Performance Analysis of the 3GPP-LTE Physical Control Channels
© S. J. Thiruvengadam and L. M. A. Jalloul. 2010
Received: 8 May 2010
Accepted: 11 November 2010
Published: 28 November 2010
Maximum likelihood-based (ML) receiver structures are derived for the decoding of the downlink control channels in the new long-term evolution (LTE) standard based on multiple-input and multiple-output (MIMO) antennas and orthogonal frequency division multiplexing (OFDM). The performance of the proposed receiver structures for the physical control format indicator channel (PCFICH) and the physical hybrid-ARQ indicator channel (PHICH) is analyzed for various fading-channel models and MIMO schemes including space frequency block codes (SFBC). Analytical expressions for the average probability of error are derived for each of these physical channels. The impact of channel-estimation error on the orthogonality of the spreading codes applied to users in a PHICH group is investigated, and an expression for the signal-to-self interference plus noise ratio is derived for Single Input Multiple Output (SIMO) systems. Finally, a matched filter bound on the probability of error for the PHICH in a multipath fading channel is derived. The analytical results are validated against computer simulations.
Channel bandwidth (MHz)
Number of physical resource blocks
Sampling frequency (Msps)
Another fundamental deviation in LTE specification relative to previous standard releases is the control channel design and structure to support the capacity enhancing features such as link adaptation, physical layer hybrid automatic repeat request (ARQ), and MIMO. Correct detection of the control channel is needed before the payload information data can be successfully decoded. Thus, the overall link and system performance are dependent on the successful decoding of these control channels.
The performance of the physical downlink control channels in the typical urban (TU-3 km/h) channel was reported in  using computer simulations only, without rigorous mathematical analyses. The motivation behind this paper is to describe the analytical aspects of the performance of optimal receiver principles for the decoding of the LTE physical control channels. We develop and analyze the performance of ML receiver structures for the downlink physical control format indicator channel (PCFICH) as well as the physical hybrid ARQ indicator channel (PHICH) in the presence of additive white Gaussian noise, frequency selective fading channel with different transmit and receive antenna configurations, and space-frequency block codes (SFBC). These analyses provide insight into system performance and can be used to study sensitivity to design parameters, for example, channel models and algorithm designs. Further, it would serve as a reference tool for fixed-point computer simulation models that are developed for hardware design.
The rest of the paper is organized as follows. A brief description of the LTE control channel specification is given in Section 2. The BER analyses of the physical channels PCFICH and PHICH are given in Sections 3 and 4, respectively. Section 5 contains some concluding remarks.
, , and denote element by element product, complex conjugate, and conjugate transpose, respectively. is the inner product of the vectors and . denotes the convolution operator.
2. Brief Description of the 3GPP-LTE Standard
The downlink physical channels carry information from the higher layers to the user equipment. The physical downlink shared channel (PDSCH) carries the payload-information data, physical broadcast channel (PBCH) broadcasts cell specific information for the entire cell-coverage area, physical multicast channel (PMCH) is for multicasting and broadcasting information from multiple cells, physical downlink control channel (PDCCH) carries scheduling information, physical control format indicator channel (PCFICH) conveys the number of OFDM symbols used for PDCCH and physical hybrid ARQ indicator Channel (PHICH) transmits the HARQ acknowledgment from the base station (BS). BS in 3GPP-LTE is typically referred to as eNodeB. Downlink control signaling occupies up to 4 OFDM symbols of the first slot of each subframe, followed by data transmission that starts at the next OFDM symbol as the control signaling ends. This enables support for microsleep which provides battery-life savings and reduced buffering and latency . Reference signals transmitted by the BS are used by UE for channel estimation, timing and frequency synchronization, and cell identification.
