the kth transmitted symbol of user m, denotes the tap vector of the CIR connecting the user m and the lth receive antenna. We have assumed that each of the ( M×L) CIRs has the same length of nc.. BPSK modulation is employed here. A bank of the M ST-DFEs constitutes the MUD, and the soft outputs of the M ST-DFEs are given by
(2)
For 1≤ m ≤ M, where s^m(k) denotes the decision for the transmitted symbol sm(k) and denotes the feed forward filter weight vector of the mth user’s detector associated with the lth receive antenna, while denotes the mth user’s detector feedback filter weight vector associated with the qth user detector’s feedback signal. Again, for notational simplicity, we have assumed that each of the M ST-DFEs has the same decision delay d, all the feed forward filters have the same order nF , and all the feedback filters have the same order nB. The M detectors decisions are defined by
(3) Then the output of the mth ST-DFE can be written as
(4)
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3. MINIMUM BIT ERROR RATE MULTIUSER DETECTION The mth detector’s weight vector wm is determined by minimizing the MSE criterion
, which leads to the following MMSE solution (5)
An adaptive implementation of the MMSE solution can be realized, for example, using the LMS algorithm. The main contribution of this paper is to derive the MBER solution [8]-[10] for the weight vectors of the ST-DFEs and develop an adaptive MBER multiuser detector for the SDMA systems. The BER of the mth ST-DFE associated with the detector’s weight vector WM is given by
(6)
Where .
The MBER solution for the mth detector is then defined as the weight vector that minimizes the error probability namely
. The associated BER can alternatively be calculated according to the
(7)
Parzen window method constitutes an efficient means of estimating a pdf. Specifically, the Parzen window method estimates a pdf using a window or block of the ST-DFE output signal by placing a symmetric unimodal kernel function centered on each sample and averaging over all the data points. This density estimation technique is capable of producing reliable pdf estimates with the aid of short data records and is natural when dealing with Gaussian mixtures. The estimated BER is given by
(8)
Our main aim is to develop a sample-by-sample adaptive implementation of the MBER ST-DFE.
4. SIMULATION STUDY
In our simulation investigations perfect channel estimates are assumed in performing the space translation. Hence our attention is focused on the performance of the adaptive MBER and MMSE designs, rather than on the adaptive channel estimator, which is well documented in the classic adaptive signal-processing literature. The effect of imperfect channel estimates on the performance of a ST-DFE-MUD, however, was investigated in our simulation study. In order to avoid obfuscating the prevalent MBER/MMSE performance trends by asynchronous transmissions, we assumed synchronous communications and an identical CIR dispersion for all users. The simulation results compare the MMSE performance of a system with MBER performance of the system and shows that the MBER performance is improved when compared to the MMSE performance.
5. SIMULATION RESULTS
Bit error rate comparisons of the MMSE and MBER ST-DFE-MUDs for the four-user four-antenna time-invariant system are shown in figure 2.
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Figure 2.1. User 1 Figure 2.2. User 2
Figure 2.3. User 3
Figure 2.4. User 4
Figure 2. Simulated bit error rate comparison of the MMSE and MBER ST-DFE-MUDs for the four-user four antenna time- invariant system, where DF indicates simulated BER with detected symbols being fed back.
Figure 3.1. User 1 Figure 3.2. User 2
Figure 3.3. User 3 Figure 3.4. User 4
Figure 3. Bit error rate comparison of the MMSE and MBER ST-DFE-MUDs for the four-user four-antenna time invariant system, where “est” indicates imperfect channel estimates were used
47 6. CONCLUSION
A minimum bit error rate design has been proposed for the space-time decision feedback equalization assisted multiuser detector employed in space-division multiple-access systems. It has been shown that MBER design is capable of achieving better performance and hence of improving the attainable system capacity, compared to them MMSE design. Another interesting result observed in this paper is that the MBER ST-DFE-MUD is significantly more robust against the error propagation caused by error-prone detected symbols used in the MUD’s feedback loop, in comparison to the standard MMSE ST-DFE-MUD. This is an important advantage, especially in situations, where decision-directed adaption has to be employed.
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