One of the efficient ways to transmit high data rate is by employing a multiple-input multiple-output (MIMO) transmission. One of the MIMO schemes, known as spatial multiplexing (SM), relies on the linear independence data streams from different transmit antennas to exploit the capacity from the fading channels. Consequently, SM suffers from the effect of spatial correlation which is the limiting factor in achieving the capacity benefit that SM can offer. In an attempt to increase the robustness of the SM transmission in a wide range of correlated channels, the use of dynamic subcarrier allocation (DSA) is investigated. The effective signal-to-interference-and-noise ratio (SINR) metric is used as the performance metric to determine the subcarrier quality which can then be utilised in the allocation. Two novel variants of the subcarrier allocation scheme are proposed. It is shown that the DSA-SINR approach improves the BER performance of SM transmission in highly correlated channels environment.

Orthogonal frequency division multiplex (OFDM) is one of the effective mitigation techniques to combat the channel impairments in a wireless network. The multiuser version of OFDM, known as OFDMA, consists of multiplexing different users in the time and frequency domains by assigning subsets of subcarriers to individual users, thus allowing efficient and flexible resource allocation across frequency bands.

OFDMA transmission technology can be further enhanced with the addition of the multiantenna techniques, known as MIMO. There are two popular approaches. The first technique is space-time block code (STBC), proposed by Alamouti [

Foschini and Gans [

Example of self-interference in a 2 × 2 SM transmission.

SM schemes rely on the linear independence between the channel responses corresponding to each pair of transmit-receive antennas. As the spatial correlation increases, cross-correlation occurs between the spatial multiplexing data streams. Consequently, SM schemes suffer considerably from spatial correlation, resulting in ill-conditioned matrices, which can cause degradation of system capacity.

Several factors determine the degree of spatial correlation, such as antenna element spacing [

In practice, the spatial subchannels between different antennas are often correlated and therefore the full potential multiantenna gains may not always be obtainable. However, the received signal may still have a strong spatial signature in the sense that stronger average signal gains are received from certain spatial directions. In this paper, two novel subcarrier allocation schemes are proposed. Both variants of the subcarrier allocation scheme take advantage of independent channel variations across users to improve the network performance through frequency and spatial diversity. The performance of the proposed algorithm is analyzed when operating in different correlated channel environments.

The rest of the paper is organised as follows. The problem formulation for resource allocation in OFDMA networks is presented in Section

In this section, a mathematical definition of the SINR metric is presented. The proposed subcarrier allocation uses the SINR as a performance metric to determine the subcarrier quality for allocation purposes. SINR metric has knowledge of the channel quality at every subcarrier level, whereby it indicates the spatial information and self-interference caused by the mismatch between the spatial subchannels. The mathematical model for the received signal in a MIMO-OFDMA system, after FFT and guard removal, is described as follows:

The MMSE filter has the ability to mitigate self-interference whilst not adversely amplifying the received noise. The MMSE filter is also able to separate the spatial subchannels of the MIMO structure [

The receiver then calculates the effective SINR (SINR) per subcarrier and feeds back that information to the transmitter. Effective SINR stands for the SINR per subcarrier, obtained by linearly combining the signals from all the received antennas. The SINR metric captures the variation of the SINR in the subcarrier domain. To calculate the effective SINR, the postdetection SINR for each subcarrier needs to be calculated after the MIMO processing. The MS

MS

In an OFDMA system with users fading independently, there is likely to be a user with a good channel at any given time slot/subcarrier. By scheduling transmission so that users transmit at times and frequency resources when their channel conditions are favourable, significant gains from the effective channel can be achieved. So if a deterministic rather than random allocation of subcarriers is employed, the multiuser diversity can be exploited to ensure that most users can be allocated the best subcarriers for them with minimal clashes. As a result, bit error rate (BER) can be improved by serving the user with the strongest channel.

Initially, DSA work has focussed on SISO systems [

The proposed DSA-SINR algorithm is an alternative approach to the subcarrier allocation procedure to work in [

Variations of the proposed DSA-SINR algorithm.

“All SINR” variation

“Partial SINR” variation

As with the “All SINR” scheme, the dynamic subcarrier allocation is applied independently across spatial subchannels in “Partial SINR” scheme. However, “Partial SINR” used two different performance metrics to determine the subcarrier allocation at each of the spatial subchannels: (i) at the parallel subchannels, SINR metric is used to identify the subcarriers that are affected by self-interference, and (ii) the spatial interferers use the channel gain as a metric to determine the subcarrier allocation, which is similar to the DSA-Scheme 1. By doing the allocations in this manner, users are prevented from sharing the subcarriers with the spatial interferer, thus helping to avoid the use of an extra coding scheme and reducing the complexity of the algorithm. The combination of different performance metrics in “Partial SINR” is expected to reduce spatial correlation, whilst still seeking a maximal allocation of channel energy.

