- Research Article
- Open Access
Computationally Efficient MIMO HSDPA System-Level Modeling
© The Author(s). 2009
- Received: 30 January 2009
- Accepted: 12 August 2009
- Published: 5 October 2009
Multiple-input multiple-output (MIMO) techniques are regarded as the crucial enhancement of todays wireless access technologies to allow for a significant increase in spectral efficiency. After intensive research on single link performance, the third Generation Partnership Project (3GPP) integrated a spatial multiplexing scheme as MIMO extension of High-Speed Downlink Packet Access (HSDPA). Despite the scientific findings on the link-level performance of MIMO techniques, many questions relevant for the design and optimization of cellular networks remain unanswered. In particular, it has to be identified whether, and to which amount, the predicted MIMO link-level performance gains can be achieved in an entire network. In this paper, we present a computationally efficient link-to-system level model for system-level evaluations of MIMO HSDPA and an exemplary embedding in a MATLAB-based system-level simulator. The introduced equivalent fading parameter structure allows for a semianalytic physical-layer abstraction with high prediction accuracy and simultaneous moderate complexity.
- User Equipment
- Minimum Mean Square Error
- MIMO Channel
- Universal Mobile Telecommunication System
- Channel Quality Indicator
Mobile radio communication represents one of the most persistent growing technology markets since the introduction of the Global System for Mobile communications (GSM). Todays cellular networks utilized by mobile network operators are based on the Wideband Code-Division Multiple Access (W-CDMA) transmission standard. To satisfy the demand for high data rate in cellular mobile communication systems, spectral efficiency has to be increased. Accordingly, MIMO techniques have been in focus of research for several years now and 3GPP has considered numerous proposals for the MIMO enhancement of Frequency Division Duplex (FDD) HSDPA . In late 2006, 3GPP decided in favor of Double Transmit Antenna Array (D-TxAA) to be the next evolutionary step of the classical Single-Input Single-Output (SISO) HSDPA . For commercial deployments, large numbers of antennas at the mobile terminal are usually not desired due to limited space and battery capacity, as well as cost arguments. D-TxAA offers the flexibility to exploit MIMO gains and tries to benefit from channel quality adaptability by means of closed loop feedback.
In order to enable a comparison of a large variety of system realizations, it is desirable to have measurement and performance models that are general enough to cover different multiple access strategies and transceiver types, including multiple antenna techniques such as precoding and spatial multiplexing. It should also be possible to derive the parameters of such a model from a limited number of link-level simulations. This means that the model should ideally cover channel and interference conditions beyond those used for training. The existing system level models for SISO W-CDMA systems, see, for example, [3, 24], cannot be used in a straightforward way for MIMO-enhanced systems, and none of the published works accurately model the proposed D-TxAA transmission scheme so far. Either the utilization of Minimum Mean Squared Error (MMSE) equalizers is not supported (as recommended for MIMO HSDPA) [17, 25], multiple-stream operation is not covered , the mandatory precoding (e.g., for D-TxAA) is missing , or no full analytical description is derived to be available for system-level evaluations [12, 13]. Furthermore, all of the cited works need to compute the full complex-valued MIMO channel matrix on system level, which—together with the necessary complex multiplications, the evaluation of the precoding and the equalizer coefficients—implies a large computational burden on system level.
a computationally efficient link-to-system level model capable of accurately representing the D-TxAA physical layer,
an exemplary system-level simulator concept based on the proposed modeling.
The paper is organized as follows: in Section 2, we describe the basic concept of D-TxAA MIMO HSDPA. Consequently, we derive our proposed computationally efficient link-measurement model in Sections 3 and 4, then explain the employed link-performance model, after which we introduce a possible implementation concept of a system-level simulator in Section 5. Finally, Section 6 concludes this paper.
To be able to derive an accurate and computationally efficient system-level model, an analytical model of the W-CDMA MIMO HSDPA  link quality is required. Therefore, we adapted the framework of  in order to reflect one individual link between a base station and a user equipment.
