ame indices m, n, and frame index j are obtained as follows [2]: for D U U 0<m<k m-kk<m<U+k (7-3) U-1U+k<m<D for n=m-k mod 4 where (7-4) When the DL Basic Assignment A-MAP IE in the 1th DL subframe of the ith frame indicates use of a long TTI and l is 0 (i.e., the first subframe of the frame), the subframe index m and the frame index j are calculated according to Equation (7-3). The DL Basic Assignment A-MAP IE in the 1th (l # 0) DL subframe of the ith frame can signal the use of a long TTI. In this case, the long TTI transmission of the DL HARQ sub-packet begins in the first DL subframe of the succeeding frame. The HARQ feedback for this long TTI transmission is transmitted in the nth UL subframe of the jth frame. The subframe index n and the frame index j are derived according to Equation (7-3). In TDD mode, as shown in Figure 7-10, the UL HARQ sub-packet transmission corresponding to a UL Basic Assignment A-MAP IE in 1th DL subframe of the ith frame is scheduled in the mth UL subframe of the jth frame. The HARQ feedback is transmitted in the 1th DL subframe of the kth frame. When the UL HARQ feedback indicates a negative acknowledgement, the re-transmission of the UL 298 CHAPTER 7 The IEEE 802. 16m MAC CPS (Part II) HARQ sub-packet begins in the mth UL subframe of the pth frame. The subframe indices m, n, and frame indices j, k, and p are calculated as follows [2]: for 0<1<Q for k<I<U+Q U-1 for U+Q<I<D (7-5) = (i+ Toffset) mod 4 ==(j+1+ Toffset) mod 4 p = (k+ T" offset) mod 4 The binary-valued offsets in the above equations are included to ensure the minimum processing time is met. The legacy and IEEE 802. 16m frames are offset by a fixed number of subframes to accommodate new features such as the IEEE 802.16m preambles, superframe header (system configuration infor- mation), and control channels, as shown in Figure 7-11. The Frame Offset is a time offset between the start of the legacy frame and the start of the IEEE 802.16m frame carrying the superframe headers, defined in a unit of subframes. The subframe c