This also ensures that spatial diversity cannot be lost due to highly correlated spatial subchannels. In both variations of the allocation scheme, each of the spatial subchannels will be allocated with different sets of subcarriers. In the SISO case, Jang and Lee [

Before the allocation takes place, the

The nomenclatures are set first as references. In the following algorithm,

The “Partial SINR” variation of the DSA-SINR algorithm can be described as follows:

Initializationset

Main Process While

(a) Generate short list of users start with user with small SINR metric and channel gain. For the first iteration, assume all users have equal data rate as no subcarriers have been allocated; hence, the list may be entirely arbitrary. Find user

(c) Update

(d) Go to the next user in the short list in (a), and repeat (b) to (c) until all users are allocated another subcarrier,

For the “All SINR” variation, the allocation involves replacing the channel gain to SINR metric as the performance metric at the spatial interferer. In other words, spatial interferer performed similar subcarrier allocation to the main parallel channel.

The algorithm ranks users from the lowest to the highest SINR metric at each main spatial subchannel. Consequently, the next best subcarriers are allocated to users in rank order, allowing users with the lowest SINR, that is, users that suffer from “severe” self-interference effect or poor received signal at that particular spatial subchannel, to have the next best subcarrier with the highest SINR metric that is available for the next transmission.

The simulation is performed in an SM-OFDMA environment. Different schemes of modulation such as binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), and quadrature Amplitude Modulation (QAM) can be applied.

Modulation type affects both the data capacity in a given channel and the robustness with regard to noise and interference. The OFDM parameters and six different modulation and coding schemes (MCSs) are summarised in Tables

Physical layer parameter for OFDM system.

Parameter | Value |
---|---|

Operating frequency | 5 GHz |

Available bandwidth (BW) | 100 MHz |

Transmit information duration ( | 10 ns |

FFT size ( | 1024 |

Useable subcarriers ( | 768 |

Subcarrier spacing ( | 97.66 kHz |

Useful symbol duration ( | 10.24 |

Guard interval (GI) | 176 |

Total symbol duration ( | 12.00 |

Modulation and coding schemes (MCS) for the MIMO-OFDMA system.

Modes | 1 | 2 | 3 | 4 | 5 | 6 |

Modulation | BPSK | QPSK | QPSK | 16-QAM | 16-QAM | 64-QAM |

Coding rate | 1/2 | 1/2 | 3/4 | 1/2 | 3/4 | 3/4 |

Data bits per OFDM symbol | 768 | 1536 | 2304 | 3072 | 4608 | 6912 |

Coded bits per OFDM symbol | 1536 | 3072 | 3072 | 6144 | 6144 | 9216 |

Total bit per OFDM symbol | 1024 | 2048 | 3072 | 4096 | 6144 | 9216 |

Nominal bit rate [Mbps] | 64 | 128 | 192 | 256 | 384 | 576 |

Total bit rate [Mbps] | 85.33 | 170.67 | 256.00 | 341.33 | 256.0 | 339.00 |

“Urban Micro” environment represents a very small cell in an ultrahigh-density urban area with cell radius of approximately less than 500 m and BS antennas located at rooftop level. The MIMO channel model is simulated in a fixed channel matrix so that both receiver and transmitter are static with respect to each other and the path loss remains approximately constant during the measurement duration. The key parameters for the channel model are summarised in Table

“Urban Micro” channel model parameters.

Parameters | SCM Urban Micro |
---|---|

Bandwidth | 5 MHz |

Excess delay spread | 923 ns |

Mean delay spread | 251 ns |

Carrier frequency | 2 GHz |

A packet size of 54 bytes is considered throughout this paper. In addition, 2000 i.i.d. quasistatic Rayleigh distributed channel samples per OFDM symbol are used in each simulation to achieve stable averaging over wide fading channel condition. 16 users are considered to exploit the multiuser diversity gain with a total of 768 useable subcarriers to be equally shared among the users with FFT size,

The main aim of this paper is to investigate the SM performance at different levels of spatial correlation: from ideal to extreme correlation scenarios. In the ideal case, the channel is uncorrelated and the effect of self-interference is very minimal, while “fully” correlated channel represents the worst case scenario, whereby the effective capacity gain is equal to that of a SISO system. The spatial correlation matrix of the MIMO channel,

Correlation modes and their coefficient.

Correlation modes | Correlation coefficient | |

“Full” | 0.99 | 0.99 |

Uncorrelated | 0.00 | 0.00 |

Figure

Channel gain at every spatial subchannel (uncorrelated channel).

Channel gain at every spatial subchannel (“Full” correlation mode).

In this paper, uncorrelated channels are organised in two categories: “Default” and “Forced.” “Default” uncorrelated channel is generated from the default parameters of the representative channel model, while the “Forced” uncorrelated channel is generated by using the Kronecker product [

Correlation coefficient measurement for uncorrelated channel.

Correlation coefficient | ||
---|---|---|

Default | 0.446 | 0.320 |

“Forced” | 0.000 | 0.000 |

From the table, the correlation coefficients of default channels are higher than “Forced” channels; however, the correlation coefficient is considered at a moderate level and is acceptable in practical implementation as a MIMO channel is expected to generate some amount of spatial correlation, especially in a populated urban environment.