These spread and scrambled sequences are then mapped to the transmit antennas using a prefiltering matrix , which contains the precoding weights, , like depicted in Figure 2. At the receiver, the signals are gathered with antennas and chip-spaced sampled before they enter the discrete time Space-Time MMSE (ST-MMSE) equalizer. The MIMO channel is modeled as time-discrete, frequency-selective channel:
where the entry denotes the th sampled chip of the channel impulse response from transmit antenna to receive antenna , with a total length of chip intervals. Note that the pulse shaping, the transmit and receive filtering, as well as the sampling operation can be incorporated in the MIMO channel matrix.
For sake of notational simplicity, we define an equivalent time discrete channel that includes the prefiltering matrix and the MIMO channel , that is, , with denoting the identity matrix of size , and being the Kronecker product. With this, the input output relation at time instant , formulated by means of the equivalent channel matrix, is given by , where we introduced the receive vector , the transmit vector and the receive noise vector . Obviously, this description allows for the representation of the D-TxAA scheme.
3.1. Space-Time MMSE
Since we imply the usage of an ST-MMSE at the receiver, we have to extend our input-output relation for received samples (the equalizer span) at the receive antennas, that is, . The "stacked" versions of the parameters are defined as , and , and the equivalent channel matrix is given by
where denotes the all-zero matrix of dimension . Note that this description cannot be represented by a Kronecker product, because does not show a block structure, as indicated by the size of the zero matrices .
The covariance matrices then show the following structure:
with combining the powers , transmitted on the th stream, respectively.
The equalizer span and the detection delay are important parameters that influence the performance of the system, but an optimization of these is not treated in this paper. In general, we assume an equalizer delay of , according to .
3.2. Equivalent Fading Parameters Description
The total received signal at user can be evaluated by summing over all base-stations and all users of the th base-station, respectively, as
where and denote the pool of scrambling and spreading codes for user served by base-station . The received signal is then passed through the ST-MMSE and—if we omit the noise term for the moment—leads to the useful postequalization signal
Here, we decomposed and , where denotes the stream index and is the index of the Tx chips for all streams entering the equalizer span. Furthermore, denotes the largest integer smaller than and represents the delay of the transmit chips, and denotes the remainder of the integer division and represents the index of the substream.
After the descrambling and despreading, is multiplied with the complex conjugated scrambling and spreading codes and integrated over the period of a symbol to obtain the estimated Tx symbols . In what follows, let us assume that each Node-B (or cell-sector) uses only one scrambling sequence, thus whereas each neighboring Node-B uses a different scrambling sequence. This reflects a typical W-CDMA scenario as currently implemented for Release 4 and HSDPA and, accordingly, we will drop the notation of the scrambling sequence where it is possible to simplify the notation. In the following, we will decompose the receive power of in (6) into its different interference terms to derive the system level model. With this decomposition, it is possible to describe the characteristics of the individual interference terms by means of fading-parameters that are real-valued scalar processes. These parameters can be computed offline and loaded for the runtime of a system-level simulation, thus significantly reducing the computational burden.
3.2.1. Desired Signal
Without losing generality, we define the user and base-station of interest to be and . Then, the power of the desired signal, , is given by
where denotes the power on stream and spreading code spent for user by base-station . The fading parameter describes the equivalent fading of the useful signal power.
3.2.2. Intracell Interference
The intracell interference is composed by a number of terms, that is, the remaining intersymbol interference (ISI) after equalization, , the intercode interference when the same scrambling but a different spreading code is used, , the intracell interference from users that are not served in the same instant as the user of interest but with the same scrambling and spreading code, , and the intracell interference from users with the same scrambling but different spreading code, . From these terms, and represent the intracell interference generated by the user of interest (selfinterference):
and together with specify the intracell interference generated by all other users in the cell:
where we defined to be the user specific power spent by base-station on substream . If we apply the simplification that all streams designated for a user has the same power , the total intracell interference becomes
with . So far, the description of (10) does not allow for a decoupling into fading parameters and power terms because depends on the user index, that is, the choice of the user regarding their precoding, which is only known on system level. To be able to decompose it, we have to introduce another simplification, namely, to replace by an average over the precoding choices of the users. If we assume a uniform utilization of all precoding vector choices, the resulting term becomes
with denoting the precoding choice out of the code-book . The vector denotes the channel matrix column when applying precoding vector at the transmitter side. Due to this averaging, (11) does not depend on the user index anymore. By normalization with respect to the useful signal power , we define the precoding orthogonality:
characterizing the ability of the equalizer to cancel interference caused by multiuser scheduling.