The downlink OFDM FDD radio frame of 10 ms duration is equally divided into 10 subframes where each subframe consists of two 0.5 ms slots. Each slot has 7 or 6 OFDM symbols depending on the cyclic prefix (CP) duration. Two CP durations are supported: normal and extended. The entire time-frequency grid is divided into physical resource blocks (PRB), wherein each PRB contains 12 resource elements (subcarriers). PRBs are used to describe the mapping of physical channels to resource elements. Resource element groups (REG) are used for defining the control channels to resource element mapping. The size of the REG varies depending on the OFDM symbol number and antenna configuration . The PCFICH is always mapped into the first OFDM symbol of the first slot of each subframe. For the normal CP duration, the PHICH is also mapped into the first OFDM symbol of the first slot of each subframe. On the other hand, for the extended CP duration, the PHICH is mapped to the first 3 OFDM symbols of the first slot of each subframe. All control channels are organized as symbol-quadruplets before being mapped to a single REG. In the first OFDM symbol, two REGs per PRB are available. In the third OFDM, there are 3 REGs per PRB. In the second OFDM symbol, the number of REGs available per PRB will be 2 for single- or two-transmit antennas, and 3 for four-transmit antennas.
Power delay profiles for pedestrian B and ITU channel models.
Ped-B channel model
TU channel model
3. Physical Control Format Indicator Channel
CFI (32,2) Block code .
3.1. PCFICH with SIMO Processing
where , , , and is the SNR per tone per antenna and the scaling factors and .
3.2. Analysis of CFI with Repetition Coding
The expression in (14) is compared to that in (9).
3.3. PCFICH with Transmit Diversity Processing
Conditioned on is Gaussian with mean and variance . The probability of error is well approximated by the union bound, as shown in (10).
4. Physical Hybrid ARQ Indicator Channel
4.1. PHICH with SIMO Processing
where is an vector, and , are the power levels of the orthogonal codes (for the normal CP case), is the data bit value of the th user HI, and and is an complex channel frequency response vector. Without loss of generality, it is assumed that the desired HI channel to be decoded uses the first orthogonal code denoted as . The second and third terms in (26) denote the remaining spreading codes used for the other HI channels within a PHICH group (in this analytical model, we treat the general case of the normal CP. The extended CP is easily handled as shown in the final error-rate formulas.) The term denotes the thermal noise, which is modeled as circularly symmetric zero-mean complex Gaussian with covariance .
where in (33) is the processing gain obtained from the spreading code of length 4, and (3,1) repetition code in the case of normal CP [1, 2]. In case of extended CP, a maximum of 4 HI channels are allowed in a PHICH group, and hence a spreading code of length 2 is used for each HI channel, which results in .
4.2. PHICH with Transmit Diversity Processing
where and , is the SNR per antenna.
where the diversity order .
4.3. Matched Filter Bound for ITU Channel Models
where is tap-locations vector of at which the tap coefficient is nonzero.
In case of transmit diversity using SFBC, MFB of PHICH is the function of . For a MIMO system, the channels are assumed to be independent and have the same statistical behavior . For single-receive antenna, the MFB is a function of 12 independent chi-square distributed random variables with 2 degrees of freedom, and it is written as as in (54).
In this paper, the performance of maximum-likelihood-method-based receiver structures for PCFICH and PHICH was evaluated for different types of fading channels and antenna configurations. The effect of channel-estimation error on the orthogonality of spreading codes used in a PHICH group was studied. These analytical results provide a bound on the channel-estimation-error variance and thus, ultimately decide the channel-estimation algorithm and parameters needed to meet such a performance bound.
- 3GPP TS 36.211 : Evolved Universal Terrestrial Radio Access (E-UTRA); Physical Channels and Modulation (Release 8).
- 3GPP TS 36.212 : Evolved Universal Terrestrial Radio Access (E-UTRA); Multiplexing and Channel Coding (Release 8).
- 3GPP TS 36.306 : Evolved Universal Terrestrial Radio Access (E-UTRA); User Equipment (UE) radio access capabilities (Release 8).
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