There are two variations of the proposed DSA-SINR schemes: (i) all spatial subchannels utilising DSA-SINR scheme (here referred to as “All SINR”) and (ii) parallel spatial subchannel allocated using DSA-SINR scheme, while the “interferer” is allocated with channel gain (referred to as “Partial SINR”). The main aim of this section is to illustrate the advantages and disadvantages of both variations of the allocation scheme.

The result from Figure

BER comparison between “Partial SINR” and “All SINR” schemes in a “default” uncorrelated channel.

When simulated in a “fully” correlated channel different correlation cases, as shown in Figure ^{−3}, the “Partial SINR” scheme has an advantage of approximately 3 dB in the “Full” correlation case, while there is minimal margin of BER improvement for the uncorrelated channel.

BER performance between two variants of DSA-SINR in different correlation modes.

The dynamic combination between SINR metric in parallel channels and channel gain at spatial interferers makes the “Partial SINR” scheme a more attractive candidate to combat the debilitating effect of self-interference, compared to the “All SINR” scheme.

This can be explained by observing the allocated subcarriers for a user, at a particular time sample in a fully correlated channel between one of the parallel channels and its adjacent spatial interferer. Figure

Example of subcarrier allocation in a “fully” correlated channel based on “All SINR” scheme.

It can be observed that SINR metrics for both spatial subchannels are almost identical to each other, and since the allocation relies on the SINR metric, both the spatial subchannels allocate the subcarriers when the SINR metric is at its peak. But since each of the spatial subchannels has knowledge on the level of self-interference from the other spatial subchannel, both of the spatial subchannels eventually will share the same subcarrier indexes, resulting in poor spatial diversity gain. The variation of the allocated subcarrier is also wider across the subcarriers range, which creates diverse channel quality across the subcarrier range, but the allocation avoids the selection of subcarriers with high channel gain, resulting in poor BER performance compared to the “Partial SINR” scheme.

In the “Partial SINR” scheme, as shown in Figure

Example of subcarrier allocation in a “fully” correlated channel based on “Partial SINR” scheme.

Other than that, the “Partial SINR” scheme has lower complexity compared to the “All SINR” scheme since the “Partial SINR” scheme only uses the spatial parallel subchannels to determine the self-interference caused by the spatial interferers, while the “All SINR” scheme needs to perform the arithmetic to calculate the SINR metric at all spatial subchannels. In other words, the “Partial SINR” offers lower allocation complexity with extra BER gain compared to the “All SINR.” For the remaining part of this paper, the “Partial SINR” algorithm will be considered exclusively and the term “DSA-SINR algorithm” will be used to refer to the “Partial SINR” variant.

Figure

BER performance comparison between default and “forced” uncorrelated channels.

Figure

BER comparison between DSA-SINR and DSA-Scheme 1) in “Forced” uncorrelated channel.

The DSA-SINR performance is better than the DSA-Scheme 1 in the “Default” uncorrelated channel, as shown in Figure

BER comparison between DSA-SINR and DSA-Scheme 1 in “Default” uncorrelated channel.

Figure

BER performance of DSA-SINR across different MCSs in uncorrelated channel.

BER performance of DSA-SINR across different MCSs in a fully correlated channel.

The BER degradation is uniform as the modulation order increases. This is expected since transmission in higher-order modulation comes at the cost of reduced robustness towards noise and interference that is dominant in the fully correlated channel case.

In Figure

BER performance comparison for suboptimal allocation schemes in a fully correlated channel.

This is because DSA-Scheme 5 sacrifices greater degrees from the selection of the best available subcarrier in preference for avoiding allocation of the same or nearby subcarriers on different spatial subchannels, which depends on the size of

This paper addresses the problem of SM downlink transmission over spatially correlated fading channels from the aspect of subcarrier allocation. A novel subcarrier allocation algorithm, known as DSA-SINR, is proposed. Design considerations of the proposed algorithm are also detailed, whereby two novel variants, known as “Partial SINR” and “Full SINR,” are developed from the algorithm. From the numerical simulations and analysis, the proposed algorithm is shown to offer low complexity and to achieve substantial performance gains when operating under diverse spatial correlation cases. From the comparison analysis, “Partial SINR” showed better BER performance compared to the “Full SINR” scheme. “Partial SINR” benefited from reduced complexity since the SINR calculation is only required at the parallel subchannels.

As the spatial correlation increased in the channel, the allocation schemes were shown to reduce the effect of self-interference, particularly DSA-SINR which had superior BER performance compared to the other allocation schemes. Error analysis also revealed the limitation of DSA-Scheme 5 in mitigating the effect of self-interference. The unit of separation on the next subcarrier parameter, denoted by

The author would like to thank the National University of Malaysia for their financial support of this work, under the grant scheme UKM-GGPM-ICT-032-2011. The author also would like to thank the anonymous reviewers for their valuable feedbacks.