With this simplification, we can represent the intracell interference affecting stream by
with the intracell orthogonality fading, , being
3.2.3. Intrastream Interference
where denotes the intrastream orthogonality factor.
3.2.4. Intercell Interference
For this interference term, we will assume that all users in a neighbouring cell will apply the same precoding coefficients. If we, furthermore, restrict ourselves to the scenario that all substreams designated for one user are equally powered, the intercell interference is given by
where denotes the total transmit power of Node-B spent for the HSDPA data transmission to all served users, and is the equivalent intercell fading process.
To confirm the validity of our main assumption, that is, the application of equal precoding coefficients for all users, we performed some simulations to investigate the effect of this simplified modeling onto the intercell interference. For these simulations, we assumed equal powers on all streams, and equal powers for all active users, which is likely to be set in a realistic network deployment. Furthermore, we only evaluated the intercell interference of one neighbouring Node-B because the interference arriving from one specific neighbouring Node-B will be independent of all other neighbouring Node-Bs due to the fact that the small-scale fading of their corresponding channels (to the desired user) can be assumed independent of each other.
Hence, to assess the approximation error, we simulated the intercell interference power, as given in (16) for two cases: all users are served with random precoding vectors (PC rand) and the simplified version, in which all users are served with one specific, constant precoding vector (PC 1).
3.2.5. Thermal Noise
We model the thermal noise white and Gaussian, statistically independent and with identical power on all antennas and over all chips that enter the equalizer. Accordingly, we can calculate the power (on symbol level) of the thermal noise as
3.3. Fading Parameter Generation
To assess the characteristics of the fading parameter representation, we performed a set of simulations to statistically evaluate the defined parameters. We implemented a fading simulator where the MIMO channel coefficients were generated according to the improved Zheng Model, see [33, 34]. The MMSE equalizer weights and the precoding coefficients were determined assuming perfect channel knowledge at the receiver. Note that the precoding coefficients were chosen according to 
Accordingly, the precoding is fully determined by the choice of the mobile regarding weight , which was obtained by
where denotes the prefiltering vector of stream one, given by the first column of prefiltering matrix , specified by the value of subindexed by . The matrix is defined as , with denoting the channel matrix, associated to receive antenna . The intracell power as well as the intercell power are normalized to one at the receiver. The equalizer span and delay were chosen 30 and 15 chips, respectively. Furthermore, we implemented a realistic pre-coding delay of three slots.
Assume that and the precoding matrix is unitary (which is the case if the precoding coefficients are normalized, see Section 3.3). Then the user index-dependent beamforming orthogonality is identical to one. In particular, this holds for the averaged beamforming orthogonality .
The proof is provided in the Appendix.
Furthermore, it has to be noted that a statistical representation of the proposed fading parameters would introduce additional losses in accuracy but lead to no (or insignificant) gains in terms of computational complexity.
3.4. Influence of Non-Data Channels
So far we have considered only the effects of the data channel—the so-called High-Speed Downlink Shared CHannel (HS-DSCH)—of HSDPA, but in a network also synchronization and pilot channels are needed . In the context of our modeling, the additional interference imposed by these channels can be split into non-spread channels , for example, the synchronization channels, and the spread channels, for example, the Common Pilot CHannel (CPICH).
For non-spread channels, the additionally imposed interference can—in analogy to the derivations in Section 3.2—be split into three separate parts. Considering the total transmit power of the nonspread channels to be , the interference power directly affecting the desired stream (for which the SINR shall be calculated) is given by . The interference power added on top of all other transmitted streams is given by
and the remaining intersymbol and intercode interference can be evaluated to be . Adding these individual parts, the total interference caused by non-spread channels is given by
The interference caused by other spread channels than the HS-DSCH can be treated similarly to the intracell interference caused by loss of spreading code orthogonality. Assuming the total power of other spread channels in the cell to be , the interference caused can be evaluated to be
3.5. Resulting SINR Description
With these findings, the SINR on substream and spreading code , as observed after equalization and despreading (thus on symbol level), can easily be expressed by
where denotes the spreading factor. For D-TxAA, in particular, simplifies to , since there is only one interfering parallel substream.
The description only contains equivalent fading parameters and power terms, which do not depend on each other. Accordingly, traces for the fading parameters may be generated prior to the system-level simulation—and thus only scalar multiplications will occur in (23) when evaluated on system level. It is also worth noting that in principle only one trace for each fading parameter has to be generated—statistical independency between different realizations for different users can always be achieved by choosing independent starting indices (e.g., drawn uniformly) within the traces. Furthermore, although we only investigated the statistics in case of ITU channel profiles, we want to point out that the proposed structure can be utilized for arbitrary channel models like the Spatial Channel Model (SCM) .
3.6. Validation of the Proposed SINR Description
where and denote the transmitted and received symbols on stream , respectively.
From Figure 9, it can be observed that our proposed model fits the "true" SINR over a large range of noise power. In the single-stream transmission, the SINR increases nearly linear with decreasing noise power, whereas in the double-stream case, interference due to loss of orthogonality between the individual spreading codes leads to a saturation of the SINR. We also conducted investigations in a measurement setup , which also showed very good agreement of the model approximation with the "true" SINR.
3.7. Computational Complexity
To assess the gains in terms of computational complexity of our proposed link-measurement model, we investigated it both analytically and by means of simulations. As already mentioned in Section 3.5 the resulting description of the SINR only requires the loading of the precomputed fading parameters and a couple of real-valued scalar multiplications.
In contrast to that a full evaluation of the SINR without introducing the fading-parameter structure would lead to a large effort in calculating not only the interference terms but also to evaluate the precoding choices and the equalizer coefficients. The computational complexity of the standard SINR calculation can thus be estimated by evaluating these three terms. For the precoding, we base our analysis on (19) for which we obtain
if we assume matrix multiplications to be of order for matrices. Similarly, the complexity of the equalizer evaluation can be approximated by
Finally, the complexity of the interference power calculation is proportional to
On the other hand, assuming the computation of the fading parameters is performed offline, the complexity on system level utilizing the proposed structure would result in
which is significantly smaller than the complexity order in (28). If the same values as in the previous example are applied, the complexity of the proposed model compared to the complexity of the classical SINR estimation for an equalizer of length would in this example be , however, not considering any memory loading effects.
with and denoting the time needed to evaluate the SINR with the proposed or the classical model, respectively. It can be observed that our proposed SINR evaluation saves up to 96% of the complexity, depending on the equalizer span when the same assumptions as in (28) are in place. The reason why the difference is not even more dramatic is because of memory allocation and loading issues in MATLAB that are needed for the operation of the proposed fading parameter approach. Similarly, this effect can be seen when comparing the single-stream and double-stream case, since for the single-stream case, less loading operations have to be conducted, thus leading to larger complexity gains.
4.1. Mutual Information-Based Averaging
Utilizing the link measurement model, we can compute the SINR per stream and spreading code, , from (23). To be able to relate these SINR values to an error event, we have to define a mapping . We decided in favor of a two-step procedure, mapping the individual SINR values to an effective SINR that is able to represent the average quality of the link when the decoder has to deal with the multiplexed data of the individual spreading codes. In literature, the two most common approaches to perform such a mapping are the Exponential Effective SINR Mapping (EESM) or the Mutual Information Effective SINR Mapping (MIESM). It has been shown that the MIESM in general shows a better performance and is more robust against calibration errors . Accordingly, we decided in favor of the MIESM with a sigmoidal mapping:
where is the bit-interleaved coded modulation capacity mapping . The use of the mutual information also appears attractive in the sense that it at least conceptually accounts for the choice of the modulation alphabet. Since the mapping function is not trivial to be evaluated, we precalulated and stored it in a file that serves as a lookup table during the runtime of the system-level simulation.
The fitting parameter was found by least squares- (LS-) based fitting of the instantaneous symbol-based SINR derived from link-level simulations to the corresponding additive white Gaussian noise (AWGN) performance curves. Details on this approach can be found in , however, a full treatment of the training and validation of the model would exceed the scope of this paper. Although our focus in this work is different in terms of the transmission scheme, as well as the targeted channel models, it has to be noted that our resulting tuning parameters are close to the values obtained in .
For the desired link-performance model, let us describe the simulated AWGN performance curves by
such that the average BLER value corresponding to the effective on stream can easily be computed by a lookup table. The result then is mapped to a block error event realization by conducting a binary random experiment with probability for the event of a block error, Non-ACKnowledged (NACK), and probability for the correct reception of the transport block, ACKnowledged (ACK),
4.2. SINR-to-CQI Mapping
From the AWGN performance curves needed for the MIESM training, also the mappings for the Adaptive Modulation and Coding (AMC) operation of HSDPA can be extracted [40–42]. If the coherence time of the channel is long compared to the duration of one transmission timing interval, the UE can efficiently utilize the channel with a BLER of approximately 10% by feeding back the adequate CQI values.
4.3. HARQ Gain Modeling
Finally, it remains to specify the modeling of the Hybrid Automatic Repeat reQuest (HARQ) gains in case of retransmissions. In this contribution, we applied a model developed by Frederiksen and Kolding , defining the combined SINR after retransmissions by the recursive equation
where is the modulation order and is the code-rate of the first (initial) transmission. The parameter describes the chase combining efficiency and is the incremental redundancy gain over chase combining for the th transmission.
The combined SINR after retransmissions, , can then again be used in the BLER mapping (32) of Section 4.2 to evaluate whether the transport block was received correctly or not.
System-level simulations are important for a large number of research topics, like network algorithm testing, equipment development, network planning, or even performance testing. Major manufacturers of mobile communication equipment, like Nokia Siemens Networks, Motorola, or Ericsson thus operate their own system-level simulators to derive important results for the standardization process of 3GPP. To show the applicability of the proposed link-to-system level model, we will shortly elaborate on a possible structure of a system-level simulator utilizable for network performance testing and algorithm optimization, for example, [44, 45], and even for crosslayer topics [46–48].
According to the structure in Figure 13, the system-level simulator has at least to make some assumptions about the cell deployment, the propagation modeling, and the user mobility scenario. This network layout can, for example, be generated according to live network data or according to regular layouts as described in . Propagation models for system-level simulations then should be chosen to adequately represent the specified deployment scenario. Either measurement data is available, or analytic models, for example, those in  can be used. Furthermore, special care should be taken to ensure that the shadow fading obeys the required statistical properties, that is, spatial correlation and intersite correlation, for example, by generation according to . User mobility usually is modeled according to a random walk model, and also more sophisticated path-based test-scenarios can be implemented. Note that depending on the investigation scenario, handover management can be neglected in the simulator, which requires some measures to prevent the users from leaving the cell.
Based on the implemented and simulated network scenario, typical performance metrics derived by system-level simulations include cell and user-throughputs, fairness figures, or error statistics.
5.1. Exemplary Simulation Result
System-level simulation parameters.
19 cells, layout 1
Total power available at Node-B
Spreading codes available for HS-DSCH
Macroscale pathloss model
urban micro 
Active users in target sector
3 km/h, random direction
UE capability class
20, ST-MMSE equalizer
It is noteworthy that the double-stream (DS) operation performs slightly worse in the average cell throughput sense than the single-stream (SS) transmission. This is an effect of the higher overhead of the dynamic switching between SS and DS mode. Nevertheless, the maximum achievable throughput is significantly larger in the DS enhanced case. A more detailed investigation of the system-level characteristics of MIMO HSDPA will be part of another publication, also elaborating on optimization potential in the network algorithms.
In this paper, we introduced a computationally efficient link-to-system level model that includes the precoding, spreading/despreading, and ST-MMSE equalization. Furthermore, we introduced a suitable link-performance mapping scheme and the necessary training to achieve an accurate TTI-based BLER prediction. Together with the necessary SINR-to-CQI mapping and the HARQ modeling, we were able to describe an exemplary implementation of the proposed model in a MATLAB-based system-level simulator and presented details on our simulation methodology.
The introduced model can be utilized for various system-level simulation concepts, network performance investigations, algorithm development, and cross-layer optimizations. Future work based on this link-to-system model will focus on scheduling and interference mitigation techniques, as well as content aware cross-layer techniques.
This work has been funded by mobilkom austria AG, in cooperation with ftw., Infineon Technologies, and Siemens AG. The authors would like to thank Dr. Sven Eder (Siemens AG) and Dr. Ingo Viering (Nomor Research) for their support and valuable contributions. The views expressed in this paper are those of the authors and do not necessarily reflect the views within mobilkom austria AG